diff --git a/.gitignore b/.gitignore
index fdfa49c5f..370616ad7 100644
--- a/.gitignore
+++ b/.gitignore
@@ -475,3 +475,5 @@ erasure/src/envMap.ml
 erasure/src/envMap.mli
 erasure/src/eEtaExpanded.ml
 erasure/src/eEtaExpanded.mli
+erasure/src/pCUICEqualityDec.ml
+erasure/src/pCUICEqualityDec.mli
diff --git a/TODO.md b/TODO.md
index 11fc50edc..2f55b18ff 100644
--- a/TODO.md
+++ b/TODO.md
@@ -1,9 +1,12 @@
+# Performance
+
+- change eq_kername to use comparison rather than eq_dec, check we're not using 
+  eq_dec unnecessarily so that erasure/typechecking runs faster inside Coq 
+  (and we avoid useless sumbool to bool conversions in ML/extracted code)
 # Small stuffs
 
 - `assumption_context` should be a boolean function.
 
-- remove duplication of eq_context / eq_context_upto  and eq_decl / eq_decl_upto
-
 - Make `wf Σ` `wf_ext Σ` some typeclasses (as at the begining of PCUICCanonicity)
   et changer les : wf Σ -> en {wfΣ : wf Σ} partout, ce qui éviterait bien des
   conditions de bord triviales
diff --git a/erasure/_PluginProject.in b/erasure/_PluginProject.in
index 088e36f3c..4372ee6cc 100644
--- a/erasure/_PluginProject.in
+++ b/erasure/_PluginProject.in
@@ -5,22 +5,6 @@ src/META.coq-metacoq-erasure
 # src/classes0.mli
 # src/classes0.ml
 
-# From Coq's stdlib
-src/orderedTypeAlt.mli
-src/orderedTypeAlt.ml
-src/orderedType0.mli
-src/orderedType0.ml
-src/fMapList.mli
-src/fMapList.ml
-src/decidableType.mli
-src/decidableType.ml
-src/fMapInterface.mli
-src/fMapInterface.ml
-src/fMapAVL.mli
-src/fMapAVL.ml
-src/fMapFacts.mli
-src/fMapFacts.ml
-
 # src/string2pos.mli
 # src/string2pos.ml
 # src/canonicalTries.mli
@@ -31,8 +15,6 @@ src/uGraph0.ml
 src/uGraph0.mli
 src/wGraph.ml
 src/wGraph.mli
-src/kernames.mli
-src/kernames.ml
 src/envMap.mli
 src/envMap.ml
 
diff --git a/erasure/src/g_metacoq_erasure.mlg b/erasure/src/g_metacoq_erasure.mlg
index ffbd66ce7..3e0795120 100644
--- a/erasure/src/g_metacoq_erasure.mlg
+++ b/erasure/src/g_metacoq_erasure.mlg
@@ -23,11 +23,11 @@ let bytes_of_list l =
 
 let pr_char_list l =
   (* We allow utf8 encoding *)
-  str (Bytes.to_string (bytes_of_list l))
+  str (Caml_bytestring.caml_string_of_bytestring l)
 
 let check ~bypass ~fast env evm c =
   debug (fun () -> str"Quoting");
-  let term = time (str"Quoting") (Ast_quoter.quote_term_rec bypass env) (EConstr.to_constr evm c) in
+  let term = time (str"Quoting") (Ast_quoter.quote_term_rec ~bypass env) (EConstr.to_constr evm c) in
   let checker_flags = Config0.extraction_checker_flags in
   let erase = time (str"Erasure")
       (if fast then Erasure.erase_fast_and_print_template_program checker_flags
diff --git a/erasure/src/metacoq_erasure_plugin.mlpack b/erasure/src/metacoq_erasure_plugin.mlpack
index 6f43af023..e99df7065 100644
--- a/erasure/src/metacoq_erasure_plugin.mlpack
+++ b/erasure/src/metacoq_erasure_plugin.mlpack
@@ -5,14 +5,6 @@ Utils
 
 WGraph
 UGraph0
-OrderedTypeAlt
-OrderedType0
-Kernames
-FMapList
-DecidableType
-FMapInterface
-FMapAVL
-FMapFacts
 EnvMap
 
 WcbvEval
diff --git a/erasure/src/pCUICEqualityDec.ml b/erasure/src/pCUICEqualityDec.ml
deleted file mode 100644
index ca3e06a15..000000000
--- a/erasure/src/pCUICEqualityDec.ml
+++ /dev/null
@@ -1,52 +0,0 @@
-open All_Forall
-open BasicAst
-open Datatypes
-open List0
-open PCUICAst
-open PCUICEquality
-open Universes0
-
-(** val compare_universe_variance :
-    (Universe.t -> Universe.t -> bool) -> (Universe.t -> Universe.t -> bool)
-    -> Variance.t -> Level.t -> Level.t -> bool **)
-
-let compare_universe_variance equ lequ v u u' =
-  match v with
-  | Variance.Irrelevant -> true
-  | Variance.Covariant -> lequ (Universe.make u) (Universe.make u')
-  | Variance.Invariant -> equ (Universe.make u) (Universe.make u')
-
-(** val compare_universe_instance :
-    (Universe.t -> Universe.t -> bool) -> Level.t list -> Level.t list -> bool **)
-
-let compare_universe_instance equ u u' =
-  forallb2 equ (map Universe.make u) (map Universe.make u')
-
-(** val compare_universe_instance_variance :
-    (Universe.t -> Universe.t -> bool) -> (Universe.t -> Universe.t -> bool)
-    -> Variance.t list -> Level.t list -> Level.t list -> bool **)
-
-let rec compare_universe_instance_variance equ lequ v u u' =
-  match u with
-  | [] -> (match u' with
-           | [] -> true
-           | _ :: _ -> false)
-  | u0 :: us ->
-    (match u' with
-     | [] -> false
-     | u'0 :: us' ->
-       (match v with
-        | [] -> compare_universe_instance_variance equ lequ v us us'
-        | v0 :: vs ->
-          (&&) (compare_universe_variance equ lequ v0 u0 u'0)
-            (compare_universe_instance_variance equ lequ vs us us')))
-
-(** val compare_global_instance :
-    PCUICEnvironment.global_env -> (Universe.t -> Universe.t -> bool) ->
-    (Universe.t -> Universe.t -> bool) -> global_reference -> nat -> Level.t
-    list -> Level.t list -> bool **)
-
-let compare_global_instance _UU03a3_ equ lequ gr napp =
-  match global_variance _UU03a3_ gr napp with
-  | Some v -> compare_universe_instance_variance equ lequ v
-  | None -> compare_universe_instance equ
diff --git a/erasure/src/pCUICEqualityDec.mli b/erasure/src/pCUICEqualityDec.mli
deleted file mode 100644
index f83a9a332..000000000
--- a/erasure/src/pCUICEqualityDec.mli
+++ /dev/null
@@ -1,23 +0,0 @@
-open All_Forall
-open BasicAst
-open Datatypes
-open List0
-open PCUICAst
-open PCUICEquality
-open Universes0
-
-val compare_universe_variance :
-  (Universe.t -> Universe.t -> bool) -> (Universe.t -> Universe.t -> bool) ->
-  Variance.t -> Level.t -> Level.t -> bool
-
-val compare_universe_instance :
-  (Universe.t -> Universe.t -> bool) -> Level.t list -> Level.t list -> bool
-
-val compare_universe_instance_variance :
-  (Universe.t -> Universe.t -> bool) -> (Universe.t -> Universe.t -> bool) ->
-  Variance.t list -> Level.t list -> Level.t list -> bool
-
-val compare_global_instance :
-  PCUICEnvironment.global_env -> (Universe.t -> Universe.t -> bool) ->
-  (Universe.t -> Universe.t -> bool) -> global_reference -> nat -> Level.t
-  list -> Level.t list -> bool
diff --git a/erasure/theories/EDeps.v b/erasure/theories/EDeps.v
index 26d2947ee..c5bf924fe 100644
--- a/erasure/theories/EDeps.v
+++ b/erasure/theories/EDeps.v
@@ -461,14 +461,12 @@ Proof.
   apply PCUICWeakeningEnvConv.lookup_env_Some_fresh in H as not_fresh.
   econstructor.
   - unfold PCUICAst.declared_constant in *; cbn.
-    unfold eq_kername.
     inversion wfΣ; subst.
-    destruct kername_eq_dec as [<-|]; [congruence|].
+    destruct (eqb_spec kn0 kn) as [<-|]; [congruence|].
     eassumption.
-  - unfold ETyping.declared_constant in *. cbn -[Reflect.eqb].
+  - unfold ETyping.declared_constant in *. cbn -[ReflectEq.eqb].
     inversion wfΣ; subst.
-    change (eq_kername kn0 kn) with (Reflect.eqb kn0 kn).
-    destruct (Reflect.eqb_spec kn0 kn); [congruence|].
+    destruct (ReflectEq.eqb_spec kn0 kn); [congruence|].
     eassumption.
   - unfold erases_constant_body in *.
     destruct PCUICAst.PCUICEnvironment.cst_body eqn:body.
@@ -476,9 +474,8 @@ Proof.
       assert (PCUICAst.declared_constant (add_global_decl Σ (kn, decl)) kn0 cb).
       { unfold PCUICAst.declared_constant.
         cbn.
-        unfold eq_kername.
         inversion wfΣ; subst.
-        destruct kername_eq_dec as [<-|]; [congruence|].
+        destruct (eqb_spec kn0 kn) as [<-|]; [congruence|].
         easy. }
       inversion wfΣ; subst.
       eapply declared_constant_inv in H4; eauto.
@@ -503,21 +500,21 @@ Proof.
     invs wfΣ.
     destruct H0. split. 2: eauto.
     destruct d. split; eauto.
-    red. cbn. unfold eq_kername. destruct kername_eq_dec; eauto.
+    red. cbn. cbn in *.
+    destruct (eqb_spec (inductive_mind ind) kn). cbn in *.
     subst. 
-    eapply PCUICWeakeningEnvConv.lookup_env_Some_fresh in H5. eauto. eapply H.
+    eapply PCUICWeakeningEnvConv.lookup_env_Some_fresh in H5. eauto. eapply H. exact H0.
   - econstructor; eauto.
     destruct H as [H H'].
     split; eauto. red in H |- *.
     inv wfΣ.
     unfold PCUICEnvironment.lookup_env.
-    simpl. unfold eq_kername.
-    destruct (kername_eq_dec (inductive_mind p.1) kn); auto. subst.
+    simpl. destruct (eqb_spec (inductive_mind p.1) kn); auto. subst.
     eapply PCUICWeakeningEnvConv.lookup_env_Some_fresh in H; eauto. contradiction.
     destruct H0 as [H0 H0'].
     split; eauto. red in H0 |- *.
-    inv wfΣ. cbn. change (eq_kername (inductive_mind p.1) kn) with (Reflect.eqb (inductive_mind p.1) kn).    
-    destruct (Reflect.eqb_spec (inductive_mind p.1) kn); auto. subst.
+    inv wfΣ. cbn. change (eq_kername (inductive_mind p.1) kn) with (ReflectEq.eqb (inductive_mind p.1) kn).    
+    destruct (ReflectEq.eqb_spec (inductive_mind p.1) kn); auto. subst.
     destruct H as [H _].
     eapply PCUICWeakeningEnvConv.lookup_env_Some_fresh in H. eauto. contradiction.
   - econstructor; eauto.
@@ -525,15 +522,15 @@ Proof.
     split; eauto. red in H |- *.
     inv wfΣ. unfold PCUICEnvironment.lookup_env.
     simpl.
-    change (eq_kername (inductive_mind p.1.1) kn) with (Reflect.eqb (inductive_mind p.1.1) kn); auto.
-    destruct (Reflect.eqb_spec (inductive_mind p.1.1) kn). subst.
+    change (eq_kername (inductive_mind p.1.1) kn) with (ReflectEq.eqb (inductive_mind p.1.1) kn); auto.
+    destruct (ReflectEq.eqb_spec (inductive_mind p.1.1) kn). subst.
     eapply PCUICWeakeningEnvConv.lookup_env_Some_fresh in H; eauto. contradiction.
     apply H.
     destruct H0 as [H0 H0'].
     split; eauto. red in H0 |- *.
     inv wfΣ. simpl.
-    change (eq_kername (inductive_mind p.1.1) kn) with (Reflect.eqb (inductive_mind p.1.1) kn); auto.
-    destruct (Reflect.eqb_spec (inductive_mind p.1.1) kn); auto. subst.
+    change (eq_kername (inductive_mind p.1.1) kn) with (ReflectEq.eqb (inductive_mind p.1.1) kn); auto.
+    destruct (ReflectEq.eqb_spec (inductive_mind p.1.1) kn); auto. subst.
     destruct H as [H _].
     eapply PCUICWeakeningEnvConv.lookup_env_Some_fresh in H. eauto. contradiction.
 Qed.
@@ -716,14 +713,13 @@ Proof.
       apply IH in erg'. 2:{ depelim wf. now depelim o0. }
       assert (decl_ext: PCUICAst.declared_constant Σu kn' cst').
       { unfold PCUICAst.declared_constant in *; cbn in *.
-        unfold eq_kername in *.
-        now destruct kername_eq_dec; [|congruence]. }
+        destruct (eqb_spec kn' kn); [|congruence]. subst. contradiction. }
       specialize (proj1 erg' kn' cst' decl_ext) as (cst & decl'' & ? & ?).
       exists cst.
       split; [|split].
       * unfold declared_constant in *; cbn. rewrite decl''.
-        change (eq_kername kn' kn) with (Reflect.eqb kn' kn).
-        destruct (Reflect.eqb_spec kn' kn); auto. congruence.
+        change (eq_kername kn' kn) with (ReflectEq.eqb kn' kn).
+        destruct (ReflectEq.eqb_spec kn' kn); auto. congruence.
       * inversion wf; subst.
         eapply declared_constant_inv in decl_ext; eauto.
         2: exact weaken_env_prop_typing.
@@ -745,14 +741,13 @@ Proof.
       destruct decli as [decli ?]. split; auto.
       red in decli |- *. simpl in decli |- *.
       unfold PCUICEnvironment.lookup_env in decli |- *. simpl in *.
-      unfold eq_kername in decli |- *.
-      destruct kername_eq_dec. subst. discriminate. auto.
+      destruct (eqb_spec (inductive_mind k) kn).  subst. discriminate. auto.
       destruct IH as [mdecl' [idecl' [decli' er]]].
       exists mdecl', idecl'. split; auto.
       red. destruct decli'; split; auto.
       red in decli.
       unfold declared_minductive in *.
-      simpl. unfold eq_kername. destruct kername_eq_dec; subst; auto.
+      simpl. destruct (eqb_spec (inductive_mind k) kn); subst; auto.
       unfold PCUICAst.declared_minductive in decli.
       unfold PCUICEnvironment.lookup_env in decli.
       simpl in decli. rewrite eq_kername_refl in decli. intuition discriminate.
@@ -762,16 +757,15 @@ Proof.
       simpl in decli |- *.
       unfold PCUICAst.declared_minductive, PCUICEnvironment.lookup_env in decli.
       simpl in decli.
-      unfold eq_kername in decli |- *. simpl in *.
-      destruct kername_eq_dec. subst. noconf decli.
+      destruct (eqb_specT (inductive_mind k) kn). simpl in *. subst. noconf decli.
       destruct (Forall2_nth_error_left (proj1 H) _ _ H3); eauto.
       eexists _, _; intuition eauto. split; eauto. red.
-      simpl. unfold eq_kername. destruct kername_eq_dec; try congruence.
+      simpl. rewrite eqb_refl. congruence.
       destruct (proj2 IH _ _ _ (conj decli H3)) as [m' [i' [decli' ei]]].
       eexists _, _; intuition eauto.
       destruct decli'; red; split; eauto.
       red in d |- *. simpl.
-      unfold eq_kername; destruct kername_eq_dec; subst; try congruence.
+      apply neqb in n. destruct eqb; cbn in n; try congruence.
 Qed.       
 
 Lemma erases_global_erases_deps Σ Γ t T et Σ' :
diff --git a/erasure/theories/EExtends.v b/erasure/theories/EExtends.v
index 2bde68073..98ddc3476 100644
--- a/erasure/theories/EExtends.v
+++ b/erasure/theories/EExtends.v
@@ -18,7 +18,7 @@ Lemma lookup_env_Some_fresh {Σ c decl} :
   lookup_env Σ c = Some decl -> ~ (fresh_global c Σ).
 Proof.
   induction Σ; cbn. 1: congruence.
-  unfold BasicAst.eq_kername. destruct BasicAst.kername_eq_dec; subst.
+  destruct (eqb_spec c a.1); subst.
   - intros [= <-] H2. invs H2.
     contradiction.
   - intros H1 H2. apply IHΣ; tas.
@@ -37,8 +37,8 @@ Proof.
   - specialize (IHΣ'' c decl). forward IHΣ''.
     + now inv wfΣ'.
     + intros HΣ. specialize (IHΣ'' HΣ).
-      inv wfΣ'. simpl in *. unfold BasicAst.eq_kername.
-      destruct BasicAst.kername_eq_dec; subst; auto.
+      inv wfΣ'. simpl in *.
+      destruct (eqb_spec c kn); subst; auto.
       apply lookup_env_Some_fresh in IHΣ''; contradiction.
 Qed.
 
diff --git a/erasure/theories/EOptimizePropDiscr.v b/erasure/theories/EOptimizePropDiscr.v
index 0dc50a694..b9869010b 100644
--- a/erasure/theories/EOptimizePropDiscr.v
+++ b/erasure/theories/EOptimizePropDiscr.v
@@ -455,7 +455,7 @@ Lemma lookup_env_optimize Σ kn :
 Proof.
   unfold optimize_env.
   induction Σ at 2 4; simpl; auto.
-  unfold eq_kername; destruct kername_eq_dec => //.
+  case: eqb_spec => //.
 Qed.
 
 Lemma is_propositional_optimize Σ ind : 
diff --git a/erasure/theories/EPretty.v b/erasure/theories/EPretty.v
index feeebeb13..2daba3972 100644
--- a/erasure/theories/EPretty.v
+++ b/erasure/theories/EPretty.v
@@ -6,17 +6,9 @@ From MetaCoq.PCUIC Require Import PCUICPrimitive.
 
 (** * Pretty printing *)
 
-Section print_term.
+Section freshnames.
   Context (Σ : global_context).
 
-  Definition print_def {A : Set} (f : A -> string) (def : def A) :=
-    string_of_name (dname def) ^ " { struct " ^ string_of_nat (rarg def) ^ " }"
-                   ^ " := " ^ nl ^ f (dbody def).
-
-  Definition print_defs (print_term : context -> bool -> bool -> term -> string) Γ (defs : mfixpoint term) :=
-    let ctx' := List.map (fun d => {| decl_name := dname d; decl_body := None |}) defs in
-    print_list (print_def (print_term (ctx' ++ Γ) true false)) (nl ^ " with ") defs.
-
   Definition lookup_ind_decl ind i :=
     match lookup_env Σ ind with
     | Some (InductiveDecl {| ind_bodies := l |}) =>
@@ -42,7 +34,7 @@ Section print_term.
     List.forallb
       (fun decl =>
          match decl.(decl_name) with
-         | nNamed id' => negb (ident_eq id id')
+         | nNamed id' => negb (eqb id id')
          | nAnon => true
          end) Γ.
 
@@ -61,7 +53,7 @@ Section print_term.
       match i with
       | 0 => id
       | S i' =>
-        let id' := id ^ string_of_nat (n - i) in
+        let id' := id ^ (string_of_nat (n - i)) in
         if is_fresh Γ id' then id'
         else aux i'
       end
@@ -75,128 +67,156 @@ Section print_term.
     in
     if is_fresh Γ id then nNamed id
     else nNamed (fresh_id_from Γ 10 id).
+End freshnames.
+
+Module PrintTermTree.
+  Import Tree.
+  Infix "^" := append.
+
+  Section print_term.
+    Context (Σ : global_context).
 
-  Fixpoint print_term (Γ : context) (top : bool) (inapp : bool) (t : term) {struct t} :=
-  match t with
-  | tBox => "∎"
-  | tRel n =>
-    match nth_error Γ n with
-    | Some {| decl_name := na |} =>
-      match na with
-      | nAnon => "Anonymous (" ^ string_of_nat n ^ ")"
-      | nNamed id => id
+    Definition print_def {A : Set} (f : A -> t) (def : def A) :=
+      string_of_name (dname def) ^ " { struct " ^ string_of_nat (rarg def) ^ " }"
+                    ^ " := " ^ nl ^ f (dbody def).
+
+    Definition print_defs (print_term : context -> bool -> bool -> term -> t) Γ (defs : mfixpoint term) :=
+      let ctx' := List.map (fun d => {| decl_name := dname d; decl_body := None |}) defs in
+      print_list (print_def (print_term (ctx' ++ Γ)%list true false)) (nl ^ " with ") defs.
+
+
+    Fixpoint print_term (Γ : context) (top : bool) (inapp : bool) (t : term) {struct t} : Tree.t :=
+    match t with
+    | tBox => "∎"
+    | tRel n =>
+      match nth_error Γ n with
+      | Some {| decl_name := na |} =>
+        match na with
+        | nAnon => "Anonymous (" ^ string_of_nat n ^ ")"
+        | nNamed id => id
+        end
+      | None => "UnboundRel(" ^ string_of_nat n ^ ")"
       end
-    | None => "UnboundRel(" ^ string_of_nat n ^ ")"
-    end
-  | tVar n => "Var(" ^ n ^ ")"
-  | tEvar ev args => "Evar(" ^ string_of_nat ev ^ "[]" (* TODO *)  ^ ")"
-  | tLambda na body =>
-    let na' := fresh_name Γ na t in
-    parens top ("fun " ^ string_of_name na'
-                                ^ " => " ^ print_term (vass na' :: Γ) true false body)
-  | tLetIn na def body =>
-    let na' := fresh_name Γ na t in
-    parens top ("let " ^ string_of_name na' ^
-                      " := " ^ print_term Γ true false def ^ " in " ^ nl ^
-                      print_term (vdef na' def :: Γ) true false body)
-  | tApp f l =>
-    parens (top || inapp) (print_term Γ false true f ^ " " ^ print_term Γ false false l)
-  | tConst c => string_of_kername c
-  | tConstruct (mkInd i k as ind) l =>
-    match lookup_ind_decl i k with
-    | Some oib =>
-      match nth_error oib.(ind_ctors) l with
-      | Some (na, _) => na
+    | tVar n => "Var(" ^ n ^ ")"
+    | tEvar ev args => "Evar(" ^ string_of_nat ev ^ "[]" (* TODO *)  ^ ")"
+    | tLambda na body =>
+      let na' := fresh_name Γ na t in
+      parens top ("fun " ^ string_of_name na'
+                                  ^ " => " ^ print_term (vass na' :: Γ) true false body)
+    | tLetIn na def body =>
+      let na' := fresh_name Γ na t in
+      parens top ("let " ^ string_of_name na' ^
+                        " := " ^ print_term Γ true false def ^ " in " ^ nl ^
+                        print_term (vdef na' def :: Γ) true false body)
+    | tApp f l =>
+      parens (top || inapp) (print_term Γ false true f ^ " " ^ print_term Γ false false l)
+    | tConst c => string_of_kername c
+    | tConstruct (mkInd i k as ind) l =>
+      match lookup_ind_decl Σ i k with
+      | Some oib =>
+        match nth_error oib.(ind_ctors) l with
+        | Some (na, _) => na
+        | None =>
+          "UnboundConstruct(" ^ string_of_inductive ind ^ "," ^ string_of_nat l ^ ")"
+        end
       | None =>
         "UnboundConstruct(" ^ string_of_inductive ind ^ "," ^ string_of_nat l ^ ")"
       end
-    | None =>
-      "UnboundConstruct(" ^ string_of_inductive ind ^ "," ^ string_of_nat l ^ ")"
-    end
-  | tCase (mkInd mind i as ind, pars) t brs =>
-    match lookup_ind_decl mind i with
-    | Some oib =>
-      let fix print_args Γ nas br {struct nas} :=
-        match nas with
-        | [] => "=>" ^ " " ^ br Γ 
-        | na :: nas => 
-          string_of_name na ^ "  " ^ print_args (vass na :: Γ) nas br
+    | tCase (mkInd mind i as ind, pars) t brs =>
+      match lookup_ind_decl Σ mind i with
+      | Some oib =>
+        let fix print_args Γ nas br {struct nas} :=
+          match nas with
+          | [] => "=>" ^ " " ^ br Γ 
+          | na :: nas => 
+            string_of_name na ^ "  " ^ print_args (vass na :: Γ) nas br
+          end
+        in
+        let brs := map (fun '(nas, br) => print_args Γ (List.rev nas) (fun Γ => print_term Γ true false br)) brs in
+        let brs := combine brs oib.(ind_ctors) in
+        parens top ("match " ^ print_term Γ true false t ^
+                    " with " ^ nl ^
+                    print_list (fun '(b, (na, _)) => (na : String.t) ^ " " ^ b)
+                    (nl ^ " | ") brs ^ nl ^ "end" ^ nl)
+      | None =>
+        "Case(" ^ string_of_inductive ind ^ "," ^ string_of_nat i ^ "," ^ string_of_term t ^ ","
+                ^ string_of_list (fun b => string_of_term (snd b)) brs ^ ")"
+      end
+    | tProj (mkInd mind i as ind, pars, k) c =>
+      match lookup_ind_decl Σ mind i with
+      | Some oib =>
+        match nth_error oib.(ind_projs) k with
+        | Some na => print_term Γ false false c ^ ".(" ^ na ^ ")"
+        | None =>
+          "UnboundProj(" ^ string_of_inductive ind ^ "," ^ string_of_nat i ^ "," ^ string_of_nat k ^ ","
+                        ^ print_term Γ true false c ^ ")"
         end
-      in
-      let brs := map (fun '(nas, br) => print_args Γ (List.rev nas) (fun Γ => print_term Γ true false br)) brs in
-      let brs := combine brs oib.(ind_ctors) in
-      parens top ("match " ^ print_term Γ true false t ^
-                  " with " ^ nl ^
-                  print_list (fun '(b, (na, _)) => na ^ " " ^ b)
-                  (nl ^ " | ") brs ^ nl ^ "end" ^ nl)
-    | None =>
-      "Case(" ^ string_of_inductive ind ^ "," ^ string_of_nat i ^ "," ^ string_of_term t ^ ","
-              ^ string_of_list (fun b => string_of_term (snd b)) brs ^ ")"
-    end
-  | tProj (mkInd mind i as ind, pars, k) c =>
-    match lookup_ind_decl mind i with
-    | Some oib =>
-      match nth_error oib.(ind_projs) k with
-      | Some na => print_term Γ false false c ^ ".(" ^ na ^ ")"
       | None =>
         "UnboundProj(" ^ string_of_inductive ind ^ "," ^ string_of_nat i ^ "," ^ string_of_nat k ^ ","
-                       ^ print_term Γ true false c ^ ")"
+                      ^ print_term Γ true false c ^ ")"
       end
-    | None =>
-      "UnboundProj(" ^ string_of_inductive ind ^ "," ^ string_of_nat i ^ "," ^ string_of_nat k ^ ","
-                     ^ print_term Γ true false c ^ ")"
+
+
+    | tFix l n =>
+      parens top ("let fix " ^ print_defs print_term Γ l ^ nl ^
+                            " in " ^ List.nth_default (string_of_nat n) (map (string_of_name ∘ dname) l) n)
+    | tCoFix l n =>
+      parens top ("let cofix " ^ print_defs print_term Γ l ^ nl ^
+                                " in " ^ List.nth_default (string_of_nat n) (map (string_of_name ∘ dname) l) n)
+    (* | tPrim p =>  *)
+      (* parens top (string_of_prim (print_term Γ false false) p) *)
+    end.
+  End print_term.
+
+  Definition pr Σ (t : term) := print_term Σ [] true false t.
+
+  Definition print_constant_body Σ kn decl :=
+    match decl.(cst_body) with
+    | Some b => "Definition " ^ string_of_kername kn ^ " := " ^ pr Σ b
+    | None => "Axiom " ^ string_of_kername kn
+    end.
+
+  Definition pr_allowed_elim (elims : Universes.allowed_eliminations) :=
+    match elims with 
+    | Universes.IntoSProp => "into sprop"
+    | Universes.IntoPropSProp => "into prop or sprop"
+    | Universes.IntoSetPropSProp => "into set, prop or sprop"
+    | Universes.IntoAny => "into any sort"
+    end.
+
+  Definition print_one_inductive_body npars body : Tree.t :=
+    let params := string_of_nat npars ^ " parameters" in
+    let prop := if body.(ind_propositional) then "propositional" else "computational" in
+    let kelim := pr_allowed_elim body.(ind_kelim) in
+    let ctors := print_list (fun idn => "| " ^ (idn.1 : ident) ^ " " ^ string_of_nat idn.2 ^ " arguments") nl body.(ind_ctors) in
+    let projs :=
+    match body.(ind_projs) return Tree.t with
+    | [] => ""
+    | _ => nl ^ "projections: " ^ print_list (fun x => x : ident) ", " body.(ind_projs) 
     end
+    in
+    "Inductive " ^ body.(ind_name) ^ "(" ^ params ^ "," ^ prop ^ ", elimination " ^ kelim ^ ") := " ^ nl ^ ctors ^ projs.
+
+  Definition print_inductive_body decl :=
+    print_list (print_one_inductive_body decl.(ind_npars)) nl decl.(ind_bodies).
+
+  Definition print_decl Σ '(kn, d) := 
+    match d with
+    | ConstantDecl body => print_constant_body Σ kn body
+    | InductiveDecl mind => print_inductive_body mind
+    end.
+
+  Definition print_global_context (g : global_context) := 
+    print_list (print_decl g) nl (List.rev g).
+  Notation print_env := print_global_context.
+
+  Definition print_program (p : program) : t := 
+    pr p.1 p.2 ^ nl ^ "in" ^ print_env p.1.
+
+End PrintTermTree.
+
+Definition pr Σ := Tree.to_string ∘ PrintTermTree.pr Σ.
 
+Definition print_global_context := Tree.to_string ∘ PrintTermTree.print_global_context.
 
-  | tFix l n =>
-    parens top ("let fix " ^ print_defs print_term Γ l ^ nl ^
-                          " in " ^ List.nth_default (string_of_nat n) (map (string_of_name ∘ dname) l) n)
-  | tCoFix l n =>
-    parens top ("let cofix " ^ print_defs print_term Γ l ^ nl ^
-                              " in " ^ List.nth_default (string_of_nat n) (map (string_of_name ∘ dname) l) n)
-  (* | tPrim p =>  *)
-    (* parens top (string_of_prim (print_term Γ false false) p) *)
-  end.
-
-End print_term.
-
-Definition pr Σ (t : term) := print_term Σ [] true false t.
-
-Definition print_constant_body Σ kn decl :=
-  match decl.(cst_body) with
-  | Some b => "Definition " ^ string_of_kername kn ^ " := " ^ pr Σ b
-  | None => "Axiom " ^ string_of_kername kn
-  end.
-
-Definition pr_allowed_elim (elims : Universes.allowed_eliminations) :=
-  match elims with 
-  | Universes.IntoSProp => "into sprop"
-  | Universes.IntoPropSProp => "into prop or sprop"
-  | Universes.IntoSetPropSProp => "into set, prop or sprop"
-  | Universes.IntoAny => "into any sort"
-  end.
-
-Definition print_one_inductive_body npars body :=
-  let params := string_of_nat npars ^ " parameters" in
-  let prop := if body.(ind_propositional) then "propositional" else "computational" in
-  let kelim := pr_allowed_elim body.(ind_kelim) in
-  let ctors := print_list (fun idn => "| " ^ idn.1 ^ " " ^ string_of_nat idn.2 ^ " arguments") nl body.(ind_ctors) in
-  let projs :=
-  match body.(ind_projs) with
-  | [] => ""
-  | _ => nl ^ "projections: " ^ print_list (fun x => x) ", " body.(ind_projs) 
-  end
-  in
-  "Inductive " ^ body.(ind_name) ^ "(" ^ params ^ "," ^ prop ^ ", elimination " ^ kelim ^ ") := " ^ nl ^ ctors ^ projs.
-
-Definition print_inductive_body decl :=
-  print_list (print_one_inductive_body decl.(ind_npars)) nl decl.(ind_bodies).
-
-Definition print_decl Σ '(kn, d) := 
-  match d with
-  | ConstantDecl body => print_constant_body Σ kn body
-  | InductiveDecl mind => print_inductive_body mind
-  end.
-
-Definition print_global_context (g : global_context) := 
-  print_list (print_decl g) nl (List.rev g).
+Definition print_program := Tree.to_string ∘ PrintTermTree.print_program.
diff --git a/erasure/theories/EReflect.v b/erasure/theories/EReflect.v
index 5b8f7a148..265e3590e 100644
--- a/erasure/theories/EReflect.v
+++ b/erasure/theories/EReflect.v
@@ -19,9 +19,9 @@ Local Ltac term_dec_tac term_dec :=
   repeat match goal with
          | t : term, u : term |- _ => fcase (term_dec t u)
          | n : nat, m : nat |- _ => fcase (Nat.eq_dec n m)
-         | i : ident, i' : ident |- _ => fcase (string_dec i i')
-         | i : kername, i' : kername |- _ => fcase (kername_eq_dec i i')
-         | i : string, i' : kername |- _ => fcase (string_dec i i')
+         | i : ident, i' : ident |- _ => fcase (eq_dec i i')
+         | i : kername, i' : kername |- _ => fcase (eq_dec i i')
+         | i : string, i' : kername |- _ => fcase (eq_dec i i')
          | n : name, n' : name |- _ => fcase (eq_dec n n')
          | i : prim_val _, i' : prim_val _ |- _ => fcase (eq_dec i i')
          | i : inductive, i' : inductive |- _ => fcase (eq_dec i i')
@@ -105,7 +105,7 @@ Proof.
 Defined.
 
 #[global]
-Instance ReflectEq_term : Reflect.ReflectEq _ :=
+Instance ReflectEq_term : ReflectEq.ReflectEq _ :=
   @EqDec_ReflectEq _ EqDec_term.
 
 Definition eqb_constant_body (x y : constant_body) :=
diff --git a/erasure/theories/ERemoveParams.v b/erasure/theories/ERemoveParams.v
index 6c5691d1d..7755c60a4 100644
--- a/erasure/theories/ERemoveParams.v
+++ b/erasure/theories/ERemoveParams.v
@@ -406,7 +406,7 @@ Proof.
   unfold strip_env.
   destruct Σ as [Σ map repr wf]; cbn.
   induction Σ at 2 4; simpl; auto.
-  rewrite /eq_kername; destruct kername_eq_dec => //.
+  case: eqb_spec => //.
 Qed.
 
 Lemma is_propositional_strip (Σ : GlobalContextMap.t) ind : 
@@ -557,10 +557,11 @@ Proof.
   - move=> _; rewrite /declared_constant /lookup_env /= //.
   - move=> /andP[] etaa etaΣ.
     destruct a as [kn' d']; cbn in *.
-    rewrite /declared_constant /=; rewrite /eq_kername; destruct kername_eq_dec.
-    * subst kn'. move=> [=]. intros ->.
+    rewrite /declared_constant /=.
+    case:eqb_specT => //.
+    * intros e; subst kn'. move=> [=]. intros ->.
       exists Σ. split => //. now exists [(kn, d)].
-    * move=> Hl. destruct (IHΣ etaΣ Hl) as [Σ' [ext eta]].
+    * intros ne. move=> Hl. destruct (IHΣ etaΣ Hl) as [Σ' [ext eta]].
       exists Σ'; split => //.
       destruct ext as [Σ'' ->].
       now exists ((kn', d')::Σ'').
diff --git a/erasure/theories/ETyping.v b/erasure/theories/ETyping.v
index 8916a98b7..5b260db70 100644
--- a/erasure/theories/ETyping.v
+++ b/erasure/theories/ETyping.v
@@ -42,7 +42,7 @@ Lemma elookup_env_cons_fresh {kn d Σ kn'} :
   ETyping.lookup_env ((kn, d) :: Σ) kn' = ETyping.lookup_env Σ kn'.
 Proof.
   simpl. change (eq_kername kn' kn) with (eqb kn' kn).
-  destruct (Reflect.eqb_spec kn' kn). subst => //. auto. 
+  destruct (eqb_spec kn' kn). subst => //. auto. 
 Qed.
 
 (** Knowledge of propositionality status of an inductive type and parameters *)
@@ -87,7 +87,7 @@ Lemma lookup_env_Some_fresh {Σ c decl} :
   lookup_env Σ c = Some decl -> ~ (fresh_global c Σ).
 Proof.
   induction Σ; cbn. 1: congruence.
-  unfold eq_kername; destruct kername_eq_dec; subst.
+  case: eqb_spec; intros e; subst.
   - intros [= <-] H2. inv H2.
     contradiction.
   - intros H1 H2. apply IHΣ; tas.
@@ -107,7 +107,7 @@ Proof.
     + now inv wfΣ'.
     + intros HΣ. specialize (IHΣ'' HΣ).
       inv wfΣ'. simpl in *.
-      unfold eq_kername; destruct kername_eq_dec; subst; auto.
+      case: eqb_spec; intros e; subst; auto.
       apply lookup_env_Some_fresh in IHΣ''; contradiction.
 Qed.
 
@@ -182,7 +182,7 @@ Proof.
   induction mfix; simpl; auto.
 Qed.
 
-Definition tDummy := tVar ""%string.
+Definition tDummy := tVar "".
 
 Definition iota_red npar args (br : list name * term) :=
   substl (List.rev (List.skipn npar args)) br.2.
diff --git a/erasure/theories/EWtAst.v b/erasure/theories/EWtAst.v
new file mode 100644
index 000000000..43a34124c
--- /dev/null
+++ b/erasure/theories/EWtAst.v
@@ -0,0 +1,440 @@
+(* Distributed under the terms of the MIT license. *)
+From Coq Require Import ssreflect ssrbool.
+From MetaCoq.Template Require Import utils BasicAst Universes.
+From MetaCoq.PCUIC Require Import PCUICPrimitive.
+From MetaCoq.Erasure Require Import EAst EAstUtils EInduction ECSubst ELiftSubst ETyping.
+(* EEtaExpanded.*)
+From Equations Require Import Equations.
+Set Equations Transparent.
+
+Import MCMonadNotation.
+
+(** * Well-scoped and well-formed extracted terms *)
+
+Definition isSome {A} (o : option A) : bool :=
+  match o with
+  | Some _ => true
+  | None => false
+  end.
+
+Section WellScoped.
+  Context (Σ : global_context).
+
+  Definition lookup_constant kn : option constant_body :=
+    decl <- ETyping.lookup_env Σ kn;; 
+    match decl with
+    | ConstantDecl decl => Some decl
+    | InductiveDecl mdecl => None
+    end.
+  
+  Definition lookup_minductive kn : option mutual_inductive_body :=
+    decl <- ETyping.lookup_env Σ kn;; 
+    match decl with
+    | ConstantDecl _ => None
+    | InductiveDecl mdecl => ret mdecl
+    end.
+
+  Definition lookup_inductive kn : option (mutual_inductive_body * one_inductive_body) :=
+    mdecl <- lookup_minductive (inductive_mind kn) ;;
+    idecl <- nth_error mdecl.(ind_bodies) (inductive_ind kn) ;;
+    ret (mdecl, idecl).
+
+  Definition lookup_constructor kn c : option (mutual_inductive_body * one_inductive_body * (ident × nat)) :=
+    '(mdecl, idecl) <- lookup_inductive kn ;;
+    cdecl <- nth_error idecl.(ind_ctors) c ;;
+    ret (mdecl, idecl, cdecl).
+
+  Definition lookup_projection (proj : projection) :=
+    '(mdecl, idecl) <- lookup_inductive (fst (fst proj)) ;;
+    pdecl <- List.nth_error idecl.(ind_projs) (snd proj) ;; 
+    ret (mdecl, idecl, pdecl).
+  
+  Definition declared_constant id : bool :=
+    isSome (lookup_constant id).
+  
+  Definition declared_minductive mind :=
+    isSome (lookup_minductive mind).
+  
+  Definition declared_inductive ind :=
+    isSome (lookup_inductive ind).
+  
+  Definition declared_constructor kn c :=
+    isSome (lookup_constructor kn c).
+  
+  Definition declared_projection kn :=
+    isSome (lookup_projection kn).
+  
+  Equations well_scoped (n : nat) (t : EAst.term) : bool :=
+  { | n, tBox => true
+    | n, tRel i := i <? n
+    | n, tVar _ := false
+    | n, tEvar m l := well_scoped_terms n l
+    | _, tConst kn := declared_constant kn
+    | _, tConstruct kn k := declared_constructor kn k
+    | n, tLambda na b := well_scoped (S n) b
+    | n, tLetIn na b b' := well_scoped n b && well_scoped (S n) b'
+    | n, tApp f u := well_scoped n f && well_scoped n u
+    | n, tCase (ind, pars) c brs :=
+      declared_inductive ind && well_scoped n c && well_scoped_brs n brs
+    | n, tProj p c := 
+      declared_projection p && well_scoped n c
+    | n, tFix mfix idx :=
+      well_scoped_mfix (#|mfix| + n) mfix 
+    | n, tCoFix mfix idx :=
+      well_scoped_mfix (#|mfix| + n) mfix }
+  where well_scoped_terms (n : nat) (l : list term) : bool :=
+  { | n, [] := true;
+    | n, (t :: ts) := well_scoped n t && well_scoped_terms n ts }
+  where well_scoped_brs (n : nat) (brs : list (list name × term)) : bool :=
+  { | n, [] := true;
+    | n, (br :: brs) := well_scoped (#|br.1| + n) br.2 && well_scoped_brs n brs }
+  where well_scoped_mfix (n : nat) (mfix : mfixpoint term) : bool :=
+  { | n, [] := true;
+    | n, (d :: defs) := well_scoped n d.(dbody) && well_scoped_mfix n defs }.
+
+  Lemma well_scoped_closed n t : well_scoped n t -> closedn n t.
+  Proof.
+    revert n t.
+    apply (well_scoped_elim
+      (fun n t e => e -> closedn n t)
+      (fun n l e => e -> forallb (closedn n) l)
+      (fun n l e => e -> forallb (fun br => closedn (#|br.1| + n) (snd br)) l)
+      (fun n l e => e -> forallb (closedn n ∘ dbody) l)); cbn => //.
+    all:intros *; intros; simp well_scoped.
+    all:rtoProp; intuition eauto.
+  Qed.
+
+  Definition eterm n := { t : EAst.term | well_scoped n t }.
+  Definition eterm_term {n} (e : eterm n) := proj1_sig e.
+  Definition well_scoped_eterm {n} (e : eterm n) : well_scoped n (eterm_term e) := proj2_sig e.
+End WellScoped.
+
+Arguments eterm_term {Σ n}.
+
+Coercion eterm_term : eterm >-> term.
+Coercion well_scoped_eterm : eterm >-> is_true.
+
+Module Constructors.
+  Section Constructors.
+  Context {Σ : global_context} {n : nat}.
+  
+  Obligation Tactic := idtac.
+  Program Definition tBox : eterm Σ n := tBox.
+  Next Obligation. cbn. exact eq_refl. Defined.
+  
+  
+  Program Definition tRel (i : nat) (Hi : i < n) : eterm Σ n := tRel i.
+  Next Obligation. cbn; intros. eapply Nat.leb_le, Hi. Defined.
+  
+  Lemma andP (a b : bool) : a -> b -> a && b.
+  Proof. destruct a, b; cbn; intros; try exact eq_refl; try discriminate. Defined.
+
+  Program Definition tEvar k (l : list (eterm Σ n)) : eterm Σ n := tEvar k (map eterm_term l).
+  Next Obligation.
+    cbn; intros.
+    induction l; cbn. exact eq_refl.
+    apply andP. exact a. exact IHl. 
+  Defined.
+  
+  Program Definition tLambda na (b : eterm Σ (S n)) : eterm Σ n := tLambda na b.
+  Next Obligation.
+    intros. exact b.
+  Defined.
+
+  Program Definition tLetIn na (b : eterm Σ n) (b' : eterm Σ (S n)) : eterm Σ n := tLetIn na b b'.
+  Next Obligation.
+    intros. cbn. apply andP. exact b. exact b'.
+  Defined.
+
+  Lemma ap {A B : Type} (f : A -> B) (x y : A) : x = y -> f x = f y.
+  Proof. destruct 1. exact eq_refl. Defined.
+
+  Lemma map_app {A B : Type} (f : A -> B) (l l' : list A) : map f (l ++ l') = map f l ++ map f l'.
+  Proof.
+    induction l; cbn. exact eq_refl.
+    now apply ap.
+  Defined.
+
+  Program Definition tApp (f : eterm Σ n) (l : list (eterm Σ n)) (napp : ~~ isApp f) (nnil : l <> nil) : eterm Σ n :=
+    mkApps f (map eterm_term l).
+  Next Obligation.
+    induction l using rev_ind => //.
+    intros Hf Hl.
+    specialize (IHl Hf).
+    rewrite map_app EAstUtils.mkApps_app /=.
+    apply andP.
+    - destruct l; cbn; [exact f|].
+      apply IHl. intros Heq. congruence.
+    - exact x.
+  Defined.
+
+  Program Definition tConst kn (isdecl : declared_constant Σ kn) : eterm Σ n := tConst kn.
+
+  Program Definition tConstruct ind k (isdecl : declared_constructor Σ ind k) : eterm Σ n := tConstruct ind k.
+  
+  Program Definition tCase ci (c : eterm Σ n) (brs : list (∑ args : list name, eterm Σ (#|args| + n)))
+    (isdecl : declared_inductive Σ ci.1) : eterm Σ n :=
+    tCase ci c (map (fun br : ∑ args, eterm Σ (#|args| + n) => (br.π1, proj1_sig br.π2)) brs).
+  Next Obligation.
+    intros. cbn.
+    destruct ci. apply andP.
+    - apply andP => //. exact c.
+    - induction brs; simp well_scoped => //.
+      cbn. rewrite IHbrs andb_true_r. exact a.π2.
+  Qed.
+
+  Program Definition tProj p (c : eterm Σ n) (isdecl : declared_projection Σ p) : eterm Σ n :=
+    tProj p c.
+  Next Obligation.
+    now cbn; intros.
+  Defined.
+  Next Obligation.
+    now cbn.
+  Defined.
+  Next Obligation.
+    cbn.
+    intros. apply andP => //. exact c.
+  Defined.
+
+  Definition edefs := ∑ mfix : mfixpoint term, well_scoped_mfix Σ (#|mfix| + n) mfix.
+
+  Program Definition tFix (mfix : edefs) idx : eterm Σ n := (tFix mfix.π1 idx).
+  Next Obligation.
+    cbn; intros. exact mfix.π2.
+  Defined.
+  
+  Program Definition tCoFix (mfix : edefs) idx : eterm Σ n := (tCoFix mfix.π1 idx).
+  Next Obligation.
+    cbn; intros; exact mfix.π2.
+  Defined.
+  End Constructors.
+End Constructors.
+
+Definition ebr_br Σ n := (fun br : ∑ args : list name, eterm Σ (#|args| + n) => (br.π1, proj1_sig br.π2)).
+
+Module View.
+  Section view.
+    Context {Σ : global_context} {n : nat}.
+
+    Inductive t : eterm Σ n -> Set :=
+    | tBox       : t Constructors.tBox
+    | tRel (i : nat) (le : i < n) : t (Constructors.tRel i le)
+    | tEvar (k : nat) l : t (Constructors.tEvar k l)
+    | tLambda na b : t (Constructors.tLambda na b)
+    | tLetIn na b b' : t (Constructors.tLetIn na b b')
+    | tApp (f : eterm Σ n) l (napp : ~~ isApp f) (nnil : l <> nil) : t (Constructors.tApp f l napp nnil)
+    | tConst kn (isdecl : declared_constant Σ kn): t (Constructors.tConst kn isdecl)
+    | tConstruct i k isdecl : t (Constructors.tConstruct i k isdecl)
+    | tCase ci c brs isdecl : t (Constructors.tCase ci c brs isdecl)
+    | tProj p c isdecl : t (Constructors.tProj p c isdecl)
+    | tFix mfix idx : t (Constructors.tFix mfix idx)
+    | tCoFix mfix idx : t (Constructors.tCoFix mfix idx).
+    Derive Signature for t.
+
+    Equations view_term {e} (v : t e) : term := 
+    | tBox => EAst.tBox
+    | tRel i le => EAst.tRel i
+    | tEvar k l => EAst.tEvar k (map eterm_term l)
+    | tLambda na b => EAst.tLambda na b
+    | tLetIn na b b' => EAst.tLetIn na b b'
+    | tApp f l napp nnil => EAst.mkApps f (map eterm_term l)
+    | tConst kn isdecl => EAst.tConst kn
+    | tConstruct i k isdecl => EAst.tConstruct i k
+    | tCase ci c brs isdecl => EAst.tCase ci c (map (ebr_br Σ n) brs)
+    | tProj p c isdecl => EAst.tProj p c
+    | tFix mfix idx => EAst.tFix mfix.π1 idx
+    | tCoFix mfix idx => EAst.tCoFix mfix.π1 idx.
+
+  End view.
+
+  Section ViewSizes.
+    Context {Σ : global_context} {n : nat}.
+
+    Lemma view_size_let_def {na} {b : eterm Σ n} {b' : eterm Σ (S n)} : size b < size (Constructors.tLetIn na b b').
+    Proof. cbn. lia. Qed.
+
+    Lemma view_size_let_body {na} {b : eterm Σ n} {b' : eterm Σ (S n)} : size b' < size (Constructors.tLetIn na b b').
+    Proof. cbn. lia. Qed.
+    
+    Lemma view_size_lambda {na} {b : eterm Σ (S n)} : size b < size (Constructors.tLambda na b).
+    Proof. cbn. lia. Qed.
+    
+  End ViewSizes.
+    
+End View.
+    
+
+Lemma well_scoped_irr {Σ n t} (ws ws' : well_scoped Σ n t) : ws = ws'.
+Proof. apply uip. Defined.
+
+Section view.
+  Context {Σ : global_context} {n : nat}.
+
+  Equations? ws_list (l : list term) (ws : well_scoped_terms Σ n l) : list (eterm Σ n) :=
+    | [], _ => []
+    | t :: ts, ws => (exist _ t _) :: ws_list ts _.
+  Proof.
+    all:move/andP: ws => [] //.
+  Qed.
+
+  Lemma ws_list_eq l ws : map eterm_term (ws_list l ws) = l.
+  Proof. funelim (ws_list l ws); cbn; auto. now rewrite H. Qed.
+
+  Equations? ws_brs (l : list (list name × term)) (ws : well_scoped_brs Σ n l) : list (∑ args, eterm Σ (#|args| + n)) :=
+    | [], _ => []
+    | t :: ts, ws => (t.1; exist _ t.2 _) :: ws_brs ts _.
+  Proof.
+    all:move/andP: ws => [] //.
+  Qed.
+
+  Lemma ws_brs_eq l ws : map (ebr_br Σ n) (ws_brs l ws) = l.
+  Proof. funelim (ws_brs l ws); cbn; auto. rewrite H. destruct t => //. Qed.
+
+  Lemma andb_left {a b} : a && b -> a.
+  Proof.
+    move/andP=>[] //.
+  Qed.
+
+  Lemma andb_right {a b} : a && b -> b.
+  Proof.
+    move/andP=>[] //.
+  Qed.
+
+  Lemma well_scoped_terms_forallb {l} : well_scoped_terms Σ n l = forallb (well_scoped Σ n) l.
+  Proof.
+    induction l; simp well_scoped; auto.
+    now rewrite IHl.
+  Qed.
+
+  Lemma well_scoped_mkApps {f l} : well_scoped Σ n (mkApps f l) -> well_scoped Σ n f && well_scoped_terms Σ n l.
+  Proof.
+    induction l using rev_ind; cbn; auto.
+    - now intros ->.
+    - rewrite mkApps_app /=.
+      move/andP=> [] wfl wx.
+      move/andP: (IHl wfl) => [] => -> wfnl /=.
+      now rewrite well_scoped_terms_forallb forallb_app -well_scoped_terms_forallb /= wfnl wx.
+  Qed.
+
+  Notation " ( x ⧆ y ) " := (exist _ x y).
+
+  Definition view (x : eterm Σ n) : View.t x.
+  Proof.
+    destruct x as [t ws].
+    set (t' := t).
+    destruct t;
+    try solve [evar (ws' : well_scoped Σ n    t' = true); rewrite (well_scoped_irr ws ws'); subst ws' t';
+      unshelve econstructor; eauto].
+    - evar (ws' : well_scoped Σ n t' = true); rewrite (well_scoped_irr ws ws'); subst ws' t'.
+      unshelve econstructor. now eapply Nat.leb_le.
+    - cbn in ws; discriminate.
+    - pose proof (ws_list_eq l ws). set(l' := ws_list l ws) in *. clearbody l'.
+      subst t'.
+      revert ws. destruct H.
+      intros ws. set (t' := tEvar _ _).
+      evar (ws' : well_scoped Σ n t' = true); rewrite (well_scoped_irr ws ws'); subst ws' t'.
+      econstructor.
+    - cbn in ws.
+      change t with (eterm_term (exist _ t ws)) in t'.
+      evar (ws' : well_scoped Σ n t' = true); rewrite (well_scoped_irr ws ws'); subst ws' t'.
+      econstructor.
+    - change t2 with (eterm_term (t2 ⧆ andb_right ws)) in t'.
+      change t1 with (eterm_term (t1 ⧆ andb_left ws)) in t'.
+      revert t'.
+      set (prf := andb_left ws).
+      set (prf' := andb_right _). clearbody prf prf'.
+      intros t'.
+      evar (ws' : well_scoped Σ n t' = true).
+      rewrite (well_scoped_irr ws ws'); subst ws' t'.
+      econstructor.
+    - destruct (decompose_app (tApp t1 t2)) eqn:da.
+      move: ws. revert t'.
+      rewrite (decompose_app_inv da).
+      intros t' ws.
+      move: (decompose_app_notApp _ _ _ da).
+      move: (EInduction.decompose_app_app _ _ _ _ da).
+      clear da t1 t2.
+      pose proof (wfa := well_scoped_mkApps ws).
+      pose proof (ws_list_eq l (andb_right wfa)).
+      set(l'' := ws_list l _) in *. clearbody l''.
+      move: ws. revert t'.
+      destruct H.
+      intros t'.
+      change t with (eterm_term (t ⧆ andb_left wfa)) in t'.
+      set (prfa := andb_left wfa) in *. clearbody prfa.
+      intros ws hl ht.
+      evar (ws' : well_scoped Σ n t' = true).
+      rewrite (well_scoped_irr ws ws'); subst ws' t'.
+      unshelve econstructor. exact ht.
+      intros hl'. subst l''. cbn in hl. congruence.
+
+    - destruct p as [ind k].
+      change t with (eterm_term (t ⧆ andb_right (andb_left ws))) in t'.
+      set (prf1 := andb_right _) in t'. clearbody prf1.
+      pose proof (ws_brs_eq _ (andb_right ws)).
+      set (prf2 := andb_right _) in *. clearbody prf2.
+      revert t' ws. destruct H.
+      intros t' ws.
+      evar (ws' : well_scoped Σ n t' = true).
+      rewrite (well_scoped_irr ws ws'); subst ws' t'.
+      unshelve econstructor.
+      cbn. apply (andb_left (andb_left ws)).
+      
+    - change t with (eterm_term (t ⧆ andb_right ws)) in t'.
+      set (prf := andb_right ws) in *. clearbody prf.
+      evar (ws' : well_scoped Σ n t' = true).
+      rewrite (well_scoped_irr ws ws'); subst ws' t'.
+      unshelve econstructor. apply (andb_left ws).
+    - change m with (((m; ws) : Constructors.edefs).π1) in t'.
+      evar (ws' : well_scoped Σ n t' = true).
+      rewrite (well_scoped_irr ws ws'); subst ws' t'.
+      econstructor.
+    - change m with (((m; ws) : Constructors.edefs).π1) in t'.
+      evar (ws' : well_scoped Σ n t' = true).
+      rewrite (well_scoped_irr ws ws'); subst ws' t'.
+      econstructor.
+  Defined.
+
+  Lemma view_term (t : eterm Σ n) (v : View.t t) : View.view_term v = t.
+  Proof.
+    induction v; cbn; reflexivity.
+  Qed.
+
+  Lemma view_view_term (t : eterm Σ n) : View.view_term (view t) = t.
+  Proof. apply view_term. Qed.
+
+  Lemma view_view_size (t : eterm Σ n) : size (View.view_term (view t)) = size t.
+  Proof. now rewrite view_view_term. Qed.
+
+End view.
+
+From Coq Require Import Relation_Definitions.
+
+Section test_view.
+  Context (Σ : global_context).
+  Import View.
+
+  Definition eterm_size : relation (∑ n, eterm Σ n) := 
+    MR lt (fun x : ∑ n, eterm Σ n => size x.π2).
+
+  Instance wf_size : WellFounded eterm_size.
+  Proof. unfold eterm_size. tc. Defined.
+  Obligation Tactic := idtac.
+
+  #[derive(eliminator=no)]
+  Equations? test_view (n : nat) (t : eterm Σ n) : bool 
+    by wf (n; t) eterm_size :=
+    test_view n t with view t := {
+      | tBox => true
+      | tRel i lei => false
+      | tApp f args notapp notnil => test_view n f
+      | _ => false
+    }.
+  Proof.
+    do 2 red. cbn. rewrite size_mkApps.
+    destruct args; cbn; try congruence. lia.
+  Qed.
+
+End test_view.
+
+
diff --git a/erasure/theories/Erasure.v b/erasure/theories/Erasure.v
index 12e8d7552..ae833caf9 100644
--- a/erasure/theories/Erasure.v
+++ b/erasure/theories/Erasure.v
@@ -18,10 +18,11 @@ From MetaCoq.Erasure Require ErasureFunction EOptimizePropDiscr ERemoveParams EW
 
 (* Used to show timings of the ML execution *)
  
-Definition time : forall {A}, string -> (unit -> A) -> unit -> A :=
-  fun A s f x => f x.
+Definition time : forall {A B}, string -> (A -> B) -> A -> B :=
+  fun A B s f x => f x.
 
-Extract Constant time => "(fun c f x -> let s = Tm_util.list_to_string c in Tm_util.time (Pp.str s) f x)".
+Extract Constant time => 
+  "(fun c f x -> let s = Caml_bytestring.caml_string_of_bytestring c in Tm_util.time (Pp.str s) f x)".
 
 (* This is the total erasure function +
   let-expansion of constructor arguments and case branches +
@@ -437,10 +438,10 @@ Local Open Scope string_scope.
   Coq definition). *)
 Program Definition erase_and_print_template_program {cf : checker_flags} (p : Ast.Env.program)
   : string :=
-  let (Σ', t) := erase_program p (todo "wf_env and welltyped term") in
-  time "Pretty printing" (fun _ => print_term Σ' [] true false t ^ nl ^ "in:" ^ nl ^ print_global_context Σ') tt.
+  let p' := erase_program p (todo "wf_env and welltyped term") in
+  time "Pretty printing" print_program p'.
 
 Program Definition erase_fast_and_print_template_program {cf : checker_flags} (p : Ast.Env.program)
   : string :=
-  let (Σ', t) := erase_program_fast p (todo "wf_env and welltyped term") in
-  time "pretty-printing" (fun _ => print_term Σ' [] true false t ^ nl ^ "in:" ^ nl ^ print_global_context Σ') tt.
+  let p' := erase_program_fast p (todo "wf_env and welltyped term") in
+  time "pretty-printing" print_program p'.
diff --git a/erasure/theories/ErasureFunction.v b/erasure/theories/ErasureFunction.v
index 6252ecd31..da91f9aff 100644
--- a/erasure/theories/ErasureFunction.v
+++ b/erasure/theories/ErasureFunction.v
@@ -1237,14 +1237,13 @@ Proof.
     red. destruct H. split; eauto.
     red in H. red.
     inv wfΣ. inv X.
-    rewrite -H. simpl. unfold lookup_env; simpl; unfold eq_kername. destruct kername_eq_dec; try congruence.
+    rewrite -H. simpl. unfold lookup_env; simpl. destruct (eqb_spec (inductive_mind p.1) kn); try congruence.
     eapply lookup_env_Some_fresh in H. subst kn; contradiction.
   - econstructor; eauto.
     red. destruct H. split; eauto.
     inv wfΣ. inv X.
     red in H |- *.
-    rewrite -H. simpl. unfold lookup_env; simpl; unfold eq_kername.
-    unfold lookup_env in H; simpl in H. destruct kername_eq_dec; try congruence.
+    rewrite -H. simpl. unfold lookup_env; simpl; destruct (eqb_spec (inductive_mind p.1.1) kn); try congruence.
     eapply lookup_env_Some_fresh in H. subst kn. contradiction.
 Qed.
 
@@ -1256,23 +1255,23 @@ Proof.
   intros wf hl. 
   eapply lookup_env_Some_fresh in hl.
   inv wf. inv X.
-  destruct (kername_eq_dec kn kn'); subst; congruence.
+  destruct (eqb_spec kn kn'); subst; congruence.
 Qed.
 
 Lemma lookup_env_cons_disc {Σ kn kn' d} : 
   kn <> kn' ->
   lookup_env (add_global_decl Σ (kn', d)) kn = lookup_env Σ kn.
 Proof.
-  intros Hk. simpl; unfold lookup_env; simpl; unfold eq_kername; simpl.
-  destruct kername_eq_dec; congruence.
+  intros Hk. simpl; unfold lookup_env; simpl.
+  destruct (eqb_spec kn kn'); congruence.
 Qed.
 
 Lemma elookup_env_cons_disc {Σ kn kn' d} : 
   kn <> kn' ->
   ETyping.lookup_env ((kn', d) :: Σ) kn = ETyping.lookup_env Σ kn.
 Proof.
-  intros Hk. simpl; unfold eq_kername.
-  destruct kername_eq_dec; congruence.
+  intros Hk. simpl.
+  destruct (eqb_spec kn kn'); congruence.
 Qed.
 
 Lemma global_erases_with_deps_cons kn kn' d d' Σ Σ' : 
@@ -1404,9 +1403,9 @@ Lemma lookup_env_closed {Σ kn decl} : ETyping.closed_env Σ -> ETyping.lookup_e
 Proof.
   induction Σ; cbn => //.
   move/andP => [] cla cle.
-  unfold eq_kername; destruct kername_eq_dec.
+  case: eqb_spec. intros e; subst.
   move=> [= <-]. apply cla.
-  now eapply IHΣ.
+  intros hne; now eapply IHΣ.
 Qed.
 
 Lemma erases_closed Σ Γ t t' : Σ;;; Γ |- t ⇝ℇ t' -> PCUICAst.closedn #|Γ| t -> ELiftSubst.closedn #|Γ| t'.
@@ -1450,7 +1449,7 @@ Proof.
     eapply KernameSet.subset_spec in sub.
     destruct (H i hin) as [[decl Hdecl]]. unfold lookup_env in Hdecl.
     cbn in Hdecl.
-    pose proof (eqb_spec i kn). unfold eqb in H0; cbn in H0.
+    pose proof (eqb_spec i kn).
     rewrite e in Hdecl. move: Hdecl. cbn -[erase_global_decls].
     elim: H0. intros -> [= <-].
     * destruct d as [|]; [left|right].
@@ -1737,19 +1736,19 @@ Proof.
   - move=> /= //.
   - intros e. destruct a as [kn' d'].
     cbn -[erase_global_decls].
-    unfold eq_kername. destruct kername_eq_dec. subst kn'.
+    case: (eqb_spec kn kn'); intros e'; subst.
     intros [= ->].
     unfold erase_global_decls.
     eapply KernameSet.mem_spec in hin. rewrite hin /=.
     now rewrite eq_kername_refl.
     intros hl. destruct d'. simpl.
     destruct KernameSet.mem. cbn.
-    unfold eq_kername. destruct kername_eq_dec => //. 
+    rewrite (negbTE (proj2 (neqb _ _) e')).
     eapply IHg => //. eapply KernameSet.union_spec. left => //.
     eapply IHg => //.
     simpl.
     destruct KernameSet.mem. cbn.
-    unfold eq_kername. destruct kername_eq_dec => //. 
+    rewrite (negbTE (proj2 (neqb _ _) e')).
     eapply IHg => //.
     eapply IHg => //. 
 Qed.
diff --git a/erasure/theories/Extraction.v b/erasure/theories/Extraction.v
index 0d992f5fe..6a5a9c29f 100644
--- a/erasure/theories/Extraction.v
+++ b/erasure/theories/Extraction.v
@@ -1,5 +1,5 @@
 (* Distributed under the terms of the MIT license. *)
-From Coq Require Import Ascii FSets ExtrOcamlBasic ExtrOcamlString ExtrOcamlZInt ExtrOCamlFloats ExtrOCamlInt63.
+From Coq Require Import Ascii FSets ExtrOcamlBasic ExtrOcamlZInt ExtrOCamlFloats ExtrOCamlInt63.
 From MetaCoq.Template Require Import utils.
 
 (** * Extraction setup for the erasure phase of template-coq.
@@ -7,11 +7,6 @@ From MetaCoq.Template Require Import utils.
     Any extracted code planning to link with the plugin
     should use these same directives for consistency.
 *)
-
-Extract Constant ascii_compare =>
- "fun x y -> match Char.compare x y with 0 -> Eq | x when x < 0 -> Lt | _ -> Gt".
-Extract Constant Ascii.compare =>
- "fun x y -> match Char.compare x y with 0 -> Eq | x when x < 0 -> Lt | _ -> Gt".
  
 Extraction Blacklist Classes config uGraph Universes Ast String List Nat Int
            UnivSubst Typing Checker Retyping OrderedType Logic Common ws_cumul_pb Classes Numeral
@@ -38,10 +33,8 @@ Extract Constant Equations.Init.pr1 => "fst".
 Extract Constant Equations.Init.pr2 => "snd".
 Extraction Inline Equations.Init.pr1 Equations.Init.pr2.
 
-Extract Constant PCUICWfEnv.guard_impl => 
-  "(fun _ _ _ _ -> true)".
-
-Extract Constant PCUICTyping.guard_checking => "{ fix_guard = (fun _ _ _ -> true); cofix_guard = (fun _ _ _ -> true) }".
+Extract Constant PCUICWfEnv.guard_impl => "(fun _ _ _ _ -> true)".
+Extract Constant PCUICTyping.guard_checking => "(fun _ _ _ _ -> true)".
 
 Cd "src".
 
diff --git a/examples/add_constructor.v b/examples/add_constructor.v
index ac9da6bc3..03b28d6ed 100644
--- a/examples/add_constructor.v
+++ b/examples/add_constructor.v
@@ -91,7 +91,7 @@ Polymorphic Definition add_constructor (tm : Ast.term)
 
 
 (** * Examples *)
-Local Open Scope string.
+Local Open Scope bs_scope.
 (** Here we add a silly constructor to bool. *)
 MetaCoq Run (
     add_constructor <% bool %> "foo" <% (fun x : Type => nat -> x -> bool -> x) %>).
diff --git a/examples/demo.v b/examples/demo.v
index cb4843b07..c05d427f4 100644
--- a/examples/demo.v
+++ b/examples/demo.v
@@ -83,9 +83,9 @@ Print eo_from_syntax.
 
 Local Notation Nat_module := (MPfile ["Datatypes"; "Init"; "Coq"], "nat").
 
-MetaCoq Unquote Definition two_from_syntax := (Ast.tApp (Ast.tConstruct (BasicAst.mkInd Nat_module 0) 1 nil)
-   (Ast.tApp (Ast.tConstruct (BasicAst.mkInd Nat_module 0) 1 nil)
-      (Ast.tConstruct (BasicAst.mkInd Nat_module 0) 0 nil :: nil) :: nil)).
+MetaCoq Unquote Definition two_from_syntax := (Ast.tApp (Ast.tConstruct (Kernames.mkInd Nat_module 0) 1 nil)
+   (Ast.tApp (Ast.tConstruct (Kernames.mkInd Nat_module 0) 1 nil)
+      (Ast.tConstruct (Kernames.mkInd Nat_module 0) 0 nil :: nil) :: nil)).
 
 MetaCoq Quote Recursively Definition plus_syntax := plus.
 
diff --git a/examples/metacoq_tour.v b/examples/metacoq_tour.v
index 15508a1de..b6dacff61 100644
--- a/examples/metacoq_tour.v
+++ b/examples/metacoq_tour.v
@@ -1,10 +1,9 @@
-From Coq Require Import String.
 From MetaCoq.Template Require config utils All.
 From MetaCoq.Template Require Import TemplateMonad.
 From MetaCoq.PCUIC Require Import PCUICAst PCUICReduction PCUICCumulativity PCUICTyping PCUICSafeLemmata.
 
 Import MCMonadNotation.
-Local Open Scope string_scope.
+Local Open Scope bs_scope.
 
 (** MetaCoq is: 
 
diff --git a/examples/tauto.v b/examples/tauto.v
index 89ec9e182..e6ab44e56 100644
--- a/examples/tauto.v
+++ b/examples/tauto.v
@@ -859,36 +859,36 @@ Equations reify (Σ : global_env_ext) (Γ : context) (P : term) : option form
       | None => None
       } ;
     | tInd ind []
-      with kername_eq_dec ind.(inductive_mind) q_and := {
-      | left e2 with args := {
+      with eqb ind.(inductive_mind) q_and := {
+      | true with args := {
         | [ A ; B ] =>
           af <- reify Σ Γ A ;;
           bf <- reify Σ Γ B ;;
           ret (And af bf) ;
         | _ => None
         } ;
-      | right _
-        with kername_eq_dec ind.(inductive_mind) q_or := {
-        | left e2 with args := {
+      | false
+        with eqb ind.(inductive_mind) q_or := {
+        | true with args := {
           | [ A ; B ] =>
             af <- reify Σ Γ A ;;
             bf <- reify Σ Γ B ;;
             ret (Or af bf) ;
           | _ => None
           } ;
-        | right _
-          with kername_eq_dec ind.(inductive_mind) q_False := {
-          | left e2 with args := {
+        | false
+          with eqb ind.(inductive_mind) q_False := {
+          | true with args := {
             | [] => ret Fa ;
             | _ => None
             } ;
-      | right _
-          with kername_eq_dec ind.(inductive_mind) q_True := {
-          | left e2 with args := {
+      | false
+          with eqb ind.(inductive_mind) q_True := {
+          | true with args := {
             | [] => ret Tr ;
             | _ => None
             } ;
-              | right _ => None
+              | false => None
        }
         }
       }} ;
diff --git a/examples/typing_correctness.v b/examples/typing_correctness.v
index e4834a990..8886f19c5 100644
--- a/examples/typing_correctness.v
+++ b/examples/typing_correctness.v
@@ -40,12 +40,10 @@ Proof.
   let wf_proof := eval hnf in (make_wf_env_ext gctx) in 
   match wf_proof with
   | CorrectDecl ?x => exact x
-  | _ => fail "Couldn't prove the global environment is well-formed"
+  | _ => idtac wf_proof; fail "Couldn't prove the global environment is well-formed"
   end.
 Defined.
 
-
-
 (** There is always a proof of `forall x : Sort s, x -> x` *)
 
 Definition inh {cf:checker_flags} (Σ : wf_env_ext) Γ T := ∑ t, forall Σ0 : global_env_ext, abstract_env_rel' Σ Σ0 -> ∥ typing Σ0 Γ t T ∥.
diff --git a/pcuic/theories/Conversion/PCUICNamelessConv.v b/pcuic/theories/Conversion/PCUICNamelessConv.v
index c8fdac30b..aa6ed976b 100644
--- a/pcuic/theories/Conversion/PCUICNamelessConv.v
+++ b/pcuic/theories/Conversion/PCUICNamelessConv.v
@@ -237,7 +237,7 @@ Proof.
   rewrite /lookup_env /=.
   induction Σ. 1: reflexivity.
   simpl.
-  unfold eq_kername; destruct kername_eq_dec; subst.
+  case: eqb_spec; intros e; subst.
   - reflexivity.
   - assumption.
 Qed.
diff --git a/pcuic/theories/Conversion/PCUICUnivSubstitutionConv.v b/pcuic/theories/Conversion/PCUICUnivSubstitutionConv.v
index 78808dd01..d1c106735 100644
--- a/pcuic/theories/Conversion/PCUICUnivSubstitutionConv.v
+++ b/pcuic/theories/Conversion/PCUICUnivSubstitutionConv.v
@@ -1641,14 +1641,14 @@ Lemma wf_universe_subst_instance {cf : checker_flags} (Σ : global_env_ext) univ
 Proof.
   destruct l; simpl; auto. rename n into t.
   intros wfΣ Hl Hu e [[l n] [inl ->]]%In_subst_instance.
-  destruct l; simpl; auto.
+  destruct l as [|s|n']; simpl; auto.
   - unfold global_ext_levels.
     apply LS.union_spec. right.
     apply global_levels_Set.
   - specialize (Hl (Level.Level s, n) inl).
     simpl in Hl. apply monomorphic_level_in_global_ext in Hl.
     eapply LS.union_spec. now right.
-  - specialize (Hl (Level.Var n0, n) inl).
+  - specialize (Hl (Level.Var n', n) inl).
     eapply LS.union_spec in Hl as [Hl|Hl].
     + red in Hu.
       unfold levels_of_udecl in Hl.
@@ -1657,7 +1657,7 @@ Proof.
         destruct u; try discriminate. lsets.
       * destruct Hu as [declu [us vc]].
         unfold subst_instance. simpl.
-        destruct (nth_error u n0) eqn:hnth.
+        destruct (nth_error u n') eqn:hnth.
         2:{ simpl. eapply LS.union_spec; right; apply global_levels_Set. }
         eapply forallb_Forall in declu.
         eapply nth_error_forall in declu; eauto.
diff --git a/pcuic/theories/Conversion/PCUICWeakeningEnvConv.v b/pcuic/theories/Conversion/PCUICWeakeningEnvConv.v
index 314e0359e..c1bffc0ca 100644
--- a/pcuic/theories/Conversion/PCUICWeakeningEnvConv.v
+++ b/pcuic/theories/Conversion/PCUICWeakeningEnvConv.v
@@ -145,7 +145,7 @@ Lemma lookup_global_Some_fresh `{checker_flags} Σ c decl :
   lookup_global Σ c = Some decl -> ~ (fresh_global c Σ).
 Proof.
   induction Σ; cbn. 1: congruence.
-  unfold eq_kername; destruct kername_eq_dec; subst.
+  destruct (eqb_spec c a.1); subst.
   - intros [= <-] H2. inv H2.
     contradiction.
   - intros H1 H2. apply IHΣ; tas.
@@ -171,7 +171,7 @@ Proof.
   - simpl. auto.
   - intros hl. depelim hΣ. specialize (IHΣ'' c decl hΣ hl).
     simpl in *.
-    unfold eq_kername; destruct kername_eq_dec; subst; auto.
+    destruct (eqb_spec c kn); subst; auto.
     apply lookup_global_Some_fresh in IHΣ''; contradiction.
 Qed.
 #[global]
@@ -550,7 +550,7 @@ Proof.
   destruct Σ as [univs Σ]; cbn in *.
   induction wfΣ; simpl. 1: discriminate.
   cbn in HH. subst udecl.
-  unfold eq_kername in HH; destruct kername_eq_dec; subst.
+  destruct (eqb_spec c kn); subst.
   - apply some_inj in HH; destruct HH. subst.
     clear -o. unfold on_udecl, on_udecl_prop in *.
     destruct o as [H1 [H2 [H3 H4]]]. repeat split.
diff --git a/pcuic/theories/Extraction.v b/pcuic/theories/Extraction.v
index f29cd4135..febd24001 100644
--- a/pcuic/theories/Extraction.v
+++ b/pcuic/theories/Extraction.v
@@ -1,6 +1,6 @@
 (* Distributed under the terms of the MIT license. *)
 Require Import MetaCoq.Template.utils.
-Require Import FSets ssreflect ExtrOcamlBasic ExtrOcamlString ExtrOcamlZInt.
+Require Import FSets ssreflect ExtrOcamlBasic ExtrOcamlZInt.
 
 (** * Extraction setup for the pcuic phase of MetaCoq.
 
diff --git a/pcuic/theories/PCUICCanonicity.v b/pcuic/theories/PCUICCanonicity.v
index 523f6e63d..2c831fa8d 100644
--- a/pcuic/theories/PCUICCanonicity.v
+++ b/pcuic/theories/PCUICCanonicity.v
@@ -155,7 +155,7 @@ Section Spines.
     eapply forallb_All in eqhd.
     destruct idx; simpl in Hl; [congruence|].
     eapply All_nth_error in eqhd; eauto.
-    now eapply Reflect.eqb_eq in eqhd.
+    now eapply ReflectEq.eqb_eq in eqhd.
   Qed.
   
   Lemma wf_cofixpoint_inv mfix idx decl :
@@ -180,7 +180,7 @@ Section Spines.
     eapply forallb_All in eqhd.
     destruct idx; simpl in Hl; [congruence|].
     eapply All_nth_error in eqhd; eauto.
-    now eapply Reflect.eqb_eq in eqhd.
+    now eapply ReflectEq.eqb_eq in eqhd.
   Qed.
 
     Lemma on_free_vars_it_mkLambda_or_LetIn {P Δ t} : 
@@ -837,7 +837,7 @@ Section WeakNormalization.
     - move=> [hargs ccum'].
       rewrite expand_lets_mkApps subst_mkApps /= in ccum'.
       eapply invert_cumul_ind_ind in ccum' as ((? & ?) & ?).
-      len in r. eapply Reflect.eqb_eq in i0. now subst ind'.
+      len in r. eapply ReflectEq.eqb_eq in i0. now subst ind'.
   Qed.
 
   Lemma check_recursivity_kind_inj {mind rk rk'} :
@@ -846,8 +846,8 @@ Section WeakNormalization.
   Proof.
     rewrite /check_recursivity_kind.
     case: lookup_env => //; case => // m.
-    elim: Reflect.eqb_spec;
-    elim: Reflect.eqb_spec; congruence.
+    elim: ReflectEq.eqb_spec;
+    elim: ReflectEq.eqb_spec; congruence.
   Qed.
 
   Lemma wt_closed_red_refl {Γ t T} : Σ ;;; Γ |- t : T -> Σ ;;; Γ ⊢ t ⇝ t.
diff --git a/pcuic/theories/PCUICConversion.v b/pcuic/theories/PCUICConversion.v
index 96630c23b..ebbf7457f 100644
--- a/pcuic/theories/PCUICConversion.v
+++ b/pcuic/theories/PCUICConversion.v
@@ -1441,7 +1441,7 @@ Section Inversions.
 
   Lemma invert_cumul_ind_ind {Γ ind ind' u u' args args'} :
     Σ ;;; Γ ⊢ mkApps (tInd ind u) args ≤ mkApps (tInd ind' u') args' ->
-    (Reflect.eqb ind ind' * PCUICEquality.R_global_instance Σ (eq_universe Σ) (leq_universe Σ) (IndRef ind) #|args| u u' *
+    (eqb ind ind' * PCUICEquality.R_global_instance Σ (eq_universe Σ) (leq_universe Σ) (IndRef ind) #|args| u u' *
       ws_cumul_pb_terms Σ Γ args args').
   Proof.
     intros ht; eapply ws_cumul_pb_Ind_l_inv in ht as (? & ? & [? ? ?]); auto.
diff --git a/pcuic/theories/PCUICExpandLetsCorrectness.v b/pcuic/theories/PCUICExpandLetsCorrectness.v
index 41f9335d1..99140df12 100644
--- a/pcuic/theories/PCUICExpandLetsCorrectness.v
+++ b/pcuic/theories/PCUICExpandLetsCorrectness.v
@@ -281,8 +281,7 @@ Proof.
   destruct Σ as [univs Σ].
   induction Σ.
   - reflexivity.
-  - cbn.
-    unfold eq_kername in *; destruct kername_eq_dec; subst.
+  - cbn. case: eqb_spec; intros e; subst.
     + destruct a; auto.
     + now rewrite IHΣ.
 Qed.
diff --git a/pcuic/theories/PCUICInductiveInversion.v b/pcuic/theories/PCUICInductiveInversion.v
index 0db1caf1b..2221fb902 100644
--- a/pcuic/theories/PCUICInductiveInversion.v
+++ b/pcuic/theories/PCUICInductiveInversion.v
@@ -238,8 +238,8 @@ Proof.
     apply decompose_app_inv in dapp => //.
     rewrite dapp. do 3 f_equal.
     symmetry.
-    change (eq_kername ind k) with (Reflect.eqb ind k) in eqk.
-    destruct (Reflect.eqb_spec ind k); auto. discriminate.
+    change (eq_kername ind k) with (ReflectEq.eqb ind k) in eqk.
+    destruct (ReflectEq.eqb_spec ind k); auto. discriminate.
     discriminate.
   - discriminate.
   - discriminate.
diff --git a/pcuic/theories/PCUICParallelReductionConfluence.v b/pcuic/theories/PCUICParallelReductionConfluence.v
index cd301000f..ca7043742 100644
--- a/pcuic/theories/PCUICParallelReductionConfluence.v
+++ b/pcuic/theories/PCUICParallelReductionConfluence.v
@@ -2051,7 +2051,7 @@ Section Rho.
         destruct (inspect_nth_error_rename (r:=r) eqbr) as [prf ->]; simp rho.
         cbv zeta. simp rho.
         cbn -[eqb]. autorewrite with len.
-        case: eqb_spec => // hlen.
+        case: eqb_specT => // hlen.
         + erewrite rename_rho_iota_red; tea => //.
           f_equal.
           pose proof (decompose_app_inv decapp). subst t.
@@ -3680,7 +3680,7 @@ Section Rho.
       rewrite rho_app_case.
       rewrite decompose_app_mkApps; auto.
       change eq_inductive with (@eqb inductive _).
-      destruct (eqb_spec ci.(ci_ind) ci.(ci_ind)); try discriminate.
+      destruct (eqb_specT ci.(ci_ind) ci.(ci_ind)); try discriminate.
       2:{ congruence. }
       unfold iota_red. eapply forallb_All in p4. eapply All2_All_mix_left in X3; tea.
       eapply All2_nth_error_Some_right in X3 as [br0 [hnth [hcl [IHbr [[predbod IHbod] breq]]]]]; tea.
@@ -3957,7 +3957,7 @@ Section Rho.
     - simpl in *. inv_on_free_vars. rewrite rho_app_proj.
       rewrite decompose_app_mkApps; auto.
       change eq_inductive with (@eqb inductive _).
-      destruct (eqb_spec i i) => //.
+      destruct (eqb_specT i i) => //.
       eapply All2_nth_error_Some_right in heq_nth_error as [t' [? ?]]; eauto.
       simpl in y. rewrite e0. simpl.
       auto. eapply y => //. 
@@ -4128,9 +4128,9 @@ Section Rho.
         subst c0. cbn -[eqb].
         simp rho.
         change eq_inductive with (@eqb inductive _).
-        destruct (eqb_spec ci.(ci_ind) ind). subst ind.
+        destruct (eqb_specT ci.(ci_ind) ind). subst ind.
         destruct (nth_error brs0 n) eqn:hbr => //.
-        case: eqb_spec => [eq|neq].
+        case: eqb_specT => [eq|neq].
         eapply pred1_mkApps_tConstruct in predc0 as [args' [? ?]]; pcuic. subst c1.
         intuition auto.
         rewrite rho_app_construct in Hc.
@@ -4277,7 +4277,7 @@ Section Rho.
         eapply pred1_mkApps_refl_tConstruct in Hc.
         destruct nth_error eqn:Heq.
         change eq_inductive with (@eqb inductive _).
-        destruct (eqb_spec ind ind0); subst.
+        destruct (eqb_specT ind ind0); subst.
         econstructor; eauto.
         now rewrite nth_error_map Heq.
         eapply pred_proj_congr, pred_mkApps; auto with pcuic.
diff --git a/pcuic/theories/PCUICSR.v b/pcuic/theories/PCUICSR.v
index 3ab0d25e0..4c35e9d4d 100644
--- a/pcuic/theories/PCUICSR.v
+++ b/pcuic/theories/PCUICSR.v
@@ -2066,7 +2066,7 @@ Proof.
     eapply wf_cofixpoint_typing_spine in t; eauto.
     unfold check_recursivity_kind in t.
     rewrite isdecl.p1 in t.
-    apply Reflect.eqb_eq in t. rewrite t /= in heq_isCoFinite.
+    apply ReflectEq.eqb_eq in t. rewrite t /= in heq_isCoFinite.
     discriminate.
     
   - (* Case congruence on a parameter *) 
diff --git a/pcuic/theories/PCUICToTemplateCorrectness.v b/pcuic/theories/PCUICToTemplateCorrectness.v
index 9d6c93b69..316ace2e0 100644
--- a/pcuic/theories/PCUICToTemplateCorrectness.v
+++ b/pcuic/theories/PCUICToTemplateCorrectness.v
@@ -141,8 +141,7 @@ Proof.
   destruct Σ as [univs Σ].
   induction Σ.
   - reflexivity.
-  - cbn.
-    unfold eq_kername in *; destruct kername_eq_dec; subst.
+  - cbn. case: eqb_spec => intros; subst.
     + destruct a; auto.
     + now rewrite IHΣ.
 Qed.
diff --git a/pcuic/theories/PCUICTyping.v b/pcuic/theories/PCUICTyping.v
index 79d496175..7ecd373c5 100644
--- a/pcuic/theories/PCUICTyping.v
+++ b/pcuic/theories/PCUICTyping.v
@@ -82,7 +82,7 @@ Definition isCoFinite (r : recursivity_kind) :=
 Definition check_recursivity_kind 
   (lookup: kername -> option global_decl) ind r :=
   match lookup ind with
-  | Some (InductiveDecl mib) => Reflect.eqb mib.(ind_finite) r
+  | Some (InductiveDecl mib) => ReflectEq.eqb mib.(ind_finite) r
   | _ => false
   end.
 
@@ -109,7 +109,7 @@ Definition wf_fixpoint_gen
   | Some (ind :: inds) =>
     (* Check that mutually recursive fixpoints are all on the same mututal
        inductive block *)
-    forallb (Reflect.eqb ind) inds &&
+    forallb (eqb ind) inds &&
     check_recursivity_kind lookup ind Finite
   | _ => false
   end.
@@ -135,7 +135,7 @@ Definition wf_cofixpoint_gen
   | Some (ind :: inds) =>
     (* Check that mutually recursive cofixpoints are all producing
        coinductives in the same mututal coinductive block *)
-    forallb (Reflect.eqb ind) inds &&
+    forallb (eqb ind) inds &&
     check_recursivity_kind lookup ind CoFinite
   | _ => false
   end.
@@ -1252,14 +1252,14 @@ Section All_local_env.
     destruct Σ as [univs Σ]; rewrite /on_global_env /lookup_env; cbn.
     intros [cu Σp].
     induction Σp; simpl. congruence.
-    unfold eq_kername; destruct kername_eq_dec; subst.
-    intros [= ->].
-    exists ({| universes := univs; declarations := Σ |}).
-    split.
-    - red; cbn. split; [split;[lsets|csets]|].
-      exists [(kn, decl)] => //.
-    - split => //.
-    - apply o0.
+    destruct (eqb_specT c kn); subst.
+    - intros [= ->].
+      exists ({| universes := univs; declarations := Σ |}).
+      split.
+      * red; cbn. split; [split;[lsets|csets]|].
+        exists [(kn, decl)] => //.
+      * split => //.
+      * apply o0.
     - intros hl. destruct (IHΣp hl) as [Σ' []].
       exists Σ'.
       split=> //.
diff --git a/pcuic/theories/PCUICWfUniverses.v b/pcuic/theories/PCUICWfUniverses.v
index 8a24fe315..d6103759e 100644
--- a/pcuic/theories/PCUICWfUniverses.v
+++ b/pcuic/theories/PCUICWfUniverses.v
@@ -90,7 +90,7 @@ Section CheckerFlags.
   Proof.
     destruct l; simpl; auto. rename n into t. 
     intros wfΣ Hl Hu e [[l n] [inl ->]]%In_subst_instance.
-    destruct l; simpl; auto.
+    destruct l as [|s|n']; simpl; auto.
     - unfold global_ext_levels.
       apply LS.union_spec. right.
       apply global_levels_Set.
@@ -98,7 +98,7 @@ Section CheckerFlags.
       simpl in Hl.
       apply monomorphic_level_in_global_ext in Hl.
       eapply LS.union_spec. now right.
-    - specialize (Hl (Level.Var n0, n) inl).
+    - specialize (Hl (Level.Var n', n) inl).
       eapply LS.union_spec in Hl as [Hl|Hl].
       + red in Hu.
         unfold levels_of_udecl in Hl.
@@ -109,9 +109,10 @@ Section CheckerFlags.
           eapply nth_error_forall in Hu; eauto.
           eapply LS.union_spec; right. eapply global_levels_Set.
         * unfold subst_instance. simpl.
-          destruct (nth_error u n0) eqn:hnth.
+          destruct (nth_error u n') eqn:hnth.
           2:{ simpl. rewrite hnth. eapply LS.union_spec; right; apply global_levels_Set. }
-          eapply nth_error_forall in Hu. 2:eauto. change (nth_error u n0) with (nth_error u n0) in *.
+          eapply nth_error_forall in Hu. 2:eauto. 
+          change (nth_error u n') with (nth_error u n') in *.
           rewrite -> hnth. simpl. apply Hu.
       + now apply not_var_global_levels in Hl.
   Qed.
diff --git a/pcuic/theories/Syntax/PCUICCases.v b/pcuic/theories/Syntax/PCUICCases.v
index 8f9ffb898..35a40f355 100644
--- a/pcuic/theories/Syntax/PCUICCases.v
+++ b/pcuic/theories/Syntax/PCUICCases.v
@@ -209,10 +209,10 @@ Definition wf_predicateb mdecl idecl (p : predicate term) : bool :=
   && forallb2 (fun na decl => eqb_binder_annot na decl.(decl_name))
     (forget_types p.(pcontext)) (decl :: idecl.(ind_indices)).
 
-Lemma wf_predicateP mdecl idecl p : reflect (wf_predicate mdecl idecl p) (wf_predicateb mdecl idecl p).
+Lemma wf_predicateP mdecl idecl p : reflectProp (wf_predicate mdecl idecl p) (wf_predicateb mdecl idecl p).
 Proof.
   rewrite /wf_predicate /wf_predicate_gen /wf_predicateb.
-  case: Reflect.eqb_spec => eqpars /= //.
+  case: ReflectEq.eqb_spec => eqpars /= //.
   * case: (forallb2P _ _ (forget_types (pcontext p)) (idecl_binder idecl :: ind_indices idecl)
       (fun na decl => eqb_annot_reflect na decl.(decl_name))); constructor => //.
     intros [_ Hi]; contradiction.
diff --git a/pcuic/theories/Syntax/PCUICReflect.v b/pcuic/theories/Syntax/PCUICReflect.v
index e48db61d4..5ae4a841f 100644
--- a/pcuic/theories/Syntax/PCUICReflect.v
+++ b/pcuic/theories/Syntax/PCUICReflect.v
@@ -31,9 +31,9 @@ Local Ltac term_dec_tac term_dec :=
            fcase (eq_dec x y)
          | x : list aname, y : list aname |- _ => fcase (eq_dec x y)
          | n : nat, m : nat |- _ => fcase (Nat.eq_dec n m)
-         | i : ident, i' : ident |- _ => fcase (string_dec i i')
-         | i : kername, i' : kername |- _ => fcase (kername_eq_dec i i')
-         | i : string, i' : kername |- _ => fcase (string_dec i i')
+         | i : ident, i' : ident |- _ => fcase (eq_dec i i')
+         | i : kername, i' : kername |- _ => fcase (eq_dec i i')
+         | i : string, i' : kername |- _ => fcase (eq_dec i i')
          | n : name, n' : name |- _ => fcase (eq_dec n n')
          | n : aname, n' : aname |- _ => fcase (eq_dec n n')
          | i : prim_val, j : prim_val |- _ => fcase (eq_dec i j)
diff --git a/pcuic/theories/Typing/PCUICWeakeningEnvTyp.v b/pcuic/theories/Typing/PCUICWeakeningEnvTyp.v
index 02ce3229f..0eb7555fd 100644
--- a/pcuic/theories/Typing/PCUICWeakeningEnvTyp.v
+++ b/pcuic/theories/Typing/PCUICWeakeningEnvTyp.v
@@ -365,7 +365,7 @@ Proof.
     destruct Hext as [univs' [Σ'' HΣ'']]. split; eauto.
     exists (Σ'' ++ [(kn, d)]). now rewrite <- app_assoc.
   }
-  unfold eq_kername; destruct kername_eq_dec; subst.
+  case: eqb_specT; intro eq; subst.
   - intros [= ->]. subst.
     clear Hext; eapply weakening_on_global_decl_ext. 3:tea. all:eauto.
   - apply IHonΣ; auto.
@@ -386,7 +386,7 @@ Proof.
     destruct Hext as [univs' [Σ'' HΣ'']]. split; eauto.
     exists (Σ'' ++ [(kn, d)]). now rewrite <- app_assoc.
   }
-  unfold eq_kername; destruct kername_eq_dec; subst.
+  case: eqb_specT; intro e; subst.
   - intros [= ->]. subst.
     clear Hext; eapply weakening_on_global_decl. 5:tea. all:eauto.
     destruct wfΣ. split => //. now depelim o2.
diff --git a/pcuic/theories/utils/PCUICAstUtils.v b/pcuic/theories/utils/PCUICAstUtils.v
index 71ed8ba2c..2b57706de 100644
--- a/pcuic/theories/utils/PCUICAstUtils.v
+++ b/pcuic/theories/utils/PCUICAstUtils.v
@@ -92,7 +92,7 @@ Lemma lookup_env_cons {kn d Σ kn' d'} : lookup_global ((kn, d) :: Σ) kn' = Som
   (kn = kn' /\ d = d') \/ (kn <> kn' /\ lookup_global Σ kn' = Some d').
 Proof.
   simpl.
-  epose proof (Reflect.eqb_spec (A:=kername) kn' kn). simpl in H.
+  epose proof (ReflectEq.eqb_spec (A:=kername) kn' kn). simpl in H.
   elim: H. intros -> [= <-]; intuition auto.
   intros diff look. intuition auto.
 Qed.
@@ -102,7 +102,7 @@ Lemma lookup_env_cons_fresh {kn d Σ kn'} :
   lookup_global ((kn, d) :: Σ) kn' = lookup_global Σ kn'.
 Proof.
   simpl.
-  epose proof (Reflect.eqb_spec (A:=kername) kn' kn). simpl in H.
+  epose proof (ReflectEq.eqb_spec (A:=kername) kn' kn). simpl in H.
   elim: H. intros -> => //. auto.
 Qed.
 
diff --git a/pcuic/theories/utils/PCUICPretty.v b/pcuic/theories/utils/PCUICPretty.v
index 5791a9c4b..d98f3da56 100644
--- a/pcuic/theories/utils/PCUICPretty.v
+++ b/pcuic/theories/utils/PCUICPretty.v
@@ -18,7 +18,7 @@ Section lookups.
     end.
 End lookups.
 
-Section print_term.
+Section fresh.
   Context (Σ : global_env_ext).
 
   Fixpoint decompose_lam (t : term) (n : nat) : (list aname) * (list term) * term :=
@@ -34,7 +34,7 @@ Section print_term.
     end.
 
   Definition is_fresh (Γ : list ident) (id : ident) :=
-    List.forallb (fun id' => negb (ident_eq id id')) Γ.
+    List.forallb (fun id' => negb (eqb id id')) Γ.
 
   Fixpoint name_from_term (t : term) :=
     match t with
@@ -47,7 +47,7 @@ Section print_term.
     | tConst c u => "x"
     | tInd (mkInd i k) u =>
       match lookup_ind_decl Σ i k with
-      | Some (_, body) => substring 0 1 (body.(ind_name))
+      | Some (_, body) => String.substring 0 1 (body.(ind_name))
       | None => "X"
       end
     | _ => "U"
@@ -109,201 +109,232 @@ Section print_term.
                             Γ
         end in
     aux Γ (MCList.rev Γ').
+End fresh.
 
-  Section Aux.
-    Context (print_term : list ident -> bool -> bool -> term -> string).
-    Definition print_defs Γ (defs : mfixpoint term) :=
-      let ctx' := fix_context defs in
-      print_list (print_def (print_term Γ true false) (print_term (fresh_names Γ ctx') true false))
-            (nl ^ " with ") defs.
+Module PrintTermTree.
+  Section env.
+    Context (Σ : global_env_ext).
+    Import bytestring.Tree.
+    Infix "^" := append.
 
-    Definition pr_context_decl Γ (c : context_decl) : ident * string :=
-      match c with
-      | {| decl_name := na; decl_type := ty; decl_body := None |} => 
-        let na' := (fresh_name Γ na.(binder_name) (Some ty)) in
-        (na', ("(" ++ na' ++ " : " ++ print_term Γ true false ty ++ ")")%string)
-      | {| decl_name := na; decl_type := ty; decl_body := Some b |} =>
-        let na' := (fresh_name Γ na.(binder_name) (Some ty)) in
-        (na', ("(" ++ na' ++ " : " ++ print_term Γ true false ty ++ " := " ++
-          print_term Γ true false b ++ ")")%string)
-      end.
-    
-    Fixpoint print_context_gen Γ Δ :=
-      match Δ with
-      | [] => (Γ, ""%string)
-      | d :: decls => 
-        let '(Γ, s) := print_context_gen Γ decls in
-        let '(na, s') := pr_context_decl Γ d in
-        match decls with
-        | [] => (na :: Γ, (s ++ s')%string)
-        | _ => (na :: Γ, (s ++ " " ++ s')%string)
-        end
-      end.
-          
-    Fixpoint print_context_names Γ Δ :=
-      match Δ with
-      | [] => (Γ, ""%string)
-      | d :: decls => 
-        let '(Γ, s) := print_context_names Γ decls in
-        let na := (fresh_name Γ d.(decl_name).(binder_name) (Some d.(decl_type))) in
-        match decls with
-        | [] => (na :: Γ, (s ++ na)%string)
-        | _ => (na :: Γ, (s ++ " " ++ na)%string)
-        end
-      end.
+    Section Aux.
+      Context (print_term : list ident -> bool -> bool -> term -> t).
 
-  End Aux.
+      Definition print_def {A} (f : A -> t) (g : A -> t) (def : def A) :=
+        string_of_name (binder_name (dname def)) ^ " { struct " ^ string_of_nat (rarg def) ^ " }" ^
+                    " : " ^ f (dtype def) ^ " := " ^ nl ^ g (dbody def).
+
+      Definition print_defs Γ (defs : mfixpoint term) :=
+        let ctx' := fix_context defs in
+        print_list (print_def (print_term Γ true false) (print_term (fresh_names Σ Γ ctx') true false))
+              (nl ^ " with ") defs.
+
+      Definition pr_context_decl Γ (c : context_decl) : ident * t :=
+        match c with
+        | {| decl_name := na; decl_type := ty; decl_body := None |} => 
+          let na' := (fresh_name Σ Γ na.(binder_name) (Some ty)) in
+          (na', ("(" ^ na' ^ " : " ^ print_term Γ true false ty ^ ")")%bs)
+        | {| decl_name := na; decl_type := ty; decl_body := Some b |} =>
+          let na' := (fresh_name Σ Γ na.(binder_name) (Some ty)) in
+          (na', ("(" ^ na' ^ " : " ^ print_term Γ true false ty ^ " := " ^
+            print_term Γ true false b ^ ")")%bs)
+        end.
+      
+      Fixpoint print_context_gen Γ Δ :=
+        match Δ with
+        | [] => (Γ, "" : t)
+        | d :: decls => 
+          let '(Γ, s) := print_context_gen Γ decls in
+          let '(na, s') := pr_context_decl Γ d in
+          match decls with
+          | [] => (na :: Γ, s ^ s')
+          | _ => (na :: Γ, s ^ " " ^ s')
+          end
+        end.
+            
+      Fixpoint print_context_names Γ Δ :=
+        match Δ with
+        | [] => (Γ, "" : t)
+        | d :: decls => 
+          let '(Γ, s) := print_context_names Γ decls in
+          let na := (fresh_name Σ Γ d.(decl_name).(binder_name) (Some d.(decl_type))) in
+          match decls with
+          | [] => (na :: Γ, (s ^ na))
+          | _ => (na :: Γ, (s ^ " " ^ na))
+          end
+        end.
+
+    End Aux.
           
-  Context (all : bool).
+    Context (all : bool).
 
-  Fixpoint print_term (Γ : list ident) (top : bool)(inapp : bool) (t : term) {struct t} :=
-  match t with
-  | tRel n =>
-    match nth_error Γ n with
-    | Some id => id
-    | None => "UnboundRel(" ^ string_of_nat n ^ ")"
-    end
-  | tVar n => "Var(" ^ n ^ ")"
-  | tEvar ev args => "Evar(" ^ string_of_nat ev ^ "[]" (* TODO *)  ^ ")"
-  | tSort s => string_of_sort s
-  | tProd na dom codom =>
-    let na' := fresh_name Γ na.(binder_name) (Some dom) in
-    parens top
-           ("∀ " ^ na' ^ " : " ^
-                     print_term Γ true false dom ^ ", " ^ print_term (na':: Γ) true false codom)
-  | tLambda na dom body =>
-    let na' := fresh_name Γ na.(binder_name) (Some dom) in
-      parens top ("fun " ^ na' ^ " : " ^ print_term Γ true false dom
-                ^ " => " ^ print_term (na':: Γ) true false body)
-  | tLetIn na def dom body =>
-    let na' := fresh_name Γ na.(binder_name) (Some dom) in
-    parens top ("let" ^ na' ^ " : " ^ print_term Γ true false dom ^
-                      " := " ^ print_term Γ true false def ^ " in " ^ nl ^
-                      print_term (na' :: Γ) true false body)
-  | tApp f l =>
-    parens (top || inapp) (print_term Γ false true f ^ " " ^ print_term Γ false false l)
-  | tConst c u => string_of_kername c ^ print_universe_instance u
-  | tInd (mkInd i k) u =>
-    match lookup_ind_decl Σ i k with
-    | Some (_, oib) => oib.(ind_name) ^ print_universe_instance u
-    | None =>
-      "UnboundInd(" ^ string_of_inductive (mkInd i k) ^ "," ^ string_of_universe_instance u ^ ")"
-    end
-  | tConstruct (mkInd i k as ind) l u =>
-    match lookup_ind_decl Σ i k with
-    | Some (_, oib) =>
-      match nth_error oib.(ind_ctors) l with
-      | Some cdecl => cdecl.(cstr_name) ^ print_universe_instance u
+    Fixpoint print_term (Γ : list ident) (top : bool)(inapp : bool) (t : term) {struct t} : Tree.t :=
+    match t with
+    | tRel n =>
+      match nth_error Γ n with
+      | Some id => id
+      | None => "UnboundRel(" ^ string_of_nat n ^ ")"
+      end
+    | tVar n => "Var(" ^ n ^ ")"
+    | tEvar ev args => "Evar(" ^ string_of_nat ev ^ "[]" (* TODO *)  ^ ")"
+    | tSort s => string_of_sort s
+    | tProd na dom codom =>
+      let na' := fresh_name Σ Γ na.(binder_name) (Some dom) in
+      parens top
+            ("∀ " ^ na' ^ " : " ^
+                      print_term Γ true false dom ^ ", " ^ print_term (na':: Γ) true false codom)
+    | tLambda na dom body =>
+      let na' := fresh_name Σ Γ na.(binder_name) (Some dom) in
+        parens top ("fun " ^ na' ^ " : " ^ print_term Γ true false dom
+                  ^ " => " ^ print_term (na':: Γ) true false body)
+    | tLetIn na def dom body =>
+      let na' := fresh_name Σ Γ na.(binder_name) (Some dom) in
+      parens top ("let" ^ na' ^ " : " ^ print_term Γ true false dom ^
+                        " := " ^ print_term Γ true false def ^ " in " ^ nl ^
+                        print_term (na' :: Γ) true false body)
+    | tApp f l =>
+      parens (top || inapp) (print_term Γ false true f ^ " " ^ print_term Γ false false l)
+    | tConst c u => string_of_kername c ^ print_universe_instance u
+    | tInd (mkInd i k) u =>
+      match lookup_ind_decl Σ i k with
+      | Some (_, oib) => oib.(ind_name) ^ print_universe_instance u
+      | None =>
+        "UnboundInd(" ^ string_of_inductive (mkInd i k) ^ "," ^ string_of_universe_instance u ^ ")"
+      end
+    | tConstruct (mkInd i k as ind) l u =>
+      match lookup_ind_decl Σ i k with
+      | Some (_, oib) =>
+        match nth_error oib.(ind_ctors) l with
+        | Some cdecl => cdecl.(cstr_name) ^ print_universe_instance u
+        | None =>
+          "UnboundConstruct(" ^ string_of_inductive ind ^ "," ^ string_of_nat l ^ ","
+                              ^ string_of_universe_instance u ^ ")"
+        end
       | None =>
         "UnboundConstruct(" ^ string_of_inductive ind ^ "," ^ string_of_nat l ^ ","
                             ^ string_of_universe_instance u ^ ")"
       end
-    | None =>
-      "UnboundConstruct(" ^ string_of_inductive ind ^ "," ^ string_of_nat l ^ ","
-                          ^ string_of_universe_instance u ^ ")"
-    end
-  | tCase {| ci_ind := mkInd mind i as ind; ci_npar := pars |} p t brs =>
-    match lookup_ind_decl Σ mind i with
-    | Some (_, oib) =>
-      let Γret := p.(pcontext) in
-      let Γret := fresh_names Γ Γret in
-      let ret_binders := firstn #|pcontext p| Γret in
-      let (as_name, indices) := (hd "_" ret_binders, MCList.rev (tail ret_binders)) in
-      let in_args := repeat "_" #|pparams p| ++ indices in
-      let in_str := oib.(ind_name) ^ String.concat "" (map (fun a => " " ^ a) in_args) in
+    | tCase {| ci_ind := mkInd mind i as ind; ci_npar := pars |} p t brs =>
+      match lookup_ind_decl Σ mind i with
+      | Some (_, oib) =>
+        let Γret := p.(pcontext) in
+        let Γret := fresh_names Σ Γ Γret in
+        let ret_binders := firstn #|pcontext p| Γret in
+        let (as_name, indices) := (hd "_" ret_binders, MCList.rev (tail ret_binders)) in
+        let in_args := (repeat "_" #|pparams p| ++ indices)%list in
+        let in_str := oib.(ind_name) ^ concat "" (map (fun a : String.t => " " ^ a) in_args) in
 
-      let brs := map (fun br => 
-          let (Γctx, pctx) := 
-            if all then print_context_gen print_term Γ br.(bcontext) 
-            else print_context_names Γ br.(bcontext)
-          in
-          pctx ^ " ⇒ " ^ print_term Γctx true false br.(bbody)) brs in
-      let brs := combine brs oib.(ind_ctors) in
-                            
-      parens top ("match " ^ print_term Γ true false t ^
-                  " as " ^ as_name ^
-                  " in " ^ in_str ^
-                  " return " ^ print_term Γret true false (preturn p) ^
-                  " with " ^ nl ^
-                  print_list (fun '(b, cdecl) => cdecl.(cstr_name) ^ " " ^ b)
-                  (nl ^ " | ") brs ^ nl ^ "end" ^ nl)
-  | None =>
-    "Case(" ^ string_of_inductive ind ^ "," ^ string_of_nat i ^ "," ^ string_of_term t ^ ","
-            ^ string_of_predicate string_of_term p ^ "," ^ 
-            string_of_list (pretty_string_of_branch string_of_term) brs ^ ")"
-    end
-  | tProj (mkInd mind i as ind, pars, k) c =>
-    match lookup_ind_decl Σ mind i with
-    | Some (_, oib) =>
-      match nth_error oib.(ind_projs) k with
-      | Some (na, _) => print_term Γ false false c ^ ".(" ^ na ^ ")"
+        let brs := map (fun br => 
+            let (Γctx, pctx) := 
+              if all then print_context_gen print_term Γ br.(bcontext) 
+              else print_context_names Γ br.(bcontext)
+            in
+            pctx ^ " ⇒ " ^ print_term Γctx true false br.(bbody)) brs in
+        let brs := combine brs oib.(ind_ctors) in
+                              
+        parens top ("match " ^ print_term Γ true false t ^
+                    " as " ^ as_name ^
+                    " in " ^ in_str ^
+                    " return " ^ print_term Γret true false (preturn p) ^
+                    " with " ^ nl ^
+                    print_list (fun '(b, cdecl) => cdecl.(cstr_name) ^ " " ^ b)
+                    (nl ^ " | ") brs ^ nl ^ "end" ^ nl)
+    | None =>
+      "Case(" ^ string_of_inductive ind ^ "," ^ string_of_nat i ^ "," ^ string_of_term t ^ ","
+              ^ string_of_predicate string_of_term p ^ "," ^ 
+              string_of_list (pretty_string_of_branch string_of_term) brs ^ ")"
+      end
+    | tProj (mkInd mind i as ind, pars, k) c =>
+      match lookup_ind_decl Σ mind i with
+      | Some (_, oib) =>
+        match nth_error oib.(ind_projs) k with
+        | Some (na, _) => print_term Γ false false c ^ ".(" ^ na ^ ")"
+        | None =>
+          "UnboundProj(" ^ string_of_inductive ind ^ "," ^ string_of_nat i ^ "," ^ string_of_nat k ^ ","
+                        ^ print_term Γ true false c ^ ")"
+        end
       | None =>
         "UnboundProj(" ^ string_of_inductive ind ^ "," ^ string_of_nat i ^ "," ^ string_of_nat k ^ ","
-                       ^ print_term Γ true false c ^ ")"
+                      ^ print_term Γ true false c ^ ")"
       end
-    | None =>
-      "UnboundProj(" ^ string_of_inductive ind ^ "," ^ string_of_nat i ^ "," ^ string_of_nat k ^ ","
-                     ^ print_term Γ true false c ^ ")"
-    end
 
 
-  | tFix l n =>
-    parens top ("let fix " ^ print_defs print_term Γ l ^ nl ^
-                          " in " ^ List.nth_default (string_of_nat n) (map (string_of_aname ∘ dname) l) n)
-  | tCoFix l n =>
-    parens top ("let cofix " ^ print_defs print_term Γ l ^ nl ^
-                              " in " ^ List.nth_default (string_of_nat n) (map (string_of_aname ∘ dname) l) n)
-  (* | tPrim i => parens top (string_of_prim (print_term Γ true false) i) *)
-  end.
+    | tFix l n =>
+      parens top ("let fix " ^ print_defs print_term Γ l ^ nl ^
+                            " in " ^ List.nth_default (string_of_nat n) (map (string_of_aname ∘ dname) l) n)
+    | tCoFix l n =>
+      parens top ("let cofix " ^ print_defs print_term Γ l ^ nl ^
+                                " in " ^ List.nth_default (string_of_nat n) (map (string_of_aname ∘ dname) l) n)
+    (* | tPrim i => parens top (string_of_prim (print_term Γ true false) i) *)
+    end.
+  End env.
 
-End print_term.
+  Import bytestring.Tree.
+  Infix "^" := append.
 
-Notation pr_term Σ Γ top := (print_term Σ true Γ top false).
+  Section env.
+    Context (Σ : global_env_ext).
+    Notation print_context := (print_context_gen Σ (print_term Σ true)).
+    Notation pr_term Γ top := (print_term Σ true Γ top false).
 
-Notation print_context Σ := (print_context_gen Σ (print_term Σ true)).
+    Definition print_one_cstr Γ (mib : mutual_inductive_body) (c : constructor_body) : t :=
+      let '(Γargs, s) := print_context Γ c.(cstr_args) in
+      c.(cstr_name) ^ " : " ^ s ^ "_" ^ print_list (pr_term Γargs true) " " c.(cstr_indices).
+    
+    Definition print_one_ind (short : bool) Γ (mib : mutual_inductive_body) (oib : one_inductive_body) : t :=
+      let '(Γpars, spars) := print_context Γ mib.(ind_params) in
+      let '(Γinds, sinds) := print_context Γpars oib.(ind_indices) in
+      oib.(ind_name) ^ spars ^ " : " ^ sinds ^ " " ^ pr_term Γinds true (tSort oib.(ind_sort)) ^ ":=" ^ nl ^
+      if short then "..."
+      else print_list (print_one_cstr Γpars mib) nl oib.(ind_ctors).
+  End env.
 
-Definition print_one_cstr Σ Γ (mib : mutual_inductive_body) (c : constructor_body) : string :=
-  let '(Γargs, s) := print_context Σ Γ c.(cstr_args) in
-  c.(cstr_name) ++ " : " ++ s ++ "_" ++ print_list (pr_term Σ Γargs true) " " c.(cstr_indices).
-  
-Definition print_one_ind (short : bool) Σ Γ (mib : mutual_inductive_body) (oib : one_inductive_body) : string :=
-  let '(Γpars, spars) := print_context Σ Γ mib.(ind_params) in
-  let '(Γinds, sinds) := print_context Σ Γpars oib.(ind_indices) in
-  oib.(ind_name) ++ spars ++ sinds ++ pr_term Σ Γinds true (tSort oib.(ind_sort)) ++ ":=" ++ nl ++
-  if short then "..."
-  else print_list (print_one_cstr Σ Γpars mib) nl oib.(ind_ctors).
+  Fixpoint print_env_aux (short : bool) (prefix : nat) (Σ : global_env) (acc : t) : t := 
+    match prefix with 
+    | 0 => match Σ.(declarations) with [] => acc | _ => ("..." ^ nl ^ acc) end
+    | S n => 
+      let univs := Σ.(universes) in
+      match Σ.(declarations) with
+      | [] => acc
+      | (kn, InductiveDecl mib) :: Σ => 
+        let Σ' := ({| universes := univs; declarations := Σ |}, mib.(ind_universes)) in
+        let names := fresh_names Σ' [] (arities_context mib.(ind_bodies)) in
+        print_env_aux short n Σ'.1
+          ("Inductive " ^ 
+          print_list (print_one_ind Σ' short names mib) nl mib.(ind_bodies) ^ "." ^ 
+          nl ^ acc)
+      | (kn, ConstantDecl cb) :: Σ =>
+        let Σ' := ({| universes := univs; declarations := Σ |}, cb.(cst_universes)) in
+        print_env_aux short n Σ'.1
+          ((match cb.(cst_body) with 
+            | Some _ => "Definition "
+            | None => "Axiom "
+          end) ^ string_of_kername kn ^ " : " ^ print_term Σ' true nil true false cb.(cst_type) ^
+          match cb.(cst_body) with
+          | Some b => 
+            if short then ("..." ^ nl)
+            else (" := " ^ nl ^ print_term Σ' true nil true false b ^ "." ^ nl)
+          | None => "."
+          end ^ acc)
+      end
+    end.
+
+  Definition print_env (short : bool) (prefix : nat) Σ := 
+    print_env_aux short prefix Σ (Tree.string "").
 
-Fixpoint print_env_aux (short : bool) (prefix : nat) univs (Σ : global_declarations) (acc : string) := 
-  match prefix with 
-  | 0 => match Σ with [] => acc | _ => ("..." ++ nl ++ acc)%string end
-  | S n => 
-  match Σ with
-  | [] => acc
-  | (kn, InductiveDecl mib) :: Σ => 
-    let Σ' := ({| universes := univs; declarations := Σ |}, mib.(ind_universes)) in
-    let names := fresh_names Σ' [] (arities_context mib.(ind_bodies)) in
-    print_env_aux short n univs Σ
-      ("Inductive " ++ 
-       print_list (print_one_ind short Σ' names mib) nl mib.(ind_bodies) ++ "." ++ 
-       nl ++ acc)%string
-  | (kn, ConstantDecl cb) :: Σ =>
-    let Σ' := ({| universes := univs; declarations := Σ |}, cb.(cst_universes)) in
-    print_env_aux short n univs Σ
-      ((match cb.(cst_body) with 
-        | Some _ => "Definition "
-        | None => "Axiom "
-      end) ++ string_of_kername kn ++ " : " ++ pr_term Σ' nil true cb.(cst_type) ++
-      match cb.(cst_body) with
-      | Some b => 
-        if short then ("..." ++ nl)%string
-        else (" := " ++ nl ++ pr_term Σ' nil true b ++ "." ++ nl)
-      | None => "."
-      end ++ acc)%string
-  end
-  end.
+  Definition print_program (short : bool) (prefix : nat) (p : program) : t := 
+    print_env short prefix (fst p) ^ nl ^ print_term (empty_ext (fst p)) true nil true false (snd p). 
 
-Definition print_env (short : bool) (prefix : nat) Σ := print_env_aux short prefix Σ.(universes) Σ.(declarations) EmptyString.
+End PrintTermTree.  
 
+Definition print_term Σ all Γ top inapp t := 
+  Tree.to_string (PrintTermTree.print_term Σ all Γ top inapp t).
+
+Definition print_context Σ Γ Δ : string := 
+  Tree.to_string (PrintTermTree.print_context_gen Σ (PrintTermTree.print_term Σ true) Γ Δ).2.
+
+Definition print_env (short : bool) (prefix : nat) Σ := 
+  Tree.to_string (PrintTermTree.print_env short prefix Σ).
+  
 Definition print_program (short : bool) (prefix : nat) (p : program) : string := 
-  print_env short prefix (fst p) ++ nl ++
-  pr_term (empty_ext (fst p)) nil true (snd p). 
+  Tree.to_string (PrintTermTree.print_program short prefix p).
\ No newline at end of file
diff --git a/safechecker/_PluginProject.in b/safechecker/_PluginProject.in
index bf97d347d..1ca874069 100644
--- a/safechecker/_PluginProject.in
+++ b/safechecker/_PluginProject.in
@@ -9,10 +9,6 @@ src/META.coq-metacoq-safechecker
 # From Coq's stdlib
 src/eqdepFacts.mli
 src/eqdepFacts.ml
-src/orderedTypeAlt.mli
-src/orderedTypeAlt.ml
-src/orderedType0.mli
-src/orderedType0.ml
 
 # From template
 src/ssrbool.ml
@@ -83,12 +79,6 @@ src/pCUICPretty.ml
 # src/string2pos.ml
 # src/canonicalTries.mli
 # src/canonicalTries.ml
-src/kernames.mli
-src/kernames.ml
-src/fMapList.mli
-src/fMapList.ml
-src/fMapAVL.mli
-src/fMapAVL.ml
 src/pCUICErrors.mli
 src/pCUICErrors.ml
 src/pCUICWfEnv.mli
diff --git a/safechecker/src/g_metacoq_safechecker.mlg b/safechecker/src/g_metacoq_safechecker.mlg
index 4e99b2958..9ddb8aec0 100644
--- a/safechecker/src/g_metacoq_safechecker.mlg
+++ b/safechecker/src/g_metacoq_safechecker.mlg
@@ -9,25 +9,17 @@ open PeanoNat.Nat
 open Datatypes
 open PCUICSafeChecker
 open Tm_util
+open Caml_bytestring
 
-let bytes_of_list l =
-  let bytes = Bytes.create (List.length l) in
-  let rec fill acc = function
-    | [] -> bytes
-    | c :: cs ->
-      Bytes.set bytes acc c;
-      fill (1 + acc) cs
-  in fill 0 l
-
-let pr_char_list l =
+let pr_string l =
   (* We allow utf8 encoding *)
-  str (Bytes.to_string (bytes_of_list l))
+  str (caml_string_of_bytestring l)
 
 let check env evm poly (c, ustate) =
   debug (fun () -> str"Quoting");
   let uctx = Evd.universe_context_set evm in
   let env = if poly then env else Environ.push_context_set ~strict:true uctx env in
-  let prog = time (str"Quoting") (Ast_quoter.quote_term_rec true env) (EConstr.to_constr evm c) in
+  let prog = time (str"Quoting") (Ast_quoter.quote_term_rec ~bypass:true ~with_universes:true env) (EConstr.to_constr evm c) in
   let uctx =
     if poly then
       let uctx = Evd.to_universe_context evm in
@@ -44,8 +36,8 @@ let check env evm poly (c, ustate) =
       uctx
   in
   match check with
-  | Coq_inl s -> Feedback.msg_info (pr_char_list s)
-  | Coq_inr s -> CErrors.user_err (pr_char_list s)
+  | Coq_inl s -> Feedback.msg_info (pr_string s)
+  | Coq_inr s -> CErrors.user_err (pr_string s)
 }
 
 VERNAC COMMAND EXTEND MetaCoqSafeCheck CLASSIFIED AS QUERY
diff --git a/safechecker/src/metacoq_safechecker_plugin.mlpack b/safechecker/src/metacoq_safechecker_plugin.mlpack
index e51f0c2b8..963e90883 100644
--- a/safechecker/src/metacoq_safechecker_plugin.mlpack
+++ b/safechecker/src/metacoq_safechecker_plugin.mlpack
@@ -2,11 +2,6 @@ Int0
 MSetAVL
 EqdepFacts
 Utils
-OrderedTypeAlt
-OrderedType0
-Kernames
-FMapList
-FMapAVL
 Ssrbool
 WGraph
 UGraph0
diff --git a/safechecker/theories/Extraction.v b/safechecker/theories/Extraction.v
index 18143f3eb..08a7d41ab 100644
--- a/safechecker/theories/Extraction.v
+++ b/safechecker/theories/Extraction.v
@@ -1,5 +1,5 @@
 (* Distributed under the terms of the MIT license. *)
-From Coq Require Import OrdersTac Ascii ExtrOcamlBasic ExtrOcamlString ExtrOcamlZInt ExtrOCamlInt63 ExtrOCamlFloats.
+From Coq Require Import OrdersTac Ascii ExtrOcamlBasic ExtrOcamlZInt ExtrOCamlInt63 ExtrOCamlFloats.
 From MetaCoq.Template Require Import utils MC_ExtrOCamlZPosInt.
 From MetaCoq.SafeChecker Require Import PCUICSafeChecker PCUICSafeConversion
      SafeTemplateChecker.
@@ -12,11 +12,6 @@ From MetaCoq.SafeChecker Require Import PCUICSafeChecker PCUICSafeConversion
 
 (** Here we could extract uint63_from/to_model to the identity *)
 
-Extract Constant ascii_compare =>
- "fun x y -> match Char.compare x y with 0 -> Eq | x when x < 0 -> Lt | _ -> Gt".
-Extract Constant Ascii.compare =>
- "fun x y -> match Char.compare x y with 0 -> Eq | x when x < 0 -> Lt | _ -> Gt".
-
 Extraction Blacklist Classes config uGraph Universes Ast String List Nat Int Init
            UnivSubst Typing Checker Retyping OrderedType Logic Common Equality Classes
            Uint63.
diff --git a/safechecker/theories/PCUICConsistency.v b/safechecker/theories/PCUICConsistency.v
index aa5049b5d..7f1610d43 100644
--- a/safechecker/theories/PCUICConsistency.v
+++ b/safechecker/theories/PCUICConsistency.v
@@ -6,7 +6,6 @@
    provided term to build an inhabitant and then canonicity to show
    that this is a contradiction. *)
 
-From Coq Require Import Ascii String.
 From Equations Require Import Equations.
 From MetaCoq.PCUIC Require Import PCUICAst.
 From MetaCoq.PCUIC Require Import PCUICAstUtils.
@@ -31,7 +30,7 @@ Local Opaque hnf.
 Fixpoint string_repeat c (n : nat) : string :=
   match n with
   | 0 => ""
-  | S n => String c (string_repeat c n)
+  | S n => String.String c (string_repeat c n)
   end.
 
 Lemma string_repeat_length c n :
@@ -55,7 +54,7 @@ Proof.
 Qed.
 
 Definition make_fresh_name (Σ : global_env) : kername :=
-  (MPfile [], string_repeat "a"%char (S (max_name_length Σ.(declarations)))).
+  (MPfile [], string_repeat "a"%byte (S (max_name_length Σ.(declarations)))).
 
 Lemma make_fresh_name_fresh Σ :
   fresh_global (make_fresh_name Σ) Σ.(declarations).
diff --git a/safechecker/theories/PCUICEqualityDec.v b/safechecker/theories/PCUICEqualityDec.v
index d2cd61e52..5ec87174f 100644
--- a/safechecker/theories/PCUICEqualityDec.v
+++ b/safechecker/theories/PCUICEqualityDec.v
@@ -168,7 +168,7 @@ Notation eqb_term_upto_univ eq leq gen_compare_global_instance :=
 Ltac eqspec :=
   lazymatch goal with
   | |- context [ eqb ?u ?v ] =>
-    destruct (eqb_spec u v) ; nodec ; subst
+    destruct (eqb_specT u v) ; nodec ; subst
   end.
 
 Ltac eqspecs :=
@@ -307,7 +307,7 @@ Proof.
       now constructor.
 Qed.
 
-Definition eqb_univ_reflect : forall u u' : Universe.t, reflect (u = u') (eqb u u').
+Definition eqb_univ_reflect : forall u u' : Universe.t, reflectProp (u = u') (eqb u u').
 Proof.
   intros u u'.
   destruct (eqb_spec u u'); constructor; auto.
@@ -333,16 +333,16 @@ Proof.
     destruct X; cbn ; subst.
     all: destruct (eqb_annot_reflect na na') => /= //.
     2: apply/andb_and; split.
-    all: apply eq_dec_to_bool_refl.
+    all: eapply eqb_refl.
   - intros hcc'.
     eapply forallb2_bcompare_decl_All2_fold in hcc'; tea.
     eapply All2_fold_impl in hcc'; tea; simpl; intuition eauto.
     move: H.
     destruct d as [na [bod|] ty], d' as [na' [bod'|] ty']; cbn in * => //.
+    + destruct (eqb_annot_reflect na na') => // /=.
+      repeat case: eqb_specT => //; intros; subst; cbn; auto; constructor; auto.
     + destruct (eqb_annot_reflect na na') => //.
-      unfold eq_dec_to_bool. repeat destruct eq_dec => //; subst; cbn; auto; constructor; auto.
-    + destruct (eqb_annot_reflect na na') => //.
-      unfold eq_dec_to_bool. repeat destruct eq_dec => //; subst; cbn; auto; constructor; auto.
+      repeat case: eqb_specT => //; intros; subst; cbn; auto; constructor; auto.
 Qed.
 
 Lemma forallb_true {A : Type} (l : list A) : forallb xpredT l.
@@ -586,7 +586,7 @@ Proof.
         intros H; now inv H.
       * constructor. intros H; now inv H.
   - cbn - [eqb].
-    destruct (eqb_spec s k) ; nodec. subst.
+    destruct (eqb_specT s k) ; nodec. subst.
     induction u in ui, ht, ht' |- *.
     + destruct ui.
       * constructor. constructor. constructor.
diff --git a/safechecker/theories/PCUICErrors.v b/safechecker/theories/PCUICErrors.v
index 9b0706181..a4b3b95e3 100644
--- a/safechecker/theories/PCUICErrors.v
+++ b/safechecker/theories/PCUICErrors.v
@@ -309,11 +309,11 @@ Definition string_of_type_error Σ (e : type_error) : string :=
       print_term Σ Γ t' ^ nl ^ "and:" ^ nl ^ print_term Σ Γ u' ^
       nl ^ "error:" ^ nl ^ string_of_conv_error Σ e ^
       (* nl ^ "in universe graph:" ^ nl ^ print_universes_graph G ^ nl ^ *)
-      " and context: " ^ nl ^ snd (print_context Σ [] Γ)
+      " and context: " ^ nl ^ print_context Σ [] Γ
   | NotConvertible Γ t u => "Terms are not convertible:" ^ nl ^
       print_term Σ Γ t ^ nl ^ "and:" ^ nl ^ print_term Σ Γ u ^
       (* nl ^ "in universe graph:" ^ nl ^ print_universes_graph G ^ nl ^ *)
-      " and context: " ^ nl ^ snd (print_context Σ [] Γ)
+      " and context: " ^ nl ^ print_context Σ [] Γ
   | NotASort t => "Not a sort: " ^ print_term Σ [] t
   | NotAProduct t t' => "Not a product" ^ print_term Σ [] t ^ nl ^
     "(after reducing to " ^ print_term Σ [] t'
diff --git a/safechecker/theories/PCUICSafeChecker.v b/safechecker/theories/PCUICSafeChecker.v
index e903dafef..fc37abd99 100644
--- a/safechecker/theories/PCUICSafeChecker.v
+++ b/safechecker/theories/PCUICSafeChecker.v
@@ -867,8 +867,8 @@ Section CheckEnv.
       rename Heq_anonymous2 into dc. *)
       symmetry in Heq_anonymous0.
       eapply decompose_prod_n_assum_inv in Heq_anonymous0; simpl in Heq_anonymous0; subst.
-      destruct (eqb_spec params (ind_params mdecl)) => //. subst params.
-      destruct (eqb_spec args (cstr_args cdecl)) => //. subst args.
+      destruct (eqb_specT params (ind_params mdecl)) => //. subst params.
+      destruct (eqb_specT args (cstr_args cdecl)) => //. subst args.
       eapply eqb_eq in eqarglen0.
       eapply eqb_eq in eqbindices.
       eapply eqb_eq in eqbpars.
@@ -1367,7 +1367,7 @@ Section CheckEnv.
         sq. rename Heq_anonymous into eqa.
         symmetry in eqa; eapply decompose_app_inv in eqa.
         subst t0.
-        move: eqhd; case: eqb_spec => // -> _.
+        move: eqhd; case: eqb_specT => // -> _.
         constructor.
         now eapply forallb_All in closedargs.
       Qed.
@@ -2103,7 +2103,7 @@ Section CheckEnv.
   Qed.
 
   Next Obligation.
-    destruct (eqb_spec params (ind_params mdecl)); [|discriminate]. subst params.
+    destruct (eqb_specT params (ind_params mdecl)); [|discriminate]. subst params.
     red. red.
     eapply nth_error_all in wfars; eauto; simpl in wfars.
     destruct wfars as [s Hs]. now exists s.
@@ -2399,12 +2399,11 @@ Section CheckEnv.
     let Σ := fst p in
     '(exist wfΣ eq) <- check_wf_ext (Σ, φ) ;;
     inft <- infer_term wfΣ (snd p) ;;
-    ret _.
+    ret (inft.π1; _).
   Next Obligation.
-    exists inft.
     assert (wfx : abstract_env_rel' x x) by reflexivity.
-    specialize_Σ wfx.
-    have [wfΣ] := (x.(wf_env_ext_wf)); sq. split; eauto.
+    have [wfΣ] := (x.(wf_env_ext_wf)).
+    cbn. specialize_Σ wfx. sq. split; eauto.
   Qed.
 
 End CheckEnv.
diff --git a/safechecker/theories/PCUICSafeConversion.v b/safechecker/theories/PCUICSafeConversion.v
index d648bde04..76fd15a54 100644
--- a/safechecker/theories/PCUICSafeConversion.v
+++ b/safechecker/theories/PCUICSafeConversion.v
@@ -2296,7 +2296,7 @@ Qed.
     apply All2_app. 1: assumption.
     constructor. 2: constructor.
     change (true = eqb u.(rarg) v.(rarg)) in eq1.
-    destruct (eqb_spec u.(rarg) v.(rarg)). 2: discriminate.
+    destruct (eqb_specT u.(rarg) v.(rarg)). 2: discriminate.
     symmetry in eqann.
     apply eqb_binder_annot_spec in eqann.
     split; auto.
@@ -2332,7 +2332,7 @@ Qed.
     constructor.
     2: eauto.
     change (true = eqb u.(rarg) v.(rarg)) in eq1.
-    destruct (eqb_spec u.(rarg) v.(rarg)). 2: discriminate.
+    destruct (eqb_specT u.(rarg) v.(rarg)). 2: discriminate.
     symmetry in eqann.
     apply eqb_binder_annot_spec in eqann.
     clear eq1.
@@ -2367,7 +2367,7 @@ Qed.
     specialize_Σ wfΣ.
     destruct H as [H]; inversion H; destruct X0 as [_ [eq_uv eqann]].
     change (?ru =? ?rv) with (eqb ru rv) in eq1.
-    destruct (eqb_spec (rarg u) (rarg v)) as [|neq_uv]; [discriminate|].
+    destruct (eqb_specT (rarg u) (rarg v)) as [|neq_uv]; [discriminate|].
     exact (neq_uv eq_uv).
   Qed.
 
@@ -3771,9 +3771,7 @@ Qed.
     eexists. eassumption.
   Qed.
   Next Obligation.
-    change (eq_dec_to_bool ci ci') with (eqb ci ci') in eq5.
-    destruct (eqb_spec ci ci'). 2: discriminate.
-    assumption.
+    now apply eqb_eq.
   Qed.
   Next Obligation.
     eapply R_positionR. all: simpl.
@@ -3782,9 +3780,7 @@ Qed.
     eapply positionR_poscat. constructor.
   Qed.
   Next Obligation.
-    change (eq_dec_to_bool ci ci') with (eqb ci ci') in eq5.
-    destruct (eqb_spec ci ci'). 2: discriminate.
-    assumption.
+    now apply eqb_eq.
   Qed.
   Next Obligation.
     unshelve eapply R_stateR.
@@ -3802,7 +3798,7 @@ Qed.
     sq.
     apply ws_cumul_pb_eq_le_gen.
     change (eq_dec_to_bool ci ci') with (eqb ci ci') in eq5.
-    destruct (eqb_spec ci ci'). 2: discriminate.
+    destruct (eqb_specT ci ci'). 2: discriminate.
     subst. eapply ws_cumul_pb_Case. all: tas.
     * clear aux eq2 eq4. eapply welltyped_zipc_zipp in h1; eauto.
       eapply welltyped_is_open_term in h1.
@@ -4536,7 +4532,7 @@ Qed.
     destruct convfix as [h1'].
     eapply conv_conv_cum_l.
     change (true = eqb idx idx') in eq4.
-    destruct (eqb_spec idx idx'). 2: discriminate.
+    destruct (eqb_specT idx idx'). 2: discriminate.
     subst.
     eapply ws_cumul_pb_Fix; eauto.
     - clear aux eee. eapply welltyped_zipc_zipp in h1; fvs.
@@ -4584,7 +4580,7 @@ Qed.
     destruct convfix as [h1'].
     eapply conv_conv_cum_l.
     change (true = eqb idx idx') in eq4.
-    destruct (eqb_spec idx idx'). 2: discriminate.
+    destruct (eqb_specT idx idx'). 2: discriminate.
     subst.
     eapply ws_cumul_pb_CoFix; eauto.
     - clear aux h1'. eapply welltyped_zipc_zipp in h1; fvs.
diff --git a/safechecker/theories/PCUICTypeChecker.v b/safechecker/theories/PCUICTypeChecker.v
index 58ace43ee..59ca06d6a 100644
--- a/safechecker/theories/PCUICTypeChecker.v
+++ b/safechecker/theories/PCUICTypeChecker.v
@@ -2202,7 +2202,7 @@ Section Typecheck.
     eapply declared_inductive_inj in isdecl as []; tea.
     subst.
     apply absurd.
-    now apply/eqb_spec.
+    now apply/eqb_specT.
   Qed.
 
   Next Obligation.
@@ -2250,7 +2250,7 @@ Section Typecheck.
     eapply infering_ind_ind in X0 as [? []].
     2-3: now auto.
     2: now econstructor ; tea ; apply closed_red_red.
-    now apply/eqb_spec.
+    now apply/eqb_specT.
   Qed.
 
   Next Obligation.
@@ -2308,20 +2308,20 @@ Section Typecheck.
     eapply infer_Proj with (pdecl := (i1, t)).
     - split. split. eassumption. cbn. rewrite hctors. reflexivity.
       split. symmetry; eassumption. cbn in *.
-      now apply beq_nat_true.
-    - cbn. destruct (ssrbool.elimT (eqb_spec ind I)); [assumption|].
+      now apply Nat.eqb_eq.
+    - cbn. destruct (ssrbool.elimT (eqb_specT ind I)); [assumption|].
       econstructor ; tea.
       now apply closed_red_red.
     - eapply type_reduction_closed in X2; eauto.
       2: now apply infering_typing.
       eapply validity in X2; eauto.
-      destruct (ssrbool.elimT (eqb_spec ind I)); auto.
+      destruct (ssrbool.elimT (eqb_specT ind I)); auto.
       unshelve eapply (PCUICInductives.isType_mkApps_Ind_inv _ decl _) in X2 as [parsubst [argsubst [sp sp' cu]]]; eauto.
-      pose proof (PCUICContextSubst.context_subst_length2 (PCUICSpine.inst_ctx_subst sp)).
-      pose proof (PCUICContextSubst.context_subst_length2 (PCUICSpine.inst_ctx_subst sp')).
-      autorewrite with len in H, H0.
+      pose proof (Hl := PCUICContextSubst.context_subst_length2 (PCUICSpine.inst_ctx_subst sp)).
+      pose proof (Hr := PCUICContextSubst.context_subst_length2 (PCUICSpine.inst_ctx_subst sp')).
+      autorewrite with len in Hl, Hr.
       destruct (on_declared_inductive decl) eqn:ond.
-      rewrite -o.(onNpars) -H.
+      rewrite -o.(onNpars) -Hl.
       forward (o0.(onProjections)).
       intros H'; rewrite H' nth_error_nil // in HH.
       destruct ind_ctors as [|cs []]; auto.
@@ -2329,7 +2329,7 @@ Section Typecheck.
       unshelve epose proof (onps.(on_projs_noidx _ _ _ _ _ _)).
       destruct (ind_indices idecl) => //.
       simpl in *.
-      rewrite List.skipn_length in H0.
+      rewrite List.skipn_length in e.
       rewrite List.firstn_length. lia.
     - destruct ind_projs => //. rewrite nth_error_nil in HH; congruence.
   Defined.
@@ -2350,7 +2350,7 @@ Section Typecheck.
     pose proof (heΣ _ wfΣ) as [heΣ].   
     cbn in *. specialize_Σ wfΣ ; sq. 
     apply absurd.
-    apply/eqb_spec.
+    apply/eqb_specT.
     cbn in *.
     sq.
     inversion X1.
diff --git a/template-coq/_CoqProject b/template-coq/_CoqProject
index 887d0440f..0444a18ec 100644
--- a/template-coq/_CoqProject
+++ b/template-coq/_CoqProject
@@ -7,6 +7,9 @@ theories/utils/canonicaltries/String2pos.v
 theories/utils/canonicaltries/CanonicalTries.v
 
 # utils
+theories/utils/ByteCompare.v
+theories/utils/ByteCompareSpec.v
+theories/utils/bytestring.v
 theories/utils/MCPrelude.v
 theories/utils/MCReflect.v
 theories/utils/All_Forall.v
@@ -23,9 +26,12 @@ theories/utils/MCSquash.v
 theories/utils/MCString.v
 theories/utils/wGraph.v
 theories/utils/MCUtils.v
+# theories/utils/ByteCompare.v
+# theories/utils/ByteCompareSpec.v
 #theories/utils/MC_ExtrOCamlInt63.v
 theories/utils/MC_ExtrOCamlNatInt.v
 theories/utils/MC_ExtrOCamlZPosInt.v
+theories/utils/ReflectEq.v
 
 # common
 theories/common/uGraph.v
@@ -33,6 +39,7 @@ theories/common/uGraph.v
 # Basic Ast files
 theories/utils.v
 theories/config.v
+theories/Kernames.v
 theories/Universes.v
 theories/BasicAst.v
 theories/Environment.v
@@ -40,7 +47,6 @@ theories/Ast.v
 theories/AstUtils.v
 theories/Reflect.v
 theories/ReflectAst.v
-theories/Kernames.v
 theories/EnvMap.v
 theories/Induction.v
 theories/EnvironmentTyping.v
diff --git a/template-coq/_PluginProject b/template-coq/_PluginProject
index bccc5ca02..8ec2dbe9d 100644
--- a/template-coq/_PluginProject
+++ b/template-coq/_PluginProject
@@ -15,6 +15,8 @@ gen-src/all_Forall.ml
 gen-src/all_Forall.mli
 gen-src/ascii.ml
 gen-src/ascii.mli
+gen-src/caml_nat.mli
+gen-src/caml_nat.ml
 gen-src/ast0.ml
 gen-src/ast0.mli
 gen-src/ast_denoter.ml
@@ -116,8 +118,10 @@ gen-src/mCReflect.mli
 gen-src/mCReflect.ml
 gen-src/primFloat.mli
 gen-src/primFloat.ml
-gen-src/decimalString.mli
-gen-src/decimalString.ml
+#gen-src/decimalString.mli
+#gen-src/decimalString.ml
+gen-src/reflectEq.mli
+gen-src/reflectEq.ml
 gen-src/mCString.ml
 gen-src/mCString.mli
 gen-src/mCUtils.ml
@@ -146,6 +150,20 @@ gen-src/orders.ml
 gen-src/orders.mli
 gen-src/ordersTac.ml
 gen-src/ordersTac.mli
+gen-src/orderedType0.mli
+gen-src/orderedType0.ml
+gen-src/orderedTypeAlt.mli
+gen-src/orderedTypeAlt.ml
+gen-src/decidableType.mli
+gen-src/decidableType.ml
+gen-src/fMapList.mli
+gen-src/fMapList.ml
+gen-src/fMapInterface.mli
+gen-src/fMapInterface.ml
+gen-src/fMapAVL.mli
+gen-src/fMapAVL.ml
+gen-src/fMapFacts.mli
+gen-src/fMapFacts.ml
 gen-src/peanoNat.ml
 gen-src/peanoNat.mli
 gen-src/plugin_core.ml
@@ -166,7 +184,22 @@ gen-src/specif.ml
 gen-src/specif.mli
 gen-src/string0.ml
 gen-src/string0.mli
+gen-src/byte0.mli
+gen-src/byte0.ml
+gen-src/byte.mli
+gen-src/byte.ml
+gen-src/caml_byte.mli
+gen-src/caml_byte.ml
+gen-src/byteCompare.mli
+gen-src/byteCompare.ml
+gen-src/byteCompareSpec.mli
+gen-src/byteCompareSpec.ml
+gen-src/bytestring.mli
+gen-src/bytestring.ml
+gen-src/caml_bytestring.ml
 gen-src/tm_util.ml
+gen-src/kernames.mli
+gen-src/kernames.ml
 gen-src/universes0.ml
 gen-src/universes0.mli
 
diff --git a/template-coq/gen-src/metacoq_template_plugin.mlpack b/template-coq/gen-src/metacoq_template_plugin.mlpack
index 646267f16..77effcede 100644
--- a/template-coq/gen-src/metacoq_template_plugin.mlpack
+++ b/template-coq/gen-src/metacoq_template_plugin.mlpack
@@ -5,6 +5,7 @@ Decimal
 Hexadecimal
 Numeral0
 Nat0
+Caml_nat
 List0
 PeanoNat
 Specif
@@ -15,15 +16,26 @@ BinNat
 BinInt
 PrimInt63
 Uint0
-Uint63
+Int63
+Byte
 Ascii
-Number
+Byte0
+Caml_byte
+ByteCompare
+ByteCompareSpec
 String0
 Orders
 OrdersTac
 OrdersFacts
 OrdersLists
+OrderedType0
+OrderedTypeAlt
 Int0
+FMapList
+FMapAVL
+DecidableType
+FMapInterface
+FMapFacts
 MSetInterface
 MSetFacts
 MSetDecide
@@ -47,6 +59,9 @@ MCRelations
 MCOption
 MCProd
 MCCompare
+ReflectEq
+Bytestring
+Caml_bytestring
 Monad_utils
 Sumbool
 Zeven
@@ -62,6 +77,7 @@ MCUtils
 Signature
 All_Forall
 Config0
+Kernames
 Universes0
 BasicAst
 Environment
diff --git a/template-coq/src/ast_denoter.ml b/template-coq/src/ast_denoter.ml
index 23ca64c8b..d51f6c9de 100644
--- a/template-coq/src/ast_denoter.ml
+++ b/template-coq/src/ast_denoter.ml
@@ -1,5 +1,6 @@
 open Names
 open Constr
+open Kernames
 open BasicAst
 open Ast0
 open Env
@@ -8,7 +9,7 @@ open Tm_util
 module BaseExtractionDenoter =
 struct
   type t = Ast0.term
-  type quoted_ident = char list
+  type quoted_ident = Bytestring.String.t
   type quoted_int = Datatypes.nat
   type quoted_int63 = Uint63.t
   type quoted_float64 = Float64.t
@@ -18,7 +19,7 @@ struct
   type quoted_relevance = relevance
   type quoted_sort = Universes0.Universe.t
   type quoted_cast_kind = cast_kind
-  type quoted_kernel_name = BasicAst.kername
+  type quoted_kernel_name = kername
   type quoted_inductive = inductive
   type quoted_proj = projection
   type quoted_global_reference = global_reference
@@ -124,8 +125,10 @@ struct
     (* | Coq_tInt i -> ACoq_tInt i *)
     (* | Coq_tFloat f -> ACoq_tFloat f *)
 
+  let unquote_string = Caml_bytestring.caml_string_of_bytestring
+
   let unquote_ident (qi: quoted_ident) : Id.t =
-    let s = list_to_string qi in
+    let s = unquote_string qi in
     Id.of_string s
 
   let unquote_relevance (r : relevance) : Sorts.relevance =
@@ -142,10 +145,7 @@ struct
     {Context.binder_name = unquote_name q.binder_name;
      Context.binder_relevance = unquote_relevance q.binder_relevance}
 
-  let rec unquote_int (q: quoted_int) : int = 
-    match q with
-    | Datatypes.O -> 0
-    | Datatypes.S x -> succ (unquote_int x)
+  let unquote_int (q: quoted_int) : int = Caml_nat.caml_int_of_nat q
   
   let unquote_evar env evm n l = 
     let id = Evar.unsafe_of_int (unquote_int n) in
@@ -192,7 +192,7 @@ struct
     match trm with
     | Universes0.Level.Coq_lzero -> Univ.Level.set
     | Universes0.Level.Level s ->
-      let s = list_to_string s in
+      let s = unquote_string s in
       let comps = CString.split_on_char '.' s in
       let last, dp = CList.sep_last comps in
       let dp = DirPath.make (List.map Id.of_string comps) in
@@ -212,7 +212,7 @@ struct
     | Universes0.Universe.Coq_lSProp -> evd, Sorts.sprop
     | Universes0.Universe.Coq_lProp -> evd, Sorts.prop
     | Universes0.Universe.Coq_lType u ->
-       (* let u = Universes0.Universe.t_set l in *)
+       let u = Universes0.Universe.t_set u in
        let ux_list = Universes0.UnivExprSet.elements u in
        let l = List.map unquote_level_expr ux_list in
        let u = List.fold_left Univ.Universe.sup (List.hd l) (List.tl l) in
@@ -222,7 +222,7 @@ struct
   = (evm,  Univ.Instance.of_array (Array.of_list (List0.map unquote_level l)))
 
 
-  let unquote_global_reference (trm : BasicAst.global_reference) : GlobRef.t =
+  let unquote_global_reference (trm : Kernames.global_reference) : GlobRef.t =
     let open GlobRef in
     match trm with
     | VarRef id -> VarRef (unquote_ident id)
diff --git a/template-coq/src/ast_quoter.ml b/template-coq/src/ast_quoter.ml
index 5812f6378..2ac1c1369 100644
--- a/template-coq/src/ast_quoter.ml
+++ b/template-coq/src/ast_quoter.ml
@@ -1,14 +1,16 @@
 open Names
 open Datatypes
+open Kernames
 open BasicAst
 open Ast0
 open Ast0.Env
 open Tm_util
+open Caml_bytestring
 
 module ExtractedASTBaseQuoter =
 struct
   type t = Ast0.term
-  type quoted_ident = char list
+  type quoted_ident = Bytestring.String.t
   type quoted_int = Datatypes.nat
   type quoted_int63 = Uint63.t
   type quoted_float64 = Float64.t
@@ -18,7 +20,7 @@ struct
   type quoted_relevance = BasicAst.relevance
   type quoted_sort = Universes0.Universe.t
   type quoted_cast_kind = cast_kind
-  type quoted_kernel_name = BasicAst.kername
+  type quoted_kernel_name = Kernames.kername
   type quoted_inductive = inductive
   type quoted_proj = projection
   type quoted_global_reference = global_reference
@@ -53,8 +55,8 @@ struct
   type quoted_global_env = global_env
   type quoted_program = program
 
-  let quote_ident id =
-    string_to_list (Id.to_string id)
+  let quote_string = bytestring_of_caml_string
+  let quote_ident id = quote_string (Id.to_string id)
 
   let quote_relevance = function
     | Sorts.Relevant -> BasicAst.Relevant
@@ -68,12 +70,7 @@ struct
     let {Context.binder_name = n; Context.binder_relevance = relevance} = ann_n in
     { BasicAst.binder_name = quote_name n; BasicAst.binder_relevance = quote_relevance relevance }
 
-  let quote_int i =
-    let rec aux acc i =
-      if i < 0 then acc
-      else aux (Datatypes.S acc) (i - 1)
-    in aux Datatypes.O (i - 1)
-
+  let quote_int = Caml_nat.nat_of_caml_int
   let quote_bool x = x
 
   let quote_int63 x = x
@@ -85,7 +82,7 @@ struct
     if Univ.Level.is_set l then Universes0.Level.Coq_lzero
     else match Univ.Level.var_index l with
          | Some x -> Universes0.Level.Var (quote_int x)
-         | None -> Universes0.Level.Level (string_to_list (Univ.Level.to_string l))
+         | None -> Universes0.Level.Level (quote_string (Univ.Level.to_string l))
 
   let quote_level (l : Univ.Level.t) : (Universes0.PropLevel.t, Universes0.Level.t) Datatypes.sum =
     try Coq_inr (quote_nonprop_level l)
@@ -120,18 +117,18 @@ struct
     | Constr.VMcast -> VmCast
 
 
-  let quote_dirpath (dp : DirPath.t) : BasicAst.dirpath =
+  let quote_dirpath (dp : DirPath.t) : Kernames.dirpath =
     let l = DirPath.repr dp in
     List.map quote_ident l
 
-  let rec quote_modpath (mp : ModPath.t) : BasicAst.modpath =
+  let rec quote_modpath (mp : ModPath.t) : Kernames.modpath =
     match mp with
     | MPfile dp -> MPfile (quote_dirpath dp)
     | MPbound mbid -> let (i, id, dp) = MBId.repr mbid in
       MPbound (quote_dirpath dp, quote_ident id, quote_int i)
     | MPdot (mp, id) -> MPdot (quote_modpath mp, quote_ident (Label.to_id id))
 
-  let quote_kn (kn : KerName.t) : BasicAst.kername =
+  let quote_kn (kn : KerName.t) : Kernames.kername =
     (quote_modpath (KerName.modpath kn),
      quote_ident (Label.to_id (KerName.label kn)))
 
diff --git a/template-coq/src/caml_byte.ml b/template-coq/src/caml_byte.ml
new file mode 100644
index 000000000..4f1f093ef
--- /dev/null
+++ b/template-coq/src/caml_byte.ml
@@ -0,0 +1,515 @@
+open Byte
+let char_of_byte = function
+| Coq_x00 -> '\000'
+| Coq_x01 -> '\001'
+| Coq_x02 -> '\002'
+| Coq_x03 -> '\003'
+| Coq_x04 -> '\004'
+| Coq_x05 -> '\005'
+| Coq_x06 -> '\006'
+| Coq_x07 -> '\007'
+| Coq_x08 -> '\008'
+| Coq_x09 -> '\009'
+| Coq_x0a -> '\010'
+| Coq_x0b -> '\011'
+| Coq_x0c -> '\012'
+| Coq_x0d -> '\013'
+| Coq_x0e -> '\014'
+| Coq_x0f -> '\015'
+| Coq_x10 -> '\016'
+| Coq_x11 -> '\017'
+| Coq_x12 -> '\018'
+| Coq_x13 -> '\019'
+| Coq_x14 -> '\020'
+| Coq_x15 -> '\021'
+| Coq_x16 -> '\022'
+| Coq_x17 -> '\023'
+| Coq_x18 -> '\024'
+| Coq_x19 -> '\025'
+| Coq_x1a -> '\026'
+| Coq_x1b -> '\027'
+| Coq_x1c -> '\028'
+| Coq_x1d -> '\029'
+| Coq_x1e -> '\030'
+| Coq_x1f -> '\031'
+| Coq_x20 -> '\032'
+| Coq_x21 -> '\033'
+| Coq_x22 -> '\034'
+| Coq_x23 -> '\035'
+| Coq_x24 -> '\036'
+| Coq_x25 -> '\037'
+| Coq_x26 -> '\038'
+| Coq_x27 -> '\039'
+| Coq_x28 -> '\040'
+| Coq_x29 -> '\041'
+| Coq_x2a -> '\042'
+| Coq_x2b -> '\043'
+| Coq_x2c -> '\044'
+| Coq_x2d -> '\045'
+| Coq_x2e -> '\046'
+| Coq_x2f -> '\047'
+| Coq_x30 -> '\048'
+| Coq_x31 -> '\049'
+| Coq_x32 -> '\050'
+| Coq_x33 -> '\051'
+| Coq_x34 -> '\052'
+| Coq_x35 -> '\053'
+| Coq_x36 -> '\054'
+| Coq_x37 -> '\055'
+| Coq_x38 -> '\056'
+| Coq_x39 -> '\057'
+| Coq_x3a -> '\058'
+| Coq_x3b -> '\059'
+| Coq_x3c -> '\060'
+| Coq_x3d -> '\061'
+| Coq_x3e -> '\062'
+| Coq_x3f -> '\063'
+| Coq_x40 -> '\064'
+| Coq_x41 -> '\065'
+| Coq_x42 -> '\066'
+| Coq_x43 -> '\067'
+| Coq_x44 -> '\068'
+| Coq_x45 -> '\069'
+| Coq_x46 -> '\070'
+| Coq_x47 -> '\071'
+| Coq_x48 -> '\072'
+| Coq_x49 -> '\073'
+| Coq_x4a -> '\074'
+| Coq_x4b -> '\075'
+| Coq_x4c -> '\076'
+| Coq_x4d -> '\077'
+| Coq_x4e -> '\078'
+| Coq_x4f -> '\079'
+| Coq_x50 -> '\080'
+| Coq_x51 -> '\081'
+| Coq_x52 -> '\082'
+| Coq_x53 -> '\083'
+| Coq_x54 -> '\084'
+| Coq_x55 -> '\085'
+| Coq_x56 -> '\086'
+| Coq_x57 -> '\087'
+| Coq_x58 -> '\088'
+| Coq_x59 -> '\089'
+| Coq_x5a -> '\090'
+| Coq_x5b -> '\091'
+| Coq_x5c -> '\092'
+| Coq_x5d -> '\093'
+| Coq_x5e -> '\094'
+| Coq_x5f -> '\095'
+| Coq_x60 -> '\096'
+| Coq_x61 -> '\097'
+| Coq_x62 -> '\098'
+| Coq_x63 -> '\099'
+| Coq_x64 -> '\100'
+| Coq_x65 -> '\101'
+| Coq_x66 -> '\102'
+| Coq_x67 -> '\103'
+| Coq_x68 -> '\104'
+| Coq_x69 -> '\105'
+| Coq_x6a -> '\106'
+| Coq_x6b -> '\107'
+| Coq_x6c -> '\108'
+| Coq_x6d -> '\109'
+| Coq_x6e -> '\110'
+| Coq_x6f -> '\111'
+| Coq_x70 -> '\112'
+| Coq_x71 -> '\113'
+| Coq_x72 -> '\114'
+| Coq_x73 -> '\115'
+| Coq_x74 -> '\116'
+| Coq_x75 -> '\117'
+| Coq_x76 -> '\118'
+| Coq_x77 -> '\119'
+| Coq_x78 -> '\120'
+| Coq_x79 -> '\121'
+| Coq_x7a -> '\122'
+| Coq_x7b -> '\123'
+| Coq_x7c -> '\124'
+| Coq_x7d -> '\125'
+| Coq_x7e -> '\126'
+| Coq_x7f -> '\127'
+| Coq_x80 -> '\128'
+| Coq_x81 -> '\129'
+| Coq_x82 -> '\130'
+| Coq_x83 -> '\131'
+| Coq_x84 -> '\132'
+| Coq_x85 -> '\133'
+| Coq_x86 -> '\134'
+| Coq_x87 -> '\135'
+| Coq_x88 -> '\136'
+| Coq_x89 -> '\137'
+| Coq_x8a -> '\138'
+| Coq_x8b -> '\139'
+| Coq_x8c -> '\140'
+| Coq_x8d -> '\141'
+| Coq_x8e -> '\142'
+| Coq_x8f -> '\143'
+| Coq_x90 -> '\144'
+| Coq_x91 -> '\145'
+| Coq_x92 -> '\146'
+| Coq_x93 -> '\147'
+| Coq_x94 -> '\148'
+| Coq_x95 -> '\149'
+| Coq_x96 -> '\150'
+| Coq_x97 -> '\151'
+| Coq_x98 -> '\152'
+| Coq_x99 -> '\153'
+| Coq_x9a -> '\154'
+| Coq_x9b -> '\155'
+| Coq_x9c -> '\156'
+| Coq_x9d -> '\157'
+| Coq_x9e -> '\158'
+| Coq_x9f -> '\159'
+| Coq_xa0 -> '\160'
+| Coq_xa1 -> '\161'
+| Coq_xa2 -> '\162'
+| Coq_xa3 -> '\163'
+| Coq_xa4 -> '\164'
+| Coq_xa5 -> '\165'
+| Coq_xa6 -> '\166'
+| Coq_xa7 -> '\167'
+| Coq_xa8 -> '\168'
+| Coq_xa9 -> '\169'
+| Coq_xaa -> '\170'
+| Coq_xab -> '\171'
+| Coq_xac -> '\172'
+| Coq_xad -> '\173'
+| Coq_xae -> '\174'
+| Coq_xaf -> '\175'
+| Coq_xb0 -> '\176'
+| Coq_xb1 -> '\177'
+| Coq_xb2 -> '\178'
+| Coq_xb3 -> '\179'
+| Coq_xb4 -> '\180'
+| Coq_xb5 -> '\181'
+| Coq_xb6 -> '\182'
+| Coq_xb7 -> '\183'
+| Coq_xb8 -> '\184'
+| Coq_xb9 -> '\185'
+| Coq_xba -> '\186'
+| Coq_xbb -> '\187'
+| Coq_xbc -> '\188'
+| Coq_xbd -> '\189'
+| Coq_xbe -> '\190'
+| Coq_xbf -> '\191'
+| Coq_xc0 -> '\192'
+| Coq_xc1 -> '\193'
+| Coq_xc2 -> '\194'
+| Coq_xc3 -> '\195'
+| Coq_xc4 -> '\196'
+| Coq_xc5 -> '\197'
+| Coq_xc6 -> '\198'
+| Coq_xc7 -> '\199'
+| Coq_xc8 -> '\200'
+| Coq_xc9 -> '\201'
+| Coq_xca -> '\202'
+| Coq_xcb -> '\203'
+| Coq_xcc -> '\204'
+| Coq_xcd -> '\205'
+| Coq_xce -> '\206'
+| Coq_xcf -> '\207'
+| Coq_xd0 -> '\208'
+| Coq_xd1 -> '\209'
+| Coq_xd2 -> '\210'
+| Coq_xd3 -> '\211'
+| Coq_xd4 -> '\212'
+| Coq_xd5 -> '\213'
+| Coq_xd6 -> '\214'
+| Coq_xd7 -> '\215'
+| Coq_xd8 -> '\216'
+| Coq_xd9 -> '\217'
+| Coq_xda -> '\218'
+| Coq_xdb -> '\219'
+| Coq_xdc -> '\220'
+| Coq_xdd -> '\221'
+| Coq_xde -> '\222'
+| Coq_xdf -> '\223'
+| Coq_xe0 -> '\224'
+| Coq_xe1 -> '\225'
+| Coq_xe2 -> '\226'
+| Coq_xe3 -> '\227'
+| Coq_xe4 -> '\228'
+| Coq_xe5 -> '\229'
+| Coq_xe6 -> '\230'
+| Coq_xe7 -> '\231'
+| Coq_xe8 -> '\232'
+| Coq_xe9 -> '\233'
+| Coq_xea -> '\234'
+| Coq_xeb -> '\235'
+| Coq_xec -> '\236'
+| Coq_xed -> '\237'
+| Coq_xee -> '\238'
+| Coq_xef -> '\239'
+| Coq_xf0 -> '\240'
+| Coq_xf1 -> '\241'
+| Coq_xf2 -> '\242'
+| Coq_xf3 -> '\243'
+| Coq_xf4 -> '\244'
+| Coq_xf5 -> '\245'
+| Coq_xf6 -> '\246'
+| Coq_xf7 -> '\247'
+| Coq_xf8 -> '\248'
+| Coq_xf9 -> '\249'
+| Coq_xfa -> '\250'
+| Coq_xfb -> '\251'
+| Coq_xfc -> '\252'
+| Coq_xfd -> '\253'
+| Coq_xfe -> '\254'
+| Coq_xff -> '\255'
+let byte_of_char = function
+| '\000' -> Coq_x00
+| '\001' -> Coq_x01
+| '\002' -> Coq_x02
+| '\003' -> Coq_x03
+| '\004' -> Coq_x04
+| '\005' -> Coq_x05
+| '\006' -> Coq_x06
+| '\007' -> Coq_x07
+| '\008' -> Coq_x08
+| '\009' -> Coq_x09
+| '\010' -> Coq_x0a
+| '\011' -> Coq_x0b
+| '\012' -> Coq_x0c
+| '\013' -> Coq_x0d
+| '\014' -> Coq_x0e
+| '\015' -> Coq_x0f
+| '\016' -> Coq_x10
+| '\017' -> Coq_x11
+| '\018' -> Coq_x12
+| '\019' -> Coq_x13
+| '\020' -> Coq_x14
+| '\021' -> Coq_x15
+| '\022' -> Coq_x16
+| '\023' -> Coq_x17
+| '\024' -> Coq_x18
+| '\025' -> Coq_x19
+| '\026' -> Coq_x1a
+| '\027' -> Coq_x1b
+| '\028' -> Coq_x1c
+| '\029' -> Coq_x1d
+| '\030' -> Coq_x1e
+| '\031' -> Coq_x1f
+| '\032' -> Coq_x20
+| '\033' -> Coq_x21
+| '\034' -> Coq_x22
+| '\035' -> Coq_x23
+| '\036' -> Coq_x24
+| '\037' -> Coq_x25
+| '\038' -> Coq_x26
+| '\039' -> Coq_x27
+| '\040' -> Coq_x28
+| '\041' -> Coq_x29
+| '\042' -> Coq_x2a
+| '\043' -> Coq_x2b
+| '\044' -> Coq_x2c
+| '\045' -> Coq_x2d
+| '\046' -> Coq_x2e
+| '\047' -> Coq_x2f
+| '\048' -> Coq_x30
+| '\049' -> Coq_x31
+| '\050' -> Coq_x32
+| '\051' -> Coq_x33
+| '\052' -> Coq_x34
+| '\053' -> Coq_x35
+| '\054' -> Coq_x36
+| '\055' -> Coq_x37
+| '\056' -> Coq_x38
+| '\057' -> Coq_x39
+| '\058' -> Coq_x3a
+| '\059' -> Coq_x3b
+| '\060' -> Coq_x3c
+| '\061' -> Coq_x3d
+| '\062' -> Coq_x3e
+| '\063' -> Coq_x3f
+| '\064' -> Coq_x40
+| '\065' -> Coq_x41
+| '\066' -> Coq_x42
+| '\067' -> Coq_x43
+| '\068' -> Coq_x44
+| '\069' -> Coq_x45
+| '\070' -> Coq_x46
+| '\071' -> Coq_x47
+| '\072' -> Coq_x48
+| '\073' -> Coq_x49
+| '\074' -> Coq_x4a
+| '\075' -> Coq_x4b
+| '\076' -> Coq_x4c
+| '\077' -> Coq_x4d
+| '\078' -> Coq_x4e
+| '\079' -> Coq_x4f
+| '\080' -> Coq_x50
+| '\081' -> Coq_x51
+| '\082' -> Coq_x52
+| '\083' -> Coq_x53
+| '\084' -> Coq_x54
+| '\085' -> Coq_x55
+| '\086' -> Coq_x56
+| '\087' -> Coq_x57
+| '\088' -> Coq_x58
+| '\089' -> Coq_x59
+| '\090' -> Coq_x5a
+| '\091' -> Coq_x5b
+| '\092' -> Coq_x5c
+| '\093' -> Coq_x5d
+| '\094' -> Coq_x5e
+| '\095' -> Coq_x5f
+| '\096' -> Coq_x60
+| '\097' -> Coq_x61
+| '\098' -> Coq_x62
+| '\099' -> Coq_x63
+| '\100' -> Coq_x64
+| '\101' -> Coq_x65
+| '\102' -> Coq_x66
+| '\103' -> Coq_x67
+| '\104' -> Coq_x68
+| '\105' -> Coq_x69
+| '\106' -> Coq_x6a
+| '\107' -> Coq_x6b
+| '\108' -> Coq_x6c
+| '\109' -> Coq_x6d
+| '\110' -> Coq_x6e
+| '\111' -> Coq_x6f
+| '\112' -> Coq_x70
+| '\113' -> Coq_x71
+| '\114' -> Coq_x72
+| '\115' -> Coq_x73
+| '\116' -> Coq_x74
+| '\117' -> Coq_x75
+| '\118' -> Coq_x76
+| '\119' -> Coq_x77
+| '\120' -> Coq_x78
+| '\121' -> Coq_x79
+| '\122' -> Coq_x7a
+| '\123' -> Coq_x7b
+| '\124' -> Coq_x7c
+| '\125' -> Coq_x7d
+| '\126' -> Coq_x7e
+| '\127' -> Coq_x7f
+| '\128' -> Coq_x80
+| '\129' -> Coq_x81
+| '\130' -> Coq_x82
+| '\131' -> Coq_x83
+| '\132' -> Coq_x84
+| '\133' -> Coq_x85
+| '\134' -> Coq_x86
+| '\135' -> Coq_x87
+| '\136' -> Coq_x88
+| '\137' -> Coq_x89
+| '\138' -> Coq_x8a
+| '\139' -> Coq_x8b
+| '\140' -> Coq_x8c
+| '\141' -> Coq_x8d
+| '\142' -> Coq_x8e
+| '\143' -> Coq_x8f
+| '\144' -> Coq_x90
+| '\145' -> Coq_x91
+| '\146' -> Coq_x92
+| '\147' -> Coq_x93
+| '\148' -> Coq_x94
+| '\149' -> Coq_x95
+| '\150' -> Coq_x96
+| '\151' -> Coq_x97
+| '\152' -> Coq_x98
+| '\153' -> Coq_x99
+| '\154' -> Coq_x9a
+| '\155' -> Coq_x9b
+| '\156' -> Coq_x9c
+| '\157' -> Coq_x9d
+| '\158' -> Coq_x9e
+| '\159' -> Coq_x9f
+| '\160' -> Coq_xa0
+| '\161' -> Coq_xa1
+| '\162' -> Coq_xa2
+| '\163' -> Coq_xa3
+| '\164' -> Coq_xa4
+| '\165' -> Coq_xa5
+| '\166' -> Coq_xa6
+| '\167' -> Coq_xa7
+| '\168' -> Coq_xa8
+| '\169' -> Coq_xa9
+| '\170' -> Coq_xaa
+| '\171' -> Coq_xab
+| '\172' -> Coq_xac
+| '\173' -> Coq_xad
+| '\174' -> Coq_xae
+| '\175' -> Coq_xaf
+| '\176' -> Coq_xb0
+| '\177' -> Coq_xb1
+| '\178' -> Coq_xb2
+| '\179' -> Coq_xb3
+| '\180' -> Coq_xb4
+| '\181' -> Coq_xb5
+| '\182' -> Coq_xb6
+| '\183' -> Coq_xb7
+| '\184' -> Coq_xb8
+| '\185' -> Coq_xb9
+| '\186' -> Coq_xba
+| '\187' -> Coq_xbb
+| '\188' -> Coq_xbc
+| '\189' -> Coq_xbd
+| '\190' -> Coq_xbe
+| '\191' -> Coq_xbf
+| '\192' -> Coq_xc0
+| '\193' -> Coq_xc1
+| '\194' -> Coq_xc2
+| '\195' -> Coq_xc3
+| '\196' -> Coq_xc4
+| '\197' -> Coq_xc5
+| '\198' -> Coq_xc6
+| '\199' -> Coq_xc7
+| '\200' -> Coq_xc8
+| '\201' -> Coq_xc9
+| '\202' -> Coq_xca
+| '\203' -> Coq_xcb
+| '\204' -> Coq_xcc
+| '\205' -> Coq_xcd
+| '\206' -> Coq_xce
+| '\207' -> Coq_xcf
+| '\208' -> Coq_xd0
+| '\209' -> Coq_xd1
+| '\210' -> Coq_xd2
+| '\211' -> Coq_xd3
+| '\212' -> Coq_xd4
+| '\213' -> Coq_xd5
+| '\214' -> Coq_xd6
+| '\215' -> Coq_xd7
+| '\216' -> Coq_xd8
+| '\217' -> Coq_xd9
+| '\218' -> Coq_xda
+| '\219' -> Coq_xdb
+| '\220' -> Coq_xdc
+| '\221' -> Coq_xdd
+| '\222' -> Coq_xde
+| '\223' -> Coq_xdf
+| '\224' -> Coq_xe0
+| '\225' -> Coq_xe1
+| '\226' -> Coq_xe2
+| '\227' -> Coq_xe3
+| '\228' -> Coq_xe4
+| '\229' -> Coq_xe5
+| '\230' -> Coq_xe6
+| '\231' -> Coq_xe7
+| '\232' -> Coq_xe8
+| '\233' -> Coq_xe9
+| '\234' -> Coq_xea
+| '\235' -> Coq_xeb
+| '\236' -> Coq_xec
+| '\237' -> Coq_xed
+| '\238' -> Coq_xee
+| '\239' -> Coq_xef
+| '\240' -> Coq_xf0
+| '\241' -> Coq_xf1
+| '\242' -> Coq_xf2
+| '\243' -> Coq_xf3
+| '\244' -> Coq_xf4
+| '\245' -> Coq_xf5
+| '\246' -> Coq_xf6
+| '\247' -> Coq_xf7
+| '\248' -> Coq_xf8
+| '\249' -> Coq_xf9
+| '\250' -> Coq_xfa
+| '\251' -> Coq_xfb
+| '\252' -> Coq_xfc
+| '\253' -> Coq_xfd
+| '\254' -> Coq_xfe
+| '\255' -> Coq_xff
diff --git a/template-coq/src/caml_byte.mli b/template-coq/src/caml_byte.mli
new file mode 100644
index 000000000..1dc00a1c5
--- /dev/null
+++ b/template-coq/src/caml_byte.mli
@@ -0,0 +1,4 @@
+open Byte
+
+val char_of_byte : byte -> char
+val byte_of_char : char -> byte
\ No newline at end of file
diff --git a/template-coq/src/caml_bytestring.ml b/template-coq/src/caml_bytestring.ml
new file mode 100644
index 000000000..3d733650f
--- /dev/null
+++ b/template-coq/src/caml_bytestring.ml
@@ -0,0 +1,27 @@
+open Byte
+open Caml_byte
+
+let rec caml_bytestring_length_aux s acc =
+  match s with
+  | Bytestring.String.EmptyString -> acc
+  | Bytestring.String.String (_, s) -> caml_bytestring_length_aux s (succ acc)
+
+let caml_bytestring_length s = caml_bytestring_length_aux s 0
+  
+let caml_string_of_bytestring (l : Bytestring.String.t) : string =
+  let len = caml_bytestring_length l in
+  let buf = Bytes.create len in
+  let rec aux i = function
+    | Bytestring.String.EmptyString -> ()
+    | Bytestring.String.String (c, cs) ->
+      Bytes.set buf i (Caml_byte.char_of_byte c); aux (succ i) cs
+  in
+  aux 0 l;
+  Bytes.to_string buf
+
+let bytestring_of_caml_string (s : string) : Bytestring.String.t =
+  let rec aux acc i =
+    if i < 0 then acc
+    else aux (Bytestring.String.String (byte_of_char s.[i], acc)) (i - 1)
+  in aux Bytestring.String.EmptyString (String.length s - 1)
+  
\ No newline at end of file
diff --git a/template-coq/src/caml_nat.ml b/template-coq/src/caml_nat.ml
new file mode 100644
index 000000000..5a78380a1
--- /dev/null
+++ b/template-coq/src/caml_nat.ml
@@ -0,0 +1,11 @@
+let nat_of_caml_int i = 
+  let rec aux acc i =
+    if i < 0 then acc
+    else aux (Datatypes.S acc) (i - 1)
+  in aux Datatypes.O (i - 1)
+
+let rec caml_int_of_nat_aux n acc =
+  match n with
+  | Datatypes.O -> acc
+  | Datatypes.S x -> caml_int_of_nat_aux x (succ acc)
+let caml_int_of_nat n = caml_int_of_nat_aux n 0
diff --git a/template-coq/src/caml_nat.mli b/template-coq/src/caml_nat.mli
new file mode 100644
index 000000000..b11cab111
--- /dev/null
+++ b/template-coq/src/caml_nat.mli
@@ -0,0 +1,3 @@
+
+val caml_int_of_nat : Datatypes.nat -> int
+val nat_of_caml_int : int -> Datatypes.nat
\ No newline at end of file
diff --git a/template-coq/src/constr_denoter.ml b/template-coq/src/constr_denoter.ml
index 2ae9a86a6..97fb9bdc0 100644
--- a/template-coq/src/constr_denoter.ml
+++ b/template-coq/src/constr_denoter.ml
@@ -81,15 +81,9 @@ struct
 
   let unquote_char trm =
     let (h,args) = app_full trm [] in
-    if constr_equall h tAscii then
-      match args with
-        a :: b :: c :: d :: e :: f :: g :: h :: [] ->
-        let bits = List.rev [a;b;c;d;e;f;g;h] in
-        let v = List.fold_left (fun a n -> (a lsl 1) lor if unquote_bool n then 1 else 0) 0 bits in
-        char_of_int v
-      | _ -> bad_term_verb trm "unquote_char"
-    else
-      not_supported trm
+    match Constr.kind h with
+    | Constr.Construct ((ind, idx), u) -> Char.chr (idx - 1)
+    | _ -> not_supported_verb trm "unquote_char"
 
   let unquote_string trm =
     let rec go n trm =
@@ -324,8 +318,8 @@ struct
       not_supported_verb trm "unquote_inductive"
 
 
-  let unquote_int=unquote_nat
-  let print_term=Printer.pr_constr_env (Global.env ()) Evd.empty
+  let unquote_int = unquote_nat
+  let print_term = Printer.pr_constr_env (Global.env ()) Evd.empty
 
 
   let unquote_global_reference (trm : Constr.t) (* of type global_reference *) : GlobRef.t =
diff --git a/template-coq/src/constr_quoter.ml b/template-coq/src/constr_quoter.ml
index 26267f63d..73bb106f1 100644
--- a/template-coq/src/constr_quoter.ml
+++ b/template-coq/src/constr_quoter.ml
@@ -104,23 +104,21 @@ struct
   (* Quote OCaml int to Coq nat *)
   let quote_int =
     (* the cache is global but only accessible through quote_int *)
-    let cache = Hashtbl.create 10 in
+    let cache = Hashtbl.create 1023 in
     let rec recurse i =
       try Hashtbl.find cache i
-      with
-	Not_found ->
-	  if i = 0 then
-	    let result = Lazy.force tO in
-	    let _ = Hashtbl.add cache i result in
-	    result
-	  else
-	    let result = constr_mkApp (tS, [| recurse (i - 1) |]) in
-	    let _ = Hashtbl.add cache i result in
-	    result
+      with Not_found ->
+        if i = 0 then
+          let result = Lazy.force tO in
+          let _ = Hashtbl.add cache i result in
+          result
+        else
+          let result = constr_mkApp (tS, [| recurse (i - 1) |]) in
+          let _ = Hashtbl.add cache i result in
+          result
     in
-    fun i ->
-    if i >= 0 then recurse i else
-      CErrors.anomaly (str "Negative int can't be unquoted to nat.")
+    fun i -> if i >= 0 then recurse i else
+      CErrors.anomaly (str "Negative int can't be quoted to nat.")
 
   let quote_bool b =
     if b then Lazy.force ttrue else Lazy.force tfalse
@@ -128,10 +126,17 @@ struct
   let quote_int63 i = constr_mkApp (tInt, [| Constr.mkInt i |])
 
   let quote_float64 f = constr_mkApp (tFloat, [| Constr.mkFloat f |])
+  let quote_inductive (kn, i) =
+    constr_mkApp (tmkInd, [| kn; i |])
 
+  let byte_ind =
+    lazy (let ty = Lazy.force tByte in
+      match Constr.kind ty with
+      | Constr.Ind (ind, u) -> ind
+      | _ -> failwith "byte_ind : tByte is not bound to an inductive type")
+  
   let quote_char i =
-    constr_mkApp (tAscii, Array.of_list (List.map (fun m -> quote_bool ((i land m) = m))
-					 (List.rev [128;64;32;16;8;4;2;1])))
+    Constr.mkConstruct (Lazy.force byte_ind, (i+1))
 
   let chars = lazy (Array.init 255 quote_char)
 
@@ -349,9 +354,6 @@ struct
     to_coq_list (prodl tident tTerm)
                 (List.map (fun (a, b) -> pairl tident tTerm a b) d)
 
-  let quote_inductive (kn, i) =
-    constr_mkApp (tmkInd, [| kn; i |])
-
   let quote_dirpath dp =
     let l = DirPath.repr dp in
     to_coq_listl tident (List.map quote_ident l)
diff --git a/template-coq/src/constr_reification.ml b/template-coq/src/constr_reification.ml
index 15029a5a0..d4a4d83d5 100644
--- a/template-coq/src/constr_reification.ml
+++ b/template-coq/src/constr_reification.ml
@@ -91,7 +91,7 @@ struct
 
   let unit_tt = resolve "metacoq.unit.intro"
 
-  let tAscii = resolve "metacoq.ascii.intro"
+  let tByte = resolve "metacoq.byte.type"
   let tlist = resolve "metacoq.list.type"
   let c_nil = resolve "metacoq.list.nil"
   let c_cons = resolve "metacoq.list.cons"
diff --git a/template-coq/src/genbytes.ml b/template-coq/src/genbytes.ml
new file mode 100644
index 000000000..6a39256cb
--- /dev/null
+++ b/template-coq/src/genbytes.ml
@@ -0,0 +1,60 @@
+(* 
+Printf.printf "let int_of_byte = \n";;
+
+for i = 0 to 255 do 
+  Printf.printf "| Coq_x%02x -> %i\n" i i
+done *)
+(*
+Printf.printf "open Byte\n";;
+
+Printf.printf "let char_of_byte = function\n";;
+
+for i = 0 to 255 do 
+  Printf.printf "| Coq_x%02x -> '\\%03i'\n" i i
+done;;
+
+Printf.printf "let byte_of_char = function\n";;
+for i = 0 to 255 do 
+  Printf.printf "| '\\%03i' -> Coq_x%02x\n" i i
+done;;
+*)
+(*
+Printf.printf "From Coq Require Import Byte.\n\n";;
+
+for i = 0 to 255 do 
+  Printf.printf "Definition is_byte_x%02x (b : byte) := match b with | x%02x => true | _ => false end.\n" i i
+done;;
+
+Printf.printf "Definition eqb (b b' : byte) :=\n  match b with\n";;
+
+for i = 0 to 255 do 
+  Printf.printf "  | x%02x => is_byte_x%02x b'\n" i i
+done;;
+Printf.printf"  end.\n";;
+
+for i = 0 to 255 do 
+  Printf.printf "Definition compare_byte_x%02x (b : byte) :=\n" i;
+  Printf.printf "  match b with\n";
+  if i != 0 then Printf.printf "  ";
+  for j = 0 to i - 1 do
+    Printf.printf "| x%02x " j
+  done;
+  if i != 0 then Printf.printf "=> Gt\n";
+  Printf.printf "  | x%02x => Eq\n" i;
+  if i != 255 then
+    Printf.printf "  | _ => Lt\n";
+  Printf.printf "  end.\n"
+done;;
+
+Printf.printf "Definition compare (b b' : byte) :=\n  match b with\n";;
+
+for i = 0 to 255 do 
+  Printf.printf "  | x%02x => compare_byte_x%02x b'\n" i i
+done;;
+Printf.printf"  end.\n";;
+*)
+
+
+for i = 0 to 255 do 
+  Printf.printf "| x%02x -> <%%x%02x%%>\n" i i
+done
diff --git a/template-coq/src/quoter.ml b/template-coq/src/quoter.ml
index 8502b06c7..2c9431486 100644
--- a/template-coq/src/quoter.ml
+++ b/template-coq/src/quoter.ml
@@ -466,7 +466,7 @@ struct
           univsty oib.mind_user_lc)
         univs mib.mind_packets
 
-  let quote_term_rec bypass env trm =
+  let quote_term_rec ~bypass ?(with_universes=true) env trm =
     let visited_terms = ref Names.KNset.empty in
     let visited_types = ref Mindset.empty in
     let universes = ref Univ.Level.Set.empty in
@@ -553,10 +553,17 @@ struct
       (x,y)
     in
     let (tm, _) = quote_rem () env trm in
-    let univs = Univ.Level.Set.union (Vars.universes_of_constr trm) !universes in
-    let decls = List.fold_right (fun (kn, d) acc -> Q.add_global_decl kn d acc)  !constants (Q.empty_global_declarations ()) in
-    let univs = Univ.Level.Set.filter (fun l -> Option.is_empty (Univ.Level.var_index l)) univs in
-    let univs = quote_ugraph ~kept:univs (Environ.universes env) in
+    let decls = List.fold_right (fun (kn, d) acc -> Q.add_global_decl kn d acc) !constants (Q.empty_global_declarations ()) in
+    let univs = 
+      if with_universes then 
+        let univs = Univ.Level.Set.union (Vars.universes_of_constr trm) !universes in
+        let univs = Univ.Level.Set.filter (fun l -> Option.is_empty (Univ.Level.var_index l)) univs in
+        quote_ugraph ~kept:univs (Environ.universes env)
+      else 
+        (debug Pp.(fun () -> str"Skipping universes: ");
+         time (Pp.str"Quoting empty universe context") 
+           (fun uctx -> Q.quote_univ_contextset uctx) Univ.ContextSet.empty)
+    in
     let env = Q.mk_global_env univs decls in
     Q.mk_program env tm
 
diff --git a/template-coq/src/run_extractable.ml b/template-coq/src/run_extractable.ml
index 136d31a3e..18c3e217b 100644
--- a/template-coq/src/run_extractable.ml
+++ b/template-coq/src/run_extractable.ml
@@ -6,8 +6,6 @@ open Tm_util
 open Ast_quoter
 open Ast_denoter
 
-(* todo : replace string_to_list and converse by (un)quote_string *)
-
 let to_reduction_strategy (s : Common0.reductionStrategy) : Plugin_core.reduction_strategy =
   match s with
    | Common0.Coq_cbv -> Plugin_core.rs_cbv
@@ -17,11 +15,11 @@ let to_reduction_strategy (s : Common0.reductionStrategy) : Plugin_core.reductio
    | Common0.Coq_lazy -> Plugin_core.rs_lazy
    | Common0.Coq_unfold x -> failwith "not yet implemented: to_reduction_strategy"
 
-let to_qualid (c : char list) : Libnames.qualid =
-  Libnames.qualid_of_string (list_to_string c)
+let to_qualid c : Libnames.qualid =
+  Libnames.qualid_of_string (unquote_string c)
 
-let of_qualid (q : Libnames.qualid) : char list =
-  string_to_list (Libnames.string_of_qualid q)
+let of_qualid (q : Libnames.qualid) =
+  quote_string (Libnames.string_of_qualid q)
 
 (* todo(gmm): this definition adapted from quoter.ml *)
 let quote_rel_decl env = function
@@ -209,8 +207,8 @@ let rec interp_tm (t : 'a coq_TM) : 'a tm =
   | Coq_tmReturn x -> tmReturn x
   | Coq_tmBind (c, k) -> tmBind (interp_tm c) (fun x -> interp_tm (k x))
   | Coq_tmPrint t -> Obj.magic (tmPrint (to_constr t))
-  | Coq_tmMsg msg -> Obj.magic (tmMsg (list_to_string msg))
-  | Coq_tmFail err -> tmFailString (list_to_string err)
+  | Coq_tmMsg msg -> Obj.magic (tmMsg (unquote_string msg))
+  | Coq_tmFail err -> tmFailString (unquote_string err)
   | Coq_tmEval (r,t) ->
     tmBind (tmEval (to_reduction_strategy r) (to_constr t))
            (fun x -> Obj.magic (tmOfConstr x))
@@ -235,7 +233,7 @@ let rec interp_tm (t : 'a coq_TM) : 'a tm =
     tmMap (fun x -> Obj.magic (List.map quote_global_reference x))
           (tmLocate (to_qualid id))
   | Coq_tmCurrentModPath ->
-    tmMap (fun mp -> Obj.magic (string_to_list (Names.ModPath.to_string mp)))
+    tmMap (fun mp -> Obj.magic (quote_string (Names.ModPath.to_string mp)))
           tmCurrentModPath
   | Coq_tmQuoteInductive kn ->
     tmBind (tmQuoteInductive (unquote_kn kn))
diff --git a/template-coq/src/run_template_monad.ml b/template-coq/src/run_template_monad.ml
index 39f2edd6c..7bde86623 100644
--- a/template-coq/src/run_template_monad.ml
+++ b/template-coq/src/run_template_monad.ml
@@ -407,7 +407,7 @@ let rec run_template_program_rec ~poly ?(intactic=false) (k : Constr.t Plugin_co
     in k ~st env evm qt
   | TmQuoteRecTransp  (bypass, trm) ->
     let bypass = unquote_bool (reduce_all env evm bypass) in
-    let qt = quote_term_rec bypass env trm in
+    let qt = quote_term_rec ~bypass ~with_universes:true env trm in
     k ~st env evm qt
   | TmQuoteInd (name, strict) ->
     let kn = unquote_kn (reduce_all env evm name) in
diff --git a/template-coq/src/tm_util.ml b/template-coq/src/tm_util.ml
index af2731488..a09a536cd 100644
--- a/template-coq/src/tm_util.ml
+++ b/template-coq/src/tm_util.ml
@@ -58,23 +58,6 @@ let debug (m : unit ->Pp.t) =
 type ('a,'b) sum =
   Left of 'a | Right of 'b
 
-(* todo(gmm): these are helper functions *)
-let string_to_list (s : string) : char list =
-  let rec aux acc i =
-    if i < 0 then acc
-    else aux (s.[i] :: acc) (i - 1)
-  in aux [] (String.length s - 1)
-
-let list_to_string (l : char list) : string =
-  let buf = Bytes.create (List.length l) in
-  let rec aux i = function
-    | [] -> ()
-    | c :: cs ->
-      Bytes.set buf i c; aux (succ i) cs
-  in
-  aux 0 l;
-  Bytes.to_string buf
-
 let rec filter_map f l =
   match l with
   | [] -> []
diff --git a/template-coq/theories/AstUtils.v b/template-coq/theories/AstUtils.v
index 4d4abfd43..9383a275a 100644
--- a/template-coq/theories/AstUtils.v
+++ b/template-coq/theories/AstUtils.v
@@ -14,7 +14,28 @@ Definition string_of_prim_int (i:Uint63.int) : string :=
 Definition string_of_float (f : PrimFloat.float) :=
   "<float>".
 
-Fixpoint string_of_term (t : term) :=
+Module string_of_term_tree.
+  Import bytestring.Tree.
+  Infix "^" := append.
+
+  Definition string_of_predicate {term} (f : term -> t) (p : predicate term) :=
+    "(" ^ "(" ^ concat "," (map f (pparams p)) ^ ")" 
+    ^ "," ^ string_of_universe_instance (puinst p)
+    ^ ",(" ^ String.concat "," (map (string_of_name ∘ binder_name) (pcontext p)) ^ ")"
+    ^ "," ^ f (preturn p) ^ ")".
+  
+  Definition string_of_branch (f : term -> t) (b : branch term) :=
+    "([" ^ String.concat "," (map (string_of_name ∘ binder_name) (bcontext b)) ^ "], "
+    ^ f (bbody b) ^ ")".
+    
+  Definition string_of_def {A} (f : A -> t) (def : def A) :=
+    "(" ^ string_of_name (binder_name (dname def))
+      ^ "," ^ string_of_relevance (binder_relevance (dname def))
+      ^ "," ^ f (dtype def)
+      ^ "," ^ f (dbody def)
+      ^ "," ^ string_of_nat (rarg def) ^ ")".
+
+  Fixpoint string_of_term (t : term) : Tree.t :=
   match t with
   | tRel n => "Rel(" ^ string_of_nat n ^ ")"
   | tVar n => "Var(" ^ n ^ ")"
@@ -53,7 +74,10 @@ Fixpoint string_of_term (t : term) :=
   (* | tInt i => "Int(" ^ string_of_prim_int i ^ ")"
   | tFloat f => "Float(" ^ string_of_float f ^ ")" *)
   end.
-  
+End string_of_term_tree.
+
+Definition string_of_term := Tree.to_string ∘ string_of_term_tree.string_of_term.
+
 Fixpoint destArity Γ (t : term) :=
   match t with
   | tProd na t b => destArity (Γ ,, vass na t) b
@@ -184,7 +208,7 @@ Fixpoint lookup_mind_decl (id : kername) (decls : global_declarations)
  := match decls with
     | nil => None
     | (kn, InductiveDecl d) :: tl =>
-      if eq_kername kn id then Some d else lookup_mind_decl id tl
+      if kn == id then Some d else lookup_mind_decl id tl
     | _ :: tl => lookup_mind_decl id tl
     end.
 
diff --git a/template-coq/theories/BasicAst.v b/template-coq/theories/BasicAst.v
index 48cb1b88e..c5dd0970b 100644
--- a/template-coq/theories/BasicAst.v
+++ b/template-coq/theories/BasicAst.v
@@ -1,75 +1,10 @@
 (* Distributed under the terms of the MIT license. *)
 From Coq Require Import ssreflect Morphisms Orders Setoid.
 From MetaCoq.Template Require Import utils.
+From MetaCoq.Template Require Export Kernames.
 From Coq Require Floats.SpecFloat.
 From Equations Require Import Equations.
 
-(** ** Reification of names ** *)
-
-(** [Comment taken from Coq's code]
-    - Id.t is the type of identifiers, that is morally a subset of strings which
-      only contains Unicode characters of the Letter kind (and a few more).
-      => [ident]
-    - Name.t is an ad-hoc variant of Id.t option allowing to handle optionally
-      named objects.
-      => [name]
-    - DirPath.t represents generic paths as sequences of identifiers.
-      => [dirpath]
-    - Label.t is an equivalent of Id.t made distinct for semantical purposes.
-      => [ident]
-    - ModPath.t are module paths.
-      => [modpath]
-    - KerName.t are absolute names of objects in Coq.
-      => [kername]
-
-    And also :
-    - Constant.t => [kername]
-    - variable => [ident]
-    - MutInd.t => [kername]
-    - inductive => [inductive]
-    - constructor => [inductive * nat]
-    - Projection.t => [projection]
-    - GlobRef.t => global_reference
-
-    Finally, we define the models of primitive types (uint63 and floats64).
-*)
-
-Definition ident   := string. (* e.g. nat *)
-Definition qualid  := string. (* e.g. Datatypes.nat *)
-
-(** Type of directory paths. Essentially a list of module identifiers. The
-    order is reversed to improve sharing. E.g. A.B.C is ["C";"B";"A"] *)
-Definition dirpath := list ident.
-#[global] Instance dirpath_eqdec : Classes.EqDec dirpath := _.
-
-Definition string_of_dirpath : dirpath -> string
-  := String.concat "." ∘ rev.
-
-(** The module part of the kernel name.
-    - MPfile is for toplevel libraries, i.e. .vo files
-    - MPbound are parameters of functors
-    - MPdot is for submodules
-*)
-Inductive modpath :=
-| MPfile  (dp : dirpath)
-| MPbound (dp : dirpath) (id : ident) (i : nat)
-| MPdot   (mp : modpath) (id : ident).
-Derive NoConfusion EqDec for modpath.
-
-Fixpoint string_of_modpath (mp : modpath) : string :=
-  match mp with
-  | MPfile dp => string_of_dirpath dp
-  | MPbound dp id _ => string_of_dirpath dp ^ "." ^ id
-  | MPdot mp id => string_of_modpath mp ^ "." ^ id
-  end.
-
-(** The absolute names of objects seen by kernel *)
-Definition kername := modpath × ident.
-#[global] Instance kername_eqdec : Classes.EqDec kername := _.
-
-Definition string_of_kername (kn : kername) :=
-  string_of_modpath kn.1 ^ "." ^ kn.2.
-
 (** Identifiers that are allowed to be anonymous (i.e. "_" in concrete syntax). *)
 Inductive name : Set :=
 | nAnon
@@ -119,96 +54,6 @@ Definition string_of_relevance (r : relevance) :=
   | Irrelevant => "Irrelevant"
   end.
 
-(** Designation of a (particular) inductive type. *)
-Record inductive : Set := mkInd { inductive_mind : kername ;
-                                  inductive_ind : nat }.
-Arguments mkInd _%string _%nat.
-
-Derive NoConfusion EqDec for inductive.
-
-Definition string_of_inductive (i : inductive) :=
-  string_of_kername (inductive_mind i) ^ "," ^ string_of_nat (inductive_ind i).
-
-Definition projection : Set := inductive * nat (* params *) * nat (* argument *).
-
-(** Kernel declaration references [global_reference] *)
-Inductive global_reference :=
-| VarRef : ident -> global_reference
-| ConstRef : kername -> global_reference
-| IndRef : inductive -> global_reference
-| ConstructRef : inductive -> nat -> global_reference.
-
-Derive NoConfusion EqDec for global_reference.
-
-
-Definition string_of_gref gr : string :=
-  match gr with
-  | VarRef v => v
-  | ConstRef s => string_of_kername s
-  | IndRef (mkInd s n) =>
-    "Inductive " ^ string_of_kername s ^ " " ^ (string_of_nat n)
-  | ConstructRef (mkInd s n) k =>
-    "Constructor " ^ string_of_kername s ^ " " ^ (string_of_nat n) ^ " " ^ (string_of_nat k)
-  end.
-
-Definition kername_eq_dec (k k0 : kername) : {k = k0} + {k <> k0} := Classes.eq_dec k k0.
-#[global] Hint Resolve kername_eq_dec : eq_dec.
-
-Definition gref_eq_dec (gr gr' : global_reference) : {gr = gr'} + {~ gr = gr'} := Classes.eq_dec gr gr'.
-
-Definition ident_eq (x y : ident) :=
-  match string_compare x y with
-  | Eq => true
-  | _ => false
-  end.
-
-Lemma ident_eq_spec x y : reflect (x = y) (ident_eq x y).
-Proof.
-  unfold ident_eq. destruct (string_compare_eq x y).
-  destruct string_compare; constructor; auto.
-  - now apply H.
-  - intro Heq; specialize (H0 Heq). discriminate.
-  - intro Heq; specialize (H0 Heq). discriminate.
-Qed.
-
-(* todo : better ? *)
-Definition eq_kername (k k0 : kername) : bool :=
-  match kername_eq_dec k k0 with
-  | left _ => true
-  | right _ => false
-  end.
-
-Lemma eq_kername_refl kn : eq_kername kn kn.
-Proof.
-  unfold eq_kername. destruct (kername_eq_dec kn kn); cbnr.
-  contradiction.
-Qed.
-
-Definition eq_inductive i i' :=
-  let 'mkInd i n := i in
-  let 'mkInd i' n' := i' in
-  eq_kername i i' && Nat.eqb n n'.
-
-Definition eq_constant := eq_kername.
-
-Definition eq_projection p p' :=
-  let '(ind, pars, arg) := p in
-  let '(ind', pars', arg') := p' in
-  eq_inductive ind ind' && Nat.eqb pars pars' && Nat.eqb arg arg'.
-
-Lemma eq_inductive_refl i : eq_inductive i i.
-Proof.
-  destruct i as [mind k].
-  unfold eq_inductive. now rewrite eq_kername_refl PeanoNat.Nat.eqb_refl.
-Qed.
-
-Lemma eq_projection_refl i : eq_projection i i.
-Proof.
-  destruct i as [[mind k] p].
-  unfold eq_projection.
-  now rewrite eq_inductive_refl !PeanoNat.Nat.eqb_refl.
-Qed.
-
 (** The kind of a cast *)
 Inductive cast_kind : Set :=
 | VmCast
diff --git a/template-coq/theories/Checker.v b/template-coq/theories/Checker.v
index 0e4f74d50..593cd815e 100644
--- a/template-coq/theories/Checker.v
+++ b/template-coq/theories/Checker.v
@@ -366,7 +366,7 @@ Fixpoint eq_term `{checker_flags} (φ : universes_graph) (t u : term) {struct t}
   match t, u with
   | tRel n, tRel n' => Nat.eqb n n'
   | tEvar ev args, tEvar ev' args' => Nat.eqb ev ev' && forallb2 (eq_term φ) args args'
-  | tVar id, tVar id' => eq_string id id'
+  | tVar id, tVar id' => eqb id id'
   | tSort s, tSort s' => check_eqb_universe φ s s'
   | tCast f k T, tCast f' k' T' => eq_term φ f f' && eq_term φ T T'
   | tApp f args, tApp f' args' => eq_term φ f f' && forallb2 (eq_term φ) args args'
@@ -398,7 +398,7 @@ Fixpoint leq_term `{checker_flags} (φ : universes_graph) (t u : term) {struct t
   match t, u with
   | tRel n, tRel n' => Nat.eqb n n'
   | tEvar ev args, tEvar ev' args' => Nat.eqb ev ev' && forallb2 (eq_term φ) args args'
-  | tVar id, tVar id' => eq_string id id'
+  | tVar id, tVar id' => eqb id id'
   | tSort s, tSort s' => check_leqb_universe φ s s'
   | tApp f args, tApp f' args' => eq_term φ f f' && forallb2 (eq_term φ) args args'
   | tCast f k T, tCast f' k' T' => eq_term φ f f' && eq_term φ T T'
diff --git a/template-coq/theories/Constants.v b/template-coq/theories/Constants.v
index 5399e00bf..37b770f8a 100644
--- a/template-coq/theories/Constants.v
+++ b/template-coq/theories/Constants.v
@@ -1,15 +1,14 @@
 (* Distributed under the terms of the MIT license. *)
-From MetaCoq.Template Require Import BasicAst uGraph TemplateMonad
+From MetaCoq.Template Require Import bytestring BasicAst uGraph TemplateMonad
      TemplateMonad.Extractable.
 
 (* Base types *)
 
-Register Coq.Strings.String.string as metacoq.string.type.
-Register Coq.Strings.String.EmptyString as metacoq.string.nil.
-Register Coq.Strings.String.String as metacoq.string.cons.
+Register bytestring.String.t as metacoq.string.type.
+Register bytestring.String.EmptyString as metacoq.string.nil.
+Register bytestring.String.String as metacoq.string.cons.
 
-Register Coq.Strings.Ascii.ascii as metacoq.ascii.type.
-Register Coq.Strings.Ascii.Ascii as metacoq.ascii.intro.
+Register Coq.Init.Byte.byte as metacoq.byte.type.
 
 Register Coq.Init.Datatypes.nat as metacoq.nat.type.
 Register Coq.Init.Datatypes.O as metacoq.nat.zero.
@@ -62,15 +61,21 @@ Register MetaCoq.Template.BasicAst.aname as metacoq.ast.aname.
 
 Register MetaCoq.Template.BasicAst.nAnon as metacoq.ast.nAnon.
 Register MetaCoq.Template.BasicAst.nNamed as metacoq.ast.nNamed.
-Register MetaCoq.Template.BasicAst.ident as metacoq.ast.ident.
-Register MetaCoq.Template.BasicAst.kername as metacoq.ast.kername.
-Register MetaCoq.Template.BasicAst.modpath as metacoq.ast.modpath.
-Register MetaCoq.Template.BasicAst.MPfile as metacoq.ast.MPfile.
-Register MetaCoq.Template.BasicAst.MPbound as metacoq.ast.MPbound.
-Register MetaCoq.Template.BasicAst.MPdot as metacoq.ast.MPdot.
+Register MetaCoq.Template.Kernames.ident as metacoq.ast.ident.
+Register MetaCoq.Template.Kernames.kername as metacoq.ast.kername.
+Register MetaCoq.Template.Kernames.modpath as metacoq.ast.modpath.
+Register MetaCoq.Template.Kernames.MPfile as metacoq.ast.MPfile.
+Register MetaCoq.Template.Kernames.MPbound as metacoq.ast.MPbound.
+Register MetaCoq.Template.Kernames.MPdot as metacoq.ast.MPdot.
+Register MetaCoq.Template.Kernames.inductive as metacoq.ast.inductive.
+Register MetaCoq.Template.Kernames.mkInd as metacoq.ast.mkInd.
+Register MetaCoq.Template.Kernames.global_reference as metacoq.ast.global_reference.
+Register MetaCoq.Template.Kernames.VarRef as metacoq.ast.VarRef.
+Register MetaCoq.Template.Kernames.ConstRef as metacoq.ast.ConstRef.
+Register MetaCoq.Template.Kernames.IndRef as metacoq.ast.IndRef.
+Register MetaCoq.Template.Kernames.ConstructRef as metacoq.ast.ConstructRef.
+
 Register MetaCoq.Template.BasicAst.name as metacoq.ast.name.
-Register MetaCoq.Template.BasicAst.inductive as metacoq.ast.inductive.
-Register MetaCoq.Template.BasicAst.mkInd as metacoq.ast.mkInd.
 Register MetaCoq.Template.BasicAst.def as metacoq.ast.def.
 Register MetaCoq.Template.BasicAst.mkdef as metacoq.ast.mkdef.
 Register MetaCoq.Template.BasicAst.cast_kind as metacoq.ast.cast_kind.
@@ -83,11 +88,6 @@ Register MetaCoq.Template.BasicAst.recursivity_kind as metacoq.ast.recursivity_k
 Register MetaCoq.Template.BasicAst.Finite as metacoq.ast.Finite.
 Register MetaCoq.Template.BasicAst.CoFinite as metacoq.ast.CoFinite.
 Register MetaCoq.Template.BasicAst.BiFinite as metacoq.ast.BiFinite.
-Register MetaCoq.Template.BasicAst.global_reference as metacoq.ast.global_reference.
-Register MetaCoq.Template.BasicAst.VarRef as metacoq.ast.VarRef.
-Register MetaCoq.Template.BasicAst.ConstRef as metacoq.ast.ConstRef.
-Register MetaCoq.Template.BasicAst.IndRef as metacoq.ast.IndRef.
-Register MetaCoq.Template.BasicAst.ConstructRef as metacoq.ast.ConstructRef.
 Register MetaCoq.Template.BasicAst.fresh_evar_id as metacoq.ast.fresh_evar_id.
 
 (* Universes *)
diff --git a/template-coq/theories/EnvMap.v b/template-coq/theories/EnvMap.v
index a046a6709..48251411c 100644
--- a/template-coq/theories/EnvMap.v
+++ b/template-coq/theories/EnvMap.v
@@ -9,9 +9,6 @@ Import String2pos.
 
 Implicit Types (cf:checker_flags).
 
-Module KernameMap := FMapAVL.Make KernameOT.OT.
-Module KernameMapFact := FMapFacts.WProperties KernameMap.
-
 Module EnvMap.
   (* We keep the definition of EnvMap polymorphic over the data associated to a kername *)
   Section Poly.
@@ -36,7 +33,7 @@ Module EnvMap.
     intros ne.
     unfold lookup, add.
     rewrite KernameMapFact.F.add_neq_o //.
-    intros eq. apply KernameOT.compare_eq in eq. congruence.
+    intros eq. apply Kername.compare_eq in eq. congruence.
   Qed.
 
   Lemma gss (e : t) kn kn' g : kn = kn' ->
@@ -45,7 +42,7 @@ Module EnvMap.
     intros eq.
     unfold lookup, add.
     rewrite KernameMapFact.F.add_eq_o //.
-    now apply KernameOT.compare_eq.
+    now apply Kername.compare_eq.
   Qed.
 
   Definition equal (g g' : t) := KernameMap.Equal g g'.
@@ -148,10 +145,10 @@ Module EnvMap.
     intros frΣ frk eq.
     intros k'.
     rewrite KernameMapFact.F.remove_o.
-    destruct KernameMap.E.eq_dec. eapply KernameOT.compare_eq in e0. subst k'.
+    destruct KernameMap.E.eq_dec. eapply Kername.compare_eq in e0. subst k'.
     - rewrite {}eq. induction frk. now cbn.
       rewrite of_global_env_cons //. depelim frΣ. simpl in H0 |- *.
-      rewrite KernameMapFact.F.add_neq_o //. intros c. eapply KernameOT.compare_eq in c. contradiction.
+      rewrite KernameMapFact.F.add_neq_o //. intros c. eapply Kername.compare_eq in c. contradiction.
       now apply IHfrk.
     - rewrite KernameMapFact.F.add_neq_o //.
   Qed.
@@ -163,11 +160,11 @@ Module EnvMap.
     unfold repr, equal, remove, add.
     intros neq k''.
     rewrite KernameMapFact.F.remove_o.
-    destruct KernameMap.E.eq_dec. eapply KernameOT.compare_eq in e0. subst k'.
-    - rewrite KernameMapFact.F.add_neq_o //. intros c. eapply KernameOT.compare_eq in c. contradiction.
+    destruct KernameMap.E.eq_dec. eapply Kername.compare_eq in e0. subst k'.
+    - rewrite KernameMapFact.F.add_neq_o //. intros c. eapply Kername.compare_eq in c. contradiction.
       rewrite KernameMapFact.F.remove_o.
       destruct KernameMap.E.eq_dec => //.
-      elimtype False; apply n. now apply KernameOT.compare_eq.
+      elimtype False; apply n. now apply Kername.compare_eq.
     - rewrite !KernameMapFact.F.add_o //.
       destruct (KernameMap.E.eq_dec k k'') => //.
       rewrite KernameMapFact.F.remove_neq_o //.
@@ -193,8 +190,7 @@ Module EnvMap.
       intros hin.
       red in eq. rewrite eq in hin.
       now eapply KernameMapFact.F.empty_in_iff in hin.
-    - cbn -[of_global_env].
-      change (eq_kername k a.1) with (eqb k a.1).
+    - cbn -[of_global_env eqb].
       destruct (eqb_spec k a.1).
       * subst. 
         rewrite of_global_env_cons //.
diff --git a/template-coq/theories/Environment.v b/template-coq/theories/Environment.v
index befa9df8c..f43c316e6 100644
--- a/template-coq/theories/Environment.v
+++ b/template-coq/theories/Environment.v
@@ -504,7 +504,7 @@ Module Environment (T : Term).
     match Σ with
     | nil => None
     | d :: tl =>
-      if eq_kername kn d.1 then Some d.2
+      if kn == d.1 then Some d.2
       else lookup_global tl kn
     end.
 
diff --git a/template-coq/theories/EtaExpand.v b/template-coq/theories/EtaExpand.v
index f796284d3..224de3870 100644
--- a/template-coq/theories/EtaExpand.v
+++ b/template-coq/theories/EtaExpand.v
@@ -5,9 +5,9 @@
     Coq's conversion, the proof is essentially [eq_refl].
     All dependencies are also expanded.*)
 
-From Coq Require Import List PeanoNat Bool Ascii String Lia.
+From Coq Require Import List PeanoNat Bool Lia.
 From MetaCoq.Template Require Export
-     utils.MCUtils (* Utility functions *)
+     utils (* Utility functions *)
      monad_utils   (* Monadic notations *)
      uGraph        (* The graph of universes *)
      BasicAst      (* The basic AST structures *)
@@ -18,8 +18,8 @@ From MetaCoq.Template Require Export
      UnivSubst     (* Substitution of universe instances *)
      Typing        (* Typing judgment *).
 
-Open Scope string.
 Open Scope nat.
+Open Scope bs.
 
 Import Template.Ast.
 Import ListNotations.
@@ -307,7 +307,8 @@ Proof.
       * cbn in H. inversion H; subst. cbn.
         simpl_list. destruct l.
         -- cbn. econstructor; eauto.
-        -- cbn. eapply expanded_tConstruct_app; eauto. cbn. now rewrite H6. todo "lifting".
+        -- cbn. eapply expanded_tConstruct_app; eauto. cbn. now rewrite H6. 
+            todo "lifting".
       * eapply expanded_mkApps_tConstruct. split. split. red. all: eauto. 
         rewrite rev_map_spec. simpl_list. rewrite EE. lia. todo "induction on X0".
     + assert (Forall(fun t : term => expanded Σ0.1 (eta_expand Σ0.1.(declarations) t)) l). {
diff --git a/template-coq/theories/Extraction.v b/template-coq/theories/Extraction.v
index e068f4c12..0a005cd9f 100644
--- a/template-coq/theories/Extraction.v
+++ b/template-coq/theories/Extraction.v
@@ -7,14 +7,9 @@
 
 From Coq Require Ascii Extraction ZArith NArith.
 From MetaCoq.Template Require Import utils Ast Reflect Induction.
-From Coq Require Import FSets ExtrOcamlBasic ExtrOcamlString ExtrOCamlFloats
+From Coq Require Import FSets ExtrOcamlBasic ExtrOCamlFloats
     ExtrOCamlInt63.
 From MetaCoq.Template Require Import MC_ExtrOCamlZPosInt.
-
-Extract Constant ascii_compare =>
- "fun x y -> match Char.compare x y with 0 -> Eq | x when x < 0 -> Lt | _ -> Gt".
-Extract Constant Ascii.compare =>
- "fun x y -> match Char.compare x y with 0 -> Eq | x when x < 0 -> Lt | _ -> Gt".
  
 Extract Inductive Equations.Init.sigma => "( * )" ["(,)"].
 Extract Constant Equations.Init.pr1 => "fst".
diff --git a/template-coq/theories/Kernames.v b/template-coq/theories/Kernames.v
index 6670cb881..5613bff39 100644
--- a/template-coq/theories/Kernames.v
+++ b/template-coq/theories/Kernames.v
@@ -1,15 +1,83 @@
 
 (* Distributed under the terms of the MIT license. *)
-From Coq Require Import Lia MSetList OrderedTypeAlt OrderedTypeEx Ascii String.
-From MetaCoq.Template Require Import MCUtils BasicAst AstUtils.
+From Coq Require Import Lia MSetList OrderedTypeAlt OrderedTypeEx FMapAVL FMapFacts MSetAVL MSetFacts MSetProperties.
+From MetaCoq.Template Require Import utils.
 From Coq Require Import ssreflect.
+From Equations Require Import Equations.
 
+Local Open Scope string_scope2.
 Definition compare_ident := string_compare.
 
+(** ** Reification of names ** *)
+
+(** [Comment taken from Coq's code]
+    - Id.t is the type of identifiers, that is morally a subset of strings which
+      only contains Unicode characters of the Letter kind (and a few more).
+      => [ident]
+    - Name.t is an ad-hoc variant of Id.t option allowing to handle optionally
+      named objects.
+      => [name]
+    - DirPath.t represents generic paths as sequences of identifiers.
+      => [dirpath]
+    - Label.t is an equivalent of Id.t made distinct for semantical purposes.
+      => [ident]
+    - ModPath.t are module paths.
+      => [modpath]
+    - KerName.t are absolute names of objects in Coq.
+      => [kername]
+
+    And also :
+    - Constant.t => [kername]
+    - variable => [ident]
+    - MutInd.t => [kername]
+    - inductive => [inductive]
+    - constructor => [inductive * nat]
+    - Projection.t => [projection]
+    - GlobRef.t => global_reference
+
+    Finally, we define the models of primitive types (uint63 and floats64).
+*)
+
+Definition ident   := string. (* e.g. nat *)
+Definition qualid  := string. (* e.g. Datatypes.nat *)
+
+(** Type of directory paths. Essentially a list of module identifiers. The
+    order is reversed to improve sharing. E.g. A.B.C is ["C";"B";"A"] *)
+Definition dirpath := list ident.
+
 Module IdentOT := StringOT.
 
 Module DirPathOT := ListOrderedType IdentOT.
-  
+
+#[global] Instance dirpath_eqdec : Classes.EqDec dirpath := _.
+
+Definition string_of_dirpath (dp : dirpath) : string := 
+  String.concat "." (List.rev dp).
+
+(** The module part of the kernel name.
+    - MPfile is for toplevel libraries, i.e. .vo files
+    - MPbound are parameters of functors
+    - MPdot is for submodules
+*)
+Inductive modpath :=
+| MPfile  (dp : dirpath)
+| MPbound (dp : dirpath) (id : ident) (i : nat)
+| MPdot   (mp : modpath) (id : ident).
+Derive NoConfusion for modpath.
+
+Fixpoint string_of_modpath (mp : modpath) : string :=
+  match mp with
+  | MPfile dp => string_of_dirpath dp
+  | MPbound dp id n => string_of_dirpath dp ^ "." ^ id ^ "." ^ string_of_nat n
+  | MPdot mp id => string_of_modpath mp ^ "." ^ id
+  end.
+
+(** The absolute names of objects seen by kernel *)
+Definition kername := modpath × ident.
+
+Definition string_of_kername (kn : kername) :=
+  string_of_modpath kn.1 ^ "." ^ kn.2.
+
 (* Eval compute in DirPathOT.compare ["foo"; "bar"] ["baz"].
  *)
 
@@ -119,6 +187,21 @@ End ModPathComp.
 
 Module ModPathOT := OrderedType_from_Alt ModPathComp.
 
+Program Definition modpath_eq_dec (x y : modpath) : { x = y } + { x <> y } := 
+  match ModPathComp.compare x y with
+  | Eq => left _
+  | _ => right _
+  end.
+Next Obligation.
+  symmetry in Heq_anonymous.
+  now eapply ModPathComp.compare_eq in Heq_anonymous.
+Qed.
+Next Obligation.
+  rewrite ModPathOT.eq_refl in H. congruence.
+Qed.
+
+#[global] Instance modpath_EqDec : Classes.EqDec modpath := { eq_dec := modpath_eq_dec }.
+
 Module KernameComp.
   Definition t := kername.
 
@@ -152,7 +235,7 @@ Module KernameComp.
     
 End KernameComp.
 
-Module KernameOT.
+Module Kername.
  Include KernameComp.
  Module OT := OrderedType_from_Alt KernameComp.
 
@@ -191,19 +274,44 @@ Module KernameOT.
       now apply irreflexivity in H.
   Qed.
 
-  Definition eq_dec : forall x y, {eq x y} + {~ eq x y}.
-  Proof.
-    intros k k'. apply kername_eq_dec.
+  Definition eqb kn kn' := 
+    match compare kn kn' with
+    | Eq => true
+    | _ => false
+    end.
+
+  #[global, program] Instance reflect_kername : ReflectEq kername := {
+    eqb := eqb
+  }.
+  Next Obligation.
+    unfold eqb. destruct compare eqn:e; constructor.
+    - now apply compare_eq in e.
+    -intros e'; subst. now rewrite OT.eq_refl in e.
+    -intros e'; subst. now rewrite OT.eq_refl in e.
   Defined.
+  
+  Definition eq_dec : forall (x y : t), { x = y } + { x <> y } := Classes.eq_dec.
+
+End Kername.
+
+Module KernameMap := FMapAVL.Make Kername.OT.
+Module KernameMapFact := FMapFacts.WProperties KernameMap.
 
-End KernameOT.
+Notation eq_kername := (eqb (A:=kername)) (only parsing).
+
+Lemma eq_kername_refl kn : eq_kername kn kn.
+Proof.
+  eapply ReflectEq.eqb_refl.
+Qed.
+
+Definition eq_constant := eq_kername.
 
 (* Local Open Scope string_scope.*)
 (* Eval compute in KernameOT.compare (MPfile ["fdejrkjl"], "A") (MPfile ["lfrk;k"], "B"). *)
   
-Module KernameSet := MSetAVL.Make KernameOT.
-Module KernameSetFact := MSetFacts.WFactsOn KernameOT KernameSet.
-Module KernameSetProp := MSetProperties.WPropertiesOn KernameOT KernameSet.
+Module KernameSet := MSetAVL.Make Kername.
+Module KernameSetFact := MSetFacts.WFactsOn Kername KernameSet.
+Module KernameSetProp := MSetProperties.WPropertiesOn Kername KernameSet.
 
 Lemma knset_in_fold_left {A} kn f (l : list A) acc : 
   KernameSet.In kn (fold_left (fun acc x => KernameSet.union (f x) acc) l acc) <->
@@ -220,3 +328,96 @@ Proof.
       destruct ina as [<-|ina'];
       intuition auto. right. now exists a'.
 Qed.
+
+(** Designation of a (particular) inductive type. *)
+Record inductive : Set := mkInd { inductive_mind : kername ;
+                                  inductive_ind : nat }.
+Arguments mkInd _%bs _%nat.
+
+Derive NoConfusion for inductive.
+
+Definition string_of_inductive (i : inductive) :=
+  string_of_kername (inductive_mind i) ^ "," ^ string_of_nat (inductive_ind i).
+
+Definition eq_inductive_def i i' :=
+  let 'mkInd i n := i in
+  let 'mkInd i' n' := i' in
+  eqb (i, n) (i', n').
+
+#[global, program] Instance reflect_eq_inductive : ReflectEq inductive := {
+  eqb := eq_inductive_def
+}.
+Next Obligation.
+  destruct x as [m n], y as [m' n']; cbn -[eqb].
+  case: eqb_spec ; nodec.
+  cbn. constructor. noconf p; reflexivity.
+Qed.
+
+Notation eq_inductive := (eqb (A:=inductive)).
+
+Lemma eq_inductive_refl i : eq_inductive i i.
+Proof.
+  apply ReflectEq.eqb_refl.
+Qed.
+
+Definition projection : Set := inductive * nat (* params *) * nat (* argument *).
+
+Definition eq_projection (p p' : projection) := eqb p p'.
+
+#[global, program] Instance reflect_eq_projection : ReflectEq projection := {
+  eqb := eq_projection
+}.
+Next Obligation.
+  unfold eq_projection.
+  case: eqb_spec ; nodec.
+  cbn. now constructor.
+Qed.
+
+Lemma eq_projection_refl i : eq_projection i i.
+Proof.
+  apply ReflectEq.eqb_refl.
+Qed.
+
+(** Kernel declaration references [global_reference] *)
+Inductive global_reference :=
+| VarRef : ident -> global_reference
+| ConstRef : kername -> global_reference
+| IndRef : inductive -> global_reference
+| ConstructRef : inductive -> nat -> global_reference.
+
+Derive NoConfusion for global_reference.
+
+Definition string_of_gref gr : string :=
+  match gr with
+  | VarRef v => v
+  | ConstRef s => string_of_kername s
+  | IndRef (mkInd s n) =>
+    "Inductive " ^ string_of_kername s ^ " " ^ (string_of_nat n)
+  | ConstructRef (mkInd s n) k =>
+    "Constructor " ^ string_of_kername s ^ " " ^ (string_of_nat n) ^ " " ^ (string_of_nat k)
+  end.
+
+Definition gref_eqb (x y : global_reference) : bool :=
+  match x, y with
+  | VarRef i, VarRef i' => eqb i i'
+  | ConstRef c, ConstRef c' => eqb c c'
+  | IndRef i, IndRef i' => eqb i i'
+  | ConstructRef i k, ConstructRef i' k' => eqb i i' && eqb k k'
+  | _, _ => false
+  end.
+
+#[global, program] Instance grep_reflect_eq : ReflectEq global_reference := 
+  {| eqb := gref_eqb |}.
+Next Obligation.
+  destruct x, y; cbn; try constructor; try congruence.
+  - destruct (eqb_spec i i0); constructor; subst; auto; congruence.
+  - destruct (eqb_spec k k0); constructor; subst; auto; congruence.
+  - destruct (eqb_spec i i0); constructor; subst; auto; congruence.
+  - destruct (eqb_spec i i0); subst; cbn; auto; try constructor; try congruence.
+    destruct (eqb_spec n n0); constructor; subst; congruence.
+Defined.
+
+Definition gref_eq_dec (gr gr' : global_reference) : {gr = gr'} + {~ gr = gr'} := Classes.eq_dec gr gr'.
+
+#[global] Hint Resolve Kername.eq_dec : eq_dec.
+
diff --git a/template-coq/theories/Pretty.v b/template-coq/theories/Pretty.v
index 5ecda6ab0..7cda8f889 100644
--- a/template-coq/theories/Pretty.v
+++ b/template-coq/theories/Pretty.v
@@ -3,7 +3,6 @@ From MetaCoq Require Import utils Ast AstUtils Environment LiftSubst Universes.
 
 (** * Pretty printing *)
 
-
 Section print_term.
   Context (Σ : global_env_ext).
 
@@ -20,7 +19,7 @@ Section print_term.
     end.
 
   Definition is_fresh (Γ : list ident) (id : ident) :=
-    List.forallb (fun id' => negb (ident_eq id id')) Γ.
+    List.forallb (fun id' => negb (eqb id id')) Γ.
 
   Definition lookup_ind_decl ind i :=
     match lookup_env Σ ind with
@@ -43,7 +42,7 @@ Section print_term.
     | tConst c u => "x"
     | tInd (mkInd i k) u =>
       match lookup_ind_decl i k with
-      | Some body => substring 0 1 (body.(ind_name))
+      | Some body => String.substring 0 1 (body.(ind_name))
       | None => "X"
       end
     (* | tInt _ => "i" *)
@@ -110,15 +109,28 @@ Section print_term.
         end in
     aux Γ (MCList.rev Γ').
 
-  Definition print_defs (print_term : list ident -> bool -> term -> string)
+End print_term.
+
+Module PrintTermTree.
+  Import bytestring.Tree.
+  Infix "^" := append.
+
+  Section env.
+  Context (Σ : global_env_ext).
+
+  Definition print_def {A} (f : A -> t) (g : A -> t) (def : def A) :=
+    string_of_name (binder_name (dname def)) ^ " { struct " ^ string_of_nat (rarg def) ^ " }" ^
+                 " : " ^ f (dtype def) ^ " := " ^ nl ^ g (dbody def).
+
+  Definition print_defs (print_term : list ident -> bool -> term -> t)
              Γ
              (defs : mfixpoint term) :=
     let ctx' := fix_context defs in
-    print_list (print_def (print_term Γ true) (print_term (fresh_names Γ ctx') true))
+    print_list (print_def (print_term Γ true) (print_term (fresh_names Σ Γ ctx') true))
                (nl ^ " with ") defs.
 
   (* TODO: SPROP: we ignore relevance on printing, maybe add print config? *)
-  Fixpoint print_term (Γ : list ident) (top : bool) (t : term) {struct t} :=
+  Fixpoint print_term (Γ : list ident) (top : bool) (t : term) {struct t} : Tree.t :=
   match t with
   | tRel n =>
     match nth_error Γ n with
@@ -130,7 +142,7 @@ Section print_term.
   | tSort s => string_of_sort s
   | tCast c k t => parens top (print_term Γ true c ^ ":"  ^ print_term Γ true t)
   | tProd na dom codom =>
-    let na' := (fresh_name Γ na.(binder_name) (Some dom)) in
+    let na' := (fresh_name Σ Γ na.(binder_name) (Some dom)) in
     if (noccur_between 0 1 codom) then
       parens top
       (print_term Γ false dom ^ " → " ^ print_term (na' :: Γ) true codom)
@@ -138,11 +150,11 @@ Section print_term.
            ("∀ " ^ na' ^ " : " ^
                      print_term Γ false dom ^ ", " ^ print_term (na' :: Γ) true codom)
   | tLambda na dom body =>
-    let na' := (fresh_name Γ na.(binder_name) (Some dom)) in
+    let na' := (fresh_name Σ Γ na.(binder_name) (Some dom)) in
     parens top ("fun " ^ na' ^ " : " ^ print_term Γ true dom
                                 ^ " ⇒ " ^ print_term (na' :: Γ) true body)
   | tLetIn na def dom body =>
-    let na' := (fresh_name Γ na.(binder_name) (Some dom)) in
+    let na' := (fresh_name Σ Γ na.(binder_name) (Some dom)) in
     parens top ("let " ^ na' ^ " : " ^ print_term Γ true dom ^
                       " := " ^ print_term Γ true def ^ " in " ^ nl ^
                       print_term (na' :: Γ) true body)
@@ -150,13 +162,13 @@ Section print_term.
     parens top (print_term Γ false f ^ " " ^ print_list (print_term Γ false) " " l)
   | tConst c u => string_of_kername c ^ print_universe_instance u
   | tInd (mkInd i k) u =>
-    match lookup_ind_decl i k with
+    match lookup_ind_decl Σ i k with
     | Some oib => oib.(ind_name) ^ print_universe_instance u
     | None =>
       "UnboundInd(" ^ string_of_inductive (mkInd i k) ^ "," ^ string_of_universe_instance u ^ ")"
     end
   | tConstruct (mkInd i k as ind) l u =>
-    match lookup_ind_decl i k with
+    match lookup_ind_decl Σ i k with
     | Some oib =>
       match nth_error oib.(ind_ctors) l with
       | Some cb => cb.(cstr_name) ^ print_universe_instance u
@@ -169,7 +181,7 @@ Section print_term.
                           ^ string_of_universe_instance u ^ ")"
     end
   | tCase {| ci_ind := mkInd mind i as ind; ci_npar := pars |} p t brs =>
-    match lookup_ind_decl mind i with
+    match lookup_ind_decl Σ mind i with
     | Some oib =>
       match build_return_context ind oib p with
       | None =>
@@ -178,17 +190,17 @@ Section print_term.
                 string_of_list (pretty_string_of_branch string_of_term) brs ^ ")"
 
       | Some Γret =>
-        let Γret := fresh_names Γ Γret in
+        let Γret := fresh_names Σ Γ Γret in
         let ret_binders := firstn #|pcontext p| Γret in
         let (as_name, indices) := (hd "_" ret_binders, MCList.rev (tail ret_binders)) in
-        let in_args := repeat "_" #|pparams p| ++ indices in
-        let in_str := oib.(ind_name) ^ String.concat "" (map (fun a => " " ^ a) in_args) in
+        let in_args := (repeat "_" #|pparams p| ++ indices)%list in
+        let in_str := oib.(ind_name) ^ concat "" (map (fun a : bytestring.string => " " ^ a) in_args) in
 
         let fix print_branch Γ names prbr {struct names} :=
             match names with
             | [] => "⇒ " ^ prbr Γ
             | na :: l =>
-              let na' := (fresh_name Γ na.(binder_name) None) in
+              let na' := (fresh_name Σ Γ na.(binder_name) None) in
                 na' ^ "  " ^ print_branch (na' :: Γ) l prbr
             end
         in
@@ -210,7 +222,7 @@ Section print_term.
               string_of_list (pretty_string_of_branch string_of_term) brs ^ ")"
     end
   | tProj (mkInd mind i as ind, pars, k) c =>
-    match lookup_ind_decl mind i with
+    match lookup_ind_decl Σ mind i with
     | Some oib =>
       match nth_error oib.(ind_projs) k with
       | Some (na, _) => print_term Γ false c ^ ".(" ^ na ^ ")"
@@ -234,74 +246,83 @@ Section print_term.
   | tFloat f => "Float(" ^ string_of_float f ^ ")" *)
   end.
 
-End print_term.
-
-Definition pr_context_decl (Σ : global_env_ext) Γ (c : context_decl) : ident * string :=
-  match c with
-  | {| decl_name := na; decl_type := ty; decl_body := None |} => 
-    let na' := (fresh_name Σ Γ na.(binder_name) (Some ty)) in
-    (na', ("(" ++ na' ++ " : " ++ print_term Σ Γ true ty ++ ")")%string)
-  | {| decl_name := na; decl_type := ty; decl_body := Some b |} =>
-    let na' := (fresh_name Σ Γ na.(binder_name) (Some ty)) in
-    (na', ("(" ++ na' ++ " : " ++ print_term Σ Γ true ty ++ " := " ++
-      print_term Σ Γ true b ++ ")")%string)
-  end.
+  Definition pr_context_decl Γ (c : context_decl) : ident * t :=
+    match c with
+    | {| decl_name := na; decl_type := ty; decl_body := None |} => 
+      let na' := (fresh_name Σ Γ na.(binder_name) (Some ty)) in
+      (na', ("(" ^ na' ^ " : " ^ print_term Γ true ty ^ ")"))
+    | {| decl_name := na; decl_type := ty; decl_body := Some b |} =>
+      let na' := (fresh_name Σ Γ na.(binder_name) (Some ty)) in
+      (na', ("(" ^ na' ^ " : " ^ print_term Γ true ty ^ " := " ^
+        print_term Γ true b ^ ")"))
+    end.
 
-Fixpoint print_context Σ Γ Δ :=
-  match Δ with
-  | [] => (Γ, ""%string)
-  | d :: decls => 
-    let '(Γ, s) := print_context Σ Γ decls in
-    let '(na, s') := pr_context_decl Σ Γ d in
-    match decls with
-    | [] => (na :: Γ, (s ++ s')%string)
-    | _ => (na :: Γ, (s ++ " " ++ s')%string)
-    end
-  end.
+  Fixpoint print_context Γ Δ : list ident * t :=
+    match Δ with
+    | [] => (Γ, "" : t)
+    | d :: decls => 
+      let '(Γ, s) := print_context Γ decls in
+      let '(na, s') := pr_context_decl Γ d in
+      match decls with
+      | [] => (na :: Γ, s ^ s')
+      | _ => (na :: Γ, s ^ " " ^ s')
+      end
+    end.
 
-Definition print_one_cstr Σ Γ (mib : mutual_inductive_body) (c : constructor_body) : string :=
-  let '(Γargs, s) := print_context Σ Γ c.(cstr_args) in
-  c.(cstr_name) ++ " : " ++ s ++ "_" ++ print_list (print_term Σ Γargs true) " " c.(cstr_indices).
+  Definition print_one_cstr Γ (mib : mutual_inductive_body) (c : constructor_body) : t :=
+    let '(Γargs, s) := print_context Γ c.(cstr_args) in
+    c.(cstr_name) ^ " : " ^ s ^ "_" ^ print_list (print_term Γargs true) " " c.(cstr_indices).
   
-Definition print_one_ind (short : bool) Σ Γ (mib : mutual_inductive_body) (oib : one_inductive_body) : string :=
-  let '(Γpars, spars) := print_context Σ Γ mib.(ind_params) in
-  let '(Γinds, sinds) := print_context Σ Γpars oib.(ind_indices) in
-  oib.(ind_name) ++ spars ++ sinds ++ print_term Σ Γinds true (tSort oib.(ind_sort)) ++ ":=" ++ nl ++
-  if short then "..."
-  else print_list (print_one_cstr Σ Γpars mib) nl oib.(ind_ctors).
+  Definition print_one_ind (short : bool) Γ (mib : mutual_inductive_body) (oib : one_inductive_body) : t :=
+    let '(Γpars, spars) := print_context Γ mib.(ind_params) in
+    let '(Γinds, sinds) := print_context Γpars oib.(ind_indices) in
+    oib.(ind_name) ^ spars ^ sinds ^ print_term Γinds true (tSort oib.(ind_sort)) ^ ":=" ^ nl ^
+    if short then "..."
+    else print_list (print_one_cstr Γpars mib) nl oib.(ind_ctors).
+  End env.
 
-Fixpoint print_env_aux (short : bool) (prefix : nat) (Σ : global_env) (acc : string) := 
-  match prefix with 
-  | 0 => match Σ.(declarations) with [] => acc | _ => ("..." ++ nl ++ acc)%string end
-  | S n => 
-  let univs := Σ.(Env.universes) in
-  match Σ.(declarations) with
-  | [] => acc
-  | (kn, InductiveDecl mib) :: Σ => 
-    let Σ' := ({| Env.universes := univs; declarations := Σ |}, mib.(ind_universes)) in
-    let names := fresh_names Σ' [] (arities_context mib.(ind_bodies)) in
-    print_env_aux short n Σ'.1
-      ("Inductive " ++ 
-       print_list (print_one_ind short Σ' names mib) nl mib.(ind_bodies) ++ "." ++ 
-       nl ++ acc)%string
-  | (kn, ConstantDecl cb) :: Σ =>
-    let Σ' := ({| Env.universes := univs; declarations := Σ |}, cb.(cst_universes)) in
-    print_env_aux short n Σ'.1
-      ((match cb.(cst_body) with 
-        | Some _ => "Definition "
-        | None => "Axiom "
-      end) ++ string_of_kername kn ++ " : " ++ print_term Σ' nil true cb.(cst_type) ++
-      match cb.(cst_body) with
-      | Some b => 
-        if short then ("..." ++ nl)%string
-        else (" := " ++ nl ++ print_term Σ' nil true b ++ "." ++ nl)
-      | None => "."
-      end ++ acc)%string
-  end
-  end.
+  Fixpoint print_env_aux (short : bool) (prefix : nat) (Σ : global_env) (acc : t) : t := 
+    match prefix with 
+    | 0 => match Σ.(declarations) with [] => acc | _ => ("..." ^ nl ^ acc) end
+    | S n => 
+      let univs := Σ.(Env.universes) in
+      match Σ.(declarations) with
+      | [] => acc
+      | (kn, InductiveDecl mib) :: Σ => 
+        let Σ' := ({| Env.universes := univs; declarations := Σ |}, mib.(ind_universes)) in
+        let names := fresh_names Σ' [] (arities_context mib.(ind_bodies)) in
+        print_env_aux short n Σ'.1
+          ("Inductive " ^ 
+          print_list (print_one_ind Σ' short names mib) nl mib.(ind_bodies) ^ "." ^ 
+          nl ^ acc)
+      | (kn, ConstantDecl cb) :: Σ =>
+        let Σ' := ({| Env.universes := univs; declarations := Σ |}, cb.(cst_universes)) in
+        print_env_aux short n Σ'.1
+          ((match cb.(cst_body) with 
+            | Some _ => "Definition "
+            | None => "Axiom "
+          end) ^ string_of_kername kn ^ " : " ^ print_term Σ' nil true cb.(cst_type) ^
+          match cb.(cst_body) with
+          | Some b => 
+            if short then ("..." ^ nl)
+            else (" := " ^ nl ^ print_term Σ' nil true b ^ "." ^ nl)
+          | None => "."
+          end ^ acc)
+      end
+    end.
+
+  Definition print_env (short : bool) (prefix : nat) Σ := 
+    print_env_aux short prefix Σ (Tree.string "").
+
+  Definition print_program (short : bool) (prefix : nat) (p : program) : t := 
+    print_env short prefix (fst p) ^ nl ^ print_term (empty_ext (fst p)) nil true (snd p). 
+
+End PrintTermTree.
+
+Definition print_term Σ Γ top := Tree.to_string ∘ PrintTermTree.print_term Σ Γ top.
 
-Definition print_env (short : bool) (prefix : nat) Σ := print_env_aux short prefix Σ EmptyString.
+Definition print_env (short : bool) (prefix : nat) Σ := 
+  Tree.to_string (PrintTermTree.print_env short prefix Σ).
 
 Definition print_program (short : bool) (prefix : nat) (p : program) : string := 
-  print_env short prefix (fst p) ++ nl ++
-  print_term (empty_ext (fst p)) nil true (snd p). 
+  Tree.to_string (PrintTermTree.print_program short prefix p).
diff --git a/template-coq/theories/Reflect.v b/template-coq/theories/Reflect.v
index 468a5ab1a..482784eaa 100644
--- a/template-coq/theories/Reflect.v
+++ b/template-coq/theories/Reflect.v
@@ -5,108 +5,8 @@ From MetaCoq.Template Require Import utils BasicAst Universes.
 Require Import ssreflect.
 From Equations Require Import Equations.
 
-(* Some reflection / EqDec lemmata *)
-
-Class ReflectEq A := {
-  eqb : A -> A -> bool ;
-  eqb_spec : forall x y : A, reflect (x = y) (eqb x y)
-}.
-
-Lemma eqb_eq {A} `{ReflectEq A} (x y : A) : eqb x y -> x = y.
-Proof.
-  elim: eqb_spec; auto.
-  discriminate.
-Qed.
-
-#[global] Instance ReflectEq_EqDec :
-  forall A, ReflectEq A -> EqDec A.
-Proof.
-  intros A [eqb h] x y.
-  destruct (h x y).
-  - left. assumption.
-  - right. assumption.
-Defined.
-
-Definition eq_dec_to_bool {A} `{EqDec A} x y :=
-  match eq_dec x y with
-  | left _ => true
-  | right _ => false
-  end.
-
-#[global] (* Not an instance to avoid loops? *)
-Lemma EqDec_ReflectEq : forall A `{EqDec A}, ReflectEq A.
-Proof.
-  intros A h.
-  unshelve econstructor.
-  - eapply eq_dec_to_bool.
-  - unfold eq_dec_to_bool.
-    intros x y. destruct (eq_dec x y).
-    all: constructor ; assumption.
-Defined.
-
-Ltac nodec :=
-  let bot := fresh "bot" in
-  try solve [ constructor ; intro bot ; inversion bot ; subst ; tauto ].
-
-Definition eq_option {A} (eqA : A -> A -> bool) (u v : option A) : bool :=
-  match u, v with
-  | Some u, Some v => eqA u v
-  | None, None => true
-  | _, _ => false
-  end.
-
-#[global] Instance reflect_option : forall {A}, ReflectEq A -> ReflectEq (option A).
-Proof.
-  intros A RA. refine {| eqb := eq_option eqb |}.
-  intros x y. destruct x, y.
-  all: cbn.
-  all: try solve [ constructor ; easy ].
-  destruct (eqb_spec a a0) ; nodec.
-  constructor. f_equal. assumption.
-Defined.
-
-Fixpoint eq_list {A} (eqA : A -> A -> bool) (l l' : list A) : bool :=
-  match l, l' with
-  | a :: l, a' :: l' =>
-    if eqA a a' then eq_list eqA l l'
-    else false
-  | [], [] => true
-  | _, _ => false
-  end.
-
-#[global] Instance reflect_list : forall {A}, ReflectEq A -> ReflectEq (list A).
-Proof.
-  intros A RA. refine {| eqb := eq_list eqb |}.
-  intro x. induction x ; intro y ; destruct y.
-  - cbn. constructor. reflexivity.
-  - cbn. constructor. discriminate.
-  - cbn. constructor. discriminate.
-  - cbn. destruct (eqb_spec a a0) ; nodec.
-    destruct (IHx y) ; nodec.
-    subst. constructor. reflexivity.
-Defined.
-
-#[global] Program Instance reflect_string : ReflectEq string := {
-  eqb := eq_string
-}.
-Next Obligation.
-  rename x into s, y into s'.
-  destruct (string_dec s s').
-  - subst. rewrite eq_string_refl. constructor. reflexivity.
-  - assert (string_compare s s' <> Eq).
-    { intro bot. apply n. apply string_compare_eq. assumption. }
-    unfold eq_string. destruct (string_compare s s').
-    + tauto.
-    + constructor. assumption.
-    + constructor. assumption.
-Defined.
-
-#[global] Instance reflect_nat : ReflectEq nat := {
-  eqb_spec := Nat.eqb_spec
-}.
-
-#[program,global] Instance reflect_prim_int : ReflectEq Numbers.Cyclic.Int63.Uint63.int :=
-  { eqb := Numbers.Cyclic.Int63.Uint63.eqb }.
+#[program,global] Instance reflect_prim_int : ReflectEq Numbers.Cyclic.Int63.Int63.int :=
+  { eqb := Numbers.Cyclic.Int63.Int63.eqb }.
 Next Obligation.
   destruct (Uint63.eqb x y) eqn:eq; constructor.
   now apply (Numbers.Cyclic.Int63.Uint63.eqb_spec x y) in eq.
@@ -122,34 +22,12 @@ Instance reflect_prim_float : ReflectEq PrimFloat.float :=
   { eqb x y := eqb (ReflectEq := EqDec_ReflectEq SpecFloat.spec_float) (FloatOps.Prim2SF x) (FloatOps.Prim2SF y) }.
 Next Obligation.
   intros. cbn -[eqb].
-  destruct (eqb_spec (ReflectEq := EqDec_ReflectEq SpecFloat.spec_float) (FloatOps.Prim2SF x) (FloatOps.Prim2SF y)); constructor.
+  destruct (eqb_spec (ReflectEq := EqDec_ReflectEq SpecFloat.spec_float) (FloatOps.Prim2SF x) (FloatOps.Prim2SF y)) as [H|H]; constructor.
   now apply FloatAxioms.Prim2SF_inj.
-  intros e; apply n. rewrite e.
+  intros e; apply H. rewrite e.
   reflexivity.
 Qed.
 
-Definition eq_level l1 l2 :=
-  match l1, l2 with
-  | Level.lzero, Level.lzero => true
-  | Level.Level s1, Level.Level s2 => eqb s1 s2
-  | Level.Var n1, Level.Var n2 => eqb n1 n2
-  | _, _ => false
-  end.
-
-#[global, program] Instance reflect_level : ReflectEq Level.t := {
-  eqb := eq_level
-}.
-Next Obligation.
-  destruct x, y.
-  all: unfold eq_level.
-  all: try solve [ constructor ; reflexivity ].
-  all: try solve [ constructor ; discriminate ].
-  - destruct (eqb_spec s s0) ; nodec.
-    constructor. f_equal. assumption.
-  - destruct (eqb_spec n n0) ; nodec.
-    constructor. subst. reflexivity.
-Defined.
-
 Definition eq_prop_level l1 l2 :=
   match l1, l2 with
   | PropLevel.lProp, PropLevel.lProp => true
@@ -185,47 +63,6 @@ Next Obligation.
   constructor; cong.
 Defined.
 
-Definition eq_prod {A B} (eqA : A -> A -> bool) (eqB : B -> B -> bool) x y :=
-  let '(a1, b1) := x in
-  let '(a2, b2) := y in
-  if eqA a1 a2 then eqB b1 b2
-  else false.
-
-Local Obligation Tactic := idtac.
-#[global, program] Instance reflect_prod : forall {A B}, ReflectEq A -> ReflectEq B -> ReflectEq (A * B) := {
-  eqb := eq_prod eqb eqb
-}.
-Next Obligation.
-  intros A B RA RB [x y] [u v].
-  unfold eq_prod.
-  destruct (eqb_spec x u) ; nodec.
-  destruct (eqb_spec y v) ; nodec.
-  subst. constructor. reflexivity.
-Defined.
-
-Lemma eq_prod_refl :
-  forall A B (eqA : A -> A -> bool) (eqB : B -> B -> bool),
-    (forall a, eqA a a) ->
-    (forall b, eqB b b) ->
-    forall p, eq_prod eqA eqB p p.
-Proof.
-  intros A B eqA eqB eqA_refl eqB_refl [a b].
-  simpl. rewrite eqA_refl. apply eqB_refl.
-Qed.
-
-Definition eq_bool b1 b2 : bool :=
-  if b1 then b2 else negb b2.
-
-#[global, program] Instance reflect_bool : ReflectEq bool := {
-  eqb := eq_bool
-}.
-Next Obligation.
-  intros x y. unfold eq_bool.
-  destruct x, y.
-  all: constructor.
-  all: try reflexivity.
-  all: discriminate.
-Defined.
 
 Definition eq_name na nb :=
   match na, nb with
@@ -278,26 +115,6 @@ Next Obligation.
   constructor; destruct x, y; simpl in *; cong.
 Defined.
 
-#[global, program] Instance reflect_kername : ReflectEq kername := {
-  eqb := eq_kername
-}.
-Next Obligation.
-  intros; unfold eq_kername; destruct kername_eq_dec; now constructor.
-Qed.
-
-
-#[global, program] Instance reflect_inductive : ReflectEq inductive := {
-  eqb := eq_inductive
-}.
-Next Obligation.
-  intros i i'. destruct i as [m n], i' as [m' n']; cbn.
-  change (eq_kername m m') with (eqb m m').
-  change (n =? n') with (eqb n n').
-  destruct (eqb_spec m m') ; nodec.
-  destruct (eqb_spec n n') ; nodec.
-  cbn. constructor. subst. reflexivity.
-Defined.
-
 Definition eq_def {A} `{ReflectEq A} (d1 d2 : def A) : bool :=
   match d1, d2 with
   | mkdef n1 t1 b1 a1, mkdef n2 t2 b2 a2 =>
@@ -348,44 +165,8 @@ Proof.
   now inversion 1. intros ->. f_equal. apply uip.
 Qed.
 
-(* move in Universes.v ?? *)
-#[global] Instance eq_dec_UnivExpr : EqDec UnivExpr.t.
-Proof. intros e e'. decide equality; apply eq_dec. Qed.
-
-#[global] Instance eq_dec_univ0 : EqDec Universe.nonEmptyUnivExprSet.
-Proof.
-  intros u v.
-  assert (H : {UnivExprSet.elements u = UnivExprSet.elements v}
-              + {~ UnivExprSet.elements u = UnivExprSet.elements v}). {
-    decide equality. apply eq_dec. }
-  destruct H as [H|H]; [left; now apply eq_universe_iff' in H|right].
-  intro X; apply H; now apply eq_universe_iff' in X.
-Defined.
-
-#[global] Instance eq_dec_univ : EqDec Universe.t.
-Proof.
-  red. decide equality.
-  apply eq_dec_univ0.
-Defined.
-
-#[global] Instance reflect_eq_univ : ReflectEq Universe.t := EqDec_ReflectEq _.
-
 #[global] Instance reflect_case_info : ReflectEq case_info := EqDec_ReflectEq case_info.
 
-Definition eq_sig_true {A f} `{ReflectEq A} (x y : { z : A | f z = true }) : bool :=
-  let '(exist x hx) := x in
-  let '(exist y hy) := y in
-  eqb x y.
-
-#[global, program] Instance reflect_sig_true {A f} `{ReflectEq A} : ReflectEq ({ z : A | f z = true }) := {
-  eqb := eq_sig_true
-}.
-Next Obligation.
-  intros A f RA. intros [x hx] [y hy]. simpl.
-  destruct (eqb_spec x y) ; nodec. subst.
-  constructor. pose proof (uip hx hy). subst. reflexivity.
-Defined.
-
 Derive NoConfusion NoConfusionHom for sig.
 Derive NoConfusion NoConfusionHom for prod.
 
@@ -435,12 +216,11 @@ Proof.
   cong.
 Defined.
 
-#[global] Instance Z_as_int : ReflectEq Int.Z_as_Int.t.
-Proof.
-  refine {| eqb := Z.eqb |}.
-  apply Z.eqb_spec.
-Defined.
-
+#[global, program] Instance Z_as_int : ReflectEq Int.Z_as_Int.t :=
+  { eqb := Z.eqb }.
+Next Obligation.
+  apply (reflect_reflectProp_2 Z.eqb_spec).
+Qed.
 
 Scheme level_lt_ind_dep := Induction for Level.lt_ Sort Prop.
 Scheme constraint_type_lt_ind_dep := Induction for ConstraintType.lt_ Sort Prop.
diff --git a/template-coq/theories/ReflectAst.v b/template-coq/theories/ReflectAst.v
index e3f942703..0c36570de 100644
--- a/template-coq/theories/ReflectAst.v
+++ b/template-coq/theories/ReflectAst.v
@@ -30,9 +30,9 @@ Local Ltac term_dec_tac term_dec :=
          | x : list aname, y : list aname |- _ =>
            fcase (eq_dec x y)
          | n : nat, m : nat |- _ => fcase (Nat.eq_dec n m)
-         | i : ident, i' : ident |- _ => fcase (string_dec i i')
-         | i : kername, i' : kername |- _ => fcase (kername_eq_dec i i')
-         | i : string, i' : kername |- _ => fcase (string_dec i i')
+         | i : ident, i' : ident |- _ => fcase (eq_dec i i')
+         | i : kername, i' : kername |- _ => fcase (eq_dec i i')
+         | i : string, i' : kername |- _ => fcase (eq_dec i i')
          | n : name, n' : name |- _ => fcase (eq_dec n n')
          | n : aname, n' : aname |- _ => fcase (eq_dec n n')
          | i : inductive, i' : inductive |- _ => fcase (eq_dec i i')
diff --git a/template-coq/theories/Typing.v b/template-coq/theories/Typing.v
index be385100a..9c93b544b 100644
--- a/template-coq/theories/Typing.v
+++ b/template-coq/theories/Typing.v
@@ -682,7 +682,7 @@ Definition isCoFinite (r : recursivity_kind) :=
 
 Definition check_recursivity_kind (Σ : global_env) ind r :=
   match lookup_env Σ ind with
-  | Some (InductiveDecl mib) => Reflect.eqb mib.(ind_finite) r
+  | Some (InductiveDecl mib) => eqb mib.(ind_finite) r
   | _ => false
   end.
 
@@ -708,7 +708,7 @@ Definition wf_fixpoint (Σ : global_env) mfix :=
   | Some (ind :: inds) =>
     (* Check that mutually recursive fixpoints are all on the same mututal
         inductive block *)
-    forallb (Reflect.eqb ind) inds &&
+    forallb (eqb ind) inds &&
     check_recursivity_kind Σ ind Finite
   | _ => false
   end.
@@ -731,7 +731,7 @@ Definition wf_cofixpoint (Σ : global_env) mfix :=
   | Some (ind :: inds) =>
     (* Check that mutually recursive cofixpoints are all producing
         coinductives in the same mututal coinductive block *)
-    forallb (Reflect.eqb ind) inds &&
+    forallb (eqb ind) inds &&
     check_recursivity_kind Σ ind CoFinite
   | _ => false
   end.
@@ -1539,12 +1539,11 @@ Lemma lookup_on_global_env `{checker_flags} {P} {Σ : global_env} {c decl} :
 Proof.
   unfold on_global_env.
   destruct Σ as [univs Σ]; cbn. intros [cu ond].
-  induction ond; simpl in * => //.
-  unfold eq_kername. destruct kername_eq_dec; subst.
-  - intros [= ->].
-    exists ({| universes := univs; declarations := Σ |}, udecl).
+  induction ond; cbn in * => //.
+  case: eqb_specT => [-> [= <-]| ne].
+  - exists ({| universes := univs; declarations := Σ |}, udecl).
     split; try constructor; tas.
-    cbn. now split => //; exists [(kn, decl)].
+    cbn. now split => //; exists [(kn, d)].
   - intros hl.
     destruct (IHond hl) as [[Σ' udecl'] [ong [[equ ext] ond']]].
     exists (Σ', udecl'). cbn in equ |- *. subst univs. repeat split; cbn; auto; try apply ong.
diff --git a/template-coq/theories/TypingWf.v b/template-coq/theories/TypingWf.v
index c556557d2..9188fab05 100644
--- a/template-coq/theories/TypingWf.v
+++ b/template-coq/theories/TypingWf.v
@@ -196,21 +196,17 @@ Proof.
   destruct Σ as [univs Σ]; cbn in *.
   rewrite /lookup_env /on_global_env /=.
   induction Σ in univs, Σ', k, d |- *; cbn => //.
-  destruct eq_kername eqn:eqk.
+  destruct (eqb_spec k a.1) as [e|e].
   * move=> wfΣ' [=]. intros <- ext.
     destruct ext as [univeq [Σ'' eq]] => /=. cbn in *.
     subst univs. rewrite eq in wfΣ'.
     destruct Σ' as [univs' Σ']; cbn in *.
     subst Σ'. destruct wfΣ' as [cu wfΣ'].
     induction Σ''. 
-    + cbn. now rewrite eqk.
-    + cbn. destruct (eq_kername k a0.1) eqn:eqk' => //.
-      change (eq_kername k a.1) with (Reflect.eqb k a.1) in eqk.
-      change (eq_kername k a0.1) with (Reflect.eqb k a0.1) in eqk'.
-      eapply eqb_eq in eqk. apply eqb_eq in eqk'. subst.
-      apply on_global_decls_extends_not_fresh in wfΣ'; eauto.
-      apply IHΣ''.
-      now depelim wfΣ'.
+    + cbn. now rewrite e eq_kername_refl.
+    + cbn. destruct (eqb_spec k a0.1) => //. subst.
+      { apply on_global_decls_extends_not_fresh in wfΣ'; eauto. }
+      subst. apply IHΣ''. now depelim wfΣ'.
   * intros HΣ' Hl [univeq [Σ'' eq]]; cbn in *. subst univs.
     rewrite eq in HΣ'. destruct HΣ'.
     eapply IHΣ; tea. split; eauto. now rewrite eq.
diff --git a/template-coq/theories/Universes.v b/template-coq/theories/Universes.v
index c6ecb6659..abfe621a3 100644
--- a/template-coq/theories/Universes.v
+++ b/template-coq/theories/Universes.v
@@ -1,6 +1,6 @@
 From Coq Require Import MSetList MSetAVL MSetFacts MSetProperties MSetDecide.
-From MetaCoq.Template Require Import utils BasicAst config.
 From Equations Require Import Equations.
+From MetaCoq.Template Require Import utils BasicAst config.
 Require Import ssreflect.
 
 Local Open Scope nat_scope.
@@ -40,13 +40,14 @@ Inductive allowed_eliminations : Set :=
 | IntoAny.
 Derive NoConfusion EqDec for allowed_eliminations.
 
+
 (** Levels are Set or Level or Var *)
 Module Level.
   Inductive t_ : Set :=
   | lzero
   | Level (_ : string)
   | Var (_ : nat) (* these are debruijn indices *).
-  Derive NoConfusion EqDec for t_.
+  Derive NoConfusion for t_.
 
   Definition t := t_.
 
@@ -84,11 +85,6 @@ Module Level.
   Definition eq : t -> t -> Prop := eq.
   Definition eq_equiv : Equivalence eq := _.
 
-  Definition eq_dec (l1 l2 : t) : {l1 = l2}+{l1 <> l2}.
-  Proof.
-    decide equality. apply string_dec. apply Peano_dec.eq_nat_dec.
-  Defined.
-
   Inductive lt_ : t -> t -> Prop :=
   | ltSetLevel s : lt_ lzero (Level s)
   | ltSetVar n : lt_ lzero (Var n)
@@ -137,7 +133,7 @@ Module Level.
   Global Instance eqb_refl : Reflexive eqb.
   Proof.
     intros []; unfold eqb; cbnr.
-    - rewrite (ssreflect.iffRL (string_compare_eq s s)). all: auto. reflexivity.
+    - rewrite (ssreflect.iffRL (string_compare_eq _ _)). all: auto. reflexivity.
     - rewrite Nat.compare_refl. reflexivity.
   Qed.
 
@@ -145,7 +141,7 @@ Module Level.
   Proof.
     destruct l, l'; cbn; try constructor; try reflexivity; try discriminate.
     - apply iff_reflect. unfold eqb; cbn.
-      destruct (CompareSpec_string s s0); split; intro HH;
+      destruct (CompareSpec_string t0 t1); split; intro HH;
         try reflexivity; try discriminate; try congruence.
       all: inversion HH; subst; now apply irreflexivity in H.
     - apply iff_reflect. unfold eqb; cbn.
@@ -154,7 +150,31 @@ Module Level.
       all: inversion HH; subst; now apply Nat.lt_irrefl in H.
   Qed.
 
+  Definition eq_level l1 l2 :=
+    match l1, l2 with
+    | Level.lzero, Level.lzero => true
+    | Level.Level s1, Level.Level s2 => ReflectEq.eqb s1 s2
+    | Level.Var n1, Level.Var n2 => ReflectEq.eqb n1 n2
+    | _, _ => false
+    end.
+  
+  #[global, program] Instance reflect_level : ReflectEq Level.t := {
+    eqb := eq_level
+  }.
+  Next Obligation.
+    destruct x, y.
+    all: unfold eq_level.
+    all: try solve [ constructor ; reflexivity ].
+    all: try solve [ constructor ; discriminate ].
+    - destruct (ReflectEq.eqb_spec t0 t1) ; nodec.
+      constructor. f_equal. assumption.
+    - destruct (ReflectEq.eqb_spec n n0) ; nodec.
+      constructor. subst. reflexivity.
+  Defined.
+
   Definition eq_leibniz (x y : t) : eq x y -> x = y := id.
+  
+  Definition eq_dec : forall (l1 l2 : t), {l1 = l2}+{l1 <> l2} := Classes.eq_dec.
 
 End Level.
 
@@ -311,10 +331,9 @@ Module UnivExpr.
     destruct (Nat.compare_spec n n0); repeat constructor; tas. congruence.
   Qed.
 
-  Definition eq_dec (l1 l2 : t) : {l1 = l2} + {l1 <> l2}.
-  Proof.
-    decide equality; apply eq_dec.
-  Defined.
+  Global Instance reflect_t : ReflectEq t := reflect_prod _ _ .
+
+  Definition eq_dec : forall (l1 l2 : t), {l1 = l2} + {l1 <> l2} := Classes.eq_dec.
 
   Definition eq_leibniz (x y : t) : eq x y -> x = y := id.
 
@@ -338,14 +357,20 @@ Module UnivExprSetProp := WPropertiesOn UnivExpr UnivExprSet.
 
 (* We have decidable equality w.r.t leibniz equality for sets of levels.
   This means universes also have a decidable equality. *)
-#[global] Instance univexprset_eq_dec : Classes.EqDec UnivExprSet.t.
-Proof.
-  intros p p'.
-  destruct (UnivExprSet.eq_dec p p').
-  - now left; eapply UnivExprSet.eq_leibniz in e.
-  - right. intros ->. apply n. reflexivity.
+#[global, program] Instance univexprset_reflect : ReflectEq UnivExprSet.t := 
+  { eqb := UnivExprSet.equal }.
+Next Obligation.
+  destruct (UnivExprSet.equal x y) eqn:e; constructor.
+  eapply UnivExprSet.equal_spec in e.
+  now eapply UnivExprSet.eq_leibniz.
+  intros e'.
+  subst y.
+  pose proof (@UnivExprSetFact.equal_1 x x).
+  forward H. reflexivity. congruence.
 Qed.
 
+#[global] Instance univexprset_eq_dec : Classes.EqDec UnivExprSet.t := Classes.eq_dec.
+
 Module Universe.
   (** A universe is a list of universe expressions which is:
         - sorted
@@ -356,19 +381,24 @@ Module Universe.
                 t_ne  : UnivExprSet.is_empty t_set = false }.
 
   Derive NoConfusion for nonEmptyUnivExprSet.
-  
-  (** This needs a propositional UIP proof to show that [is_empty = false] is a set *)
-  Set Equations With UIP.
-  #[global] Instance nonEmptyUnivExprSet_eqdec : EqDec nonEmptyUnivExprSet.
-  Proof. eqdec_proof. Qed.
+
+  (* We use uip on the is_empty condition *)
+  #[global, program] Instance univexprset_reflect : ReflectEq nonEmptyUnivExprSet := 
+    { eqb x y := eqb x.(t_set) y.(t_set) }.
+  Next Obligation.
+    destruct (eqb_spec (t_set x) (t_set y)); constructor.
+    destruct x, y; cbn in *. subst.
+    now rewrite (uip t_ne0 t_ne1).
+    intros e; subst x; apply H.
+    reflexivity.
+  Qed.
+
+  #[global] Instance eq_dec_univ0 : EqDec Universe.nonEmptyUnivExprSet := eq_dec.
 
   Inductive t_ :=
     lProp | lSProp | lType (_ : nonEmptyUnivExprSet).
   Derive NoConfusion for t_.
 
-  #[global] Instance t_eqdec : EqDec t_.
-  Proof. eqdec_proof. Qed.
-  
   Definition t := t_.
 
   Coercion t_set : nonEmptyUnivExprSet >-> UnivExprSet.t.
@@ -377,9 +407,19 @@ Module Universe.
     match u1, u2 with
     | lSProp, lSProp => true
     | lProp, lProp => true
-    | lType e1, lType e2 => UnivExprSet.equal e1.(t_set) e2.(t_set)
+    | lType e1, lType e2 => eqb e1 e2
     | _,_ => false
     end.
+  
+  #[global, program] Instance reflect_eq_universe : ReflectEq t := 
+    { eqb := eqb }.
+  Next Obligation.
+    destruct x, y; cbn; try constructor; auto; try congruence.
+    destruct (eqb_spec n n0); constructor. now f_equal.
+    congruence. 
+  Qed.
+
+  #[global] Instance eq_dec_univ : EqDec t := eq_dec.
 
   Definition make' (e : UnivExpr.t) : nonEmptyUnivExprSet
     := {| t_set := UnivExprSet.singleton e;
diff --git a/template-coq/theories/common/uGraph.v b/template-coq/theories/common/uGraph.v
index 97104334a..37c1ba248 100644
--- a/template-coq/theories/common/uGraph.v
+++ b/template-coq/theories/common/uGraph.v
@@ -75,7 +75,7 @@ Module VariableLevel.
 
   Definition eq_dec : forall x y : t, {x = y} + {x <> y}.
     intros [s|n] [s'|n']; try now constructor.
-    destruct (string_dec s s'); [left|right]; congruence.
+    destruct (Classes.eq_dec s s'); [left|right]; congruence.
     destruct (PeanoNat.Nat.eq_dec n n'); [left|right]; congruence.
   Defined.
 
@@ -151,7 +151,7 @@ Module GoodConstraint.
   Definition eq_dec : forall x y : t, {eq x y} + {~ eq x y}.
     unfold eq.
     decide equality. all: try apply VariableLevel.eq_dec.
-    apply Z.eq_dec. all:apply string_dec || apply Peano_dec.eq_nat_dec.
+    apply Z.eq_dec. all:apply Classes.eq_dec || apply Peano_dec.eq_nat_dec.
   Defined.
 
   Reserved Notation "x <c y" (at level 60).
@@ -163,7 +163,7 @@ Module GoodConstraint.
     | _, gc_le _ _ _ => Datatypes.Lt
     | gc_le _ _ _, _ => Gt
     | gc_lt_set_level n s, gc_lt_set_level n' s' =>
-      compare_cont (Nat.compare n n') (string_compare s s')%string
+      compare_cont (Nat.compare n n') (string_compare s s')
     | _, gc_lt_set_level _ _ => Datatypes.Lt
     | gc_lt_set_level _ _, _ => Gt
     | gc_le_set_var n s, gc_le_set_var n' s' =>
@@ -229,11 +229,11 @@ Module GoodConstraint.
     apply Z.compare_eq in e'; subst.
     intros H; apply VariableLevel.compare_eq in H; subst. reflexivity.
     destruct (Nat.compare_spec n n0) => /= //; subst.
-    destruct (CompareSpec_string s s0) => /= //; red in H; subst => //.
+    rewrite StringOT.compare_eq => -> //.
     destruct (Nat.compare_spec n n1) => /= //; subst.
     destruct (Nat.compare_spec n0 n2) => /= //; subst => //.
     destruct (Nat.compare_spec n n0) => /= //; subst.
-    destruct (CompareSpec_string s s0) => /= //; red in H; subst => //.
+    rewrite (StringOT.compare_eq) => -> //.
     destruct (Nat.compare_spec n n1) => /= //; subst.
     destruct (Nat.compare_spec n0 n2) => /= //; subst => //.
   Qed.
@@ -883,7 +883,7 @@ Proof.
         exists (VariableLevel.Level l'); intuition. exists (VariableLevel.Var l'); intuition.
       * intros [[l' [[H1|H1] H2]]|H].
         right. subst a. destruct l'; apply EdgeSet.add_spec; left; tas.
-        destruct l'; left; [exists (VariableLevel.Level s)|exists (VariableLevel.Var n)]; intuition.
+        destruct l'; left; [exists (VariableLevel.Level t0)|exists (VariableLevel.Var n)]; intuition.
         right. destruct a; tas; apply EdgeSet.add_spec; right; tas.
 Qed.
 
@@ -901,7 +901,7 @@ Proof.
       destruct gc; try apply (Hi.p2 _ Hgc). apply Hi.
       simpl. apply Hi.
   - apply Hi.
-  - cbn. intros l Hl. sq. destruct l.
+  - cbn. intros l Hl. sq. destruct l as [|s|n].
     exists (pathOf_refl _ _). sq. simpl. reflexivity.
     assert (He: EdgeSet.In (edge_of_level (VariableLevel.Level s)) (wGraph.E (make_graph uctx))). {
       apply make_graph_E. left. exists (VariableLevel.Level s). intuition. }
@@ -987,7 +987,7 @@ Section MakeGraph.
     : forall x, VSet.In x uctx.1
            -> labelling_of_valuation (valuation_of_labelling l) x = l x.
   Proof.
-    destruct x; cbnr.
+    destruct x as [|s|n]; cbnr.
     - intros _. now apply proj1 in Hl; cbn in Hl.
     - intro Hs. apply Nat2Pos.id.
       assert (HH: EdgeSet.In (lzero, Z.of_nat 1, vtn (VariableLevel.Level s)) (wGraph.E G)). {
@@ -2447,12 +2447,12 @@ Section AddLevelsCstrs.
     rewrite {}IHl.
     split.
     * intros [[c [eq inl]]|?]; firstorder auto.
-      destruct a; simpl in *; auto.
+      destruct a as [|s|n]; simpl in *; auto.
       rewrite -> EdgeSet.add_spec in H. intuition auto.
       subst e. left; exists (Level.Level s); intuition auto.
       rewrite -> EdgeSet.add_spec in H. intuition auto.
       subst e. left; eexists; intuition eauto. reflexivity.
-    * intros [[[] [[= <-] [->|inl]]]|?]; simpl; auto;
+    * intros [[[|s|n] [[= <-] [->|inl]]]|?]; simpl; auto;
       rewrite -> ?EdgeSet.add_spec; simpl; intuition auto.
       left. exists (Level.Level s); auto.
       left. exists (Level.Var n); auto.
diff --git a/template-coq/theories/utils.v b/template-coq/theories/utils.v
index 99fcaf2b1..16e27e7f3 100644
--- a/template-coq/theories/utils.v
+++ b/template-coq/theories/utils.v
@@ -4,13 +4,13 @@
 (** If you don't want to have the following scopes opened you should *)
 (** not import this file or close them. *)
 
-From Coq Require Export Bool ZArith Arith Lia String List.
+From Coq Require Export Bool ZArith Arith Lia List.
 
 From MetaCoq.Template Require Export utils.MCUtils monad_utils.
 
 Global Set Asymmetric Patterns.
 
-Global Open Scope string_scope.
+Global Open Scope bs_scope.
 
 Global Open Scope list_scope.
 
@@ -19,7 +19,7 @@ Global Open Scope nat_scope.
 
 (** We keep [++] for lists and use [^] for stings. *)
 Declare Scope string_scope2.
-Notation "s1 ^ s2" := (String.append s1 s2) : string_scope2.
+Notation "s1 ^ s2" := (bytestring.String.append s1 s2) : string_scope2.
 Open Scope string_scope2.
 
 (** We want [*] from type_scope but [+] from nat_scope. *)
diff --git a/template-coq/theories/utils/ByteCompare.v b/template-coq/theories/utils/ByteCompare.v
new file mode 100644
index 000000000..2a3582bd6
--- /dev/null
+++ b/template-coq/theories/utils/ByteCompare.v
@@ -0,0 +1,7 @@
+From Coq Require Import Byte NArith.BinNat.
+
+Definition eqb (x y : byte) := 
+  N.eqb (Byte.to_N x) (Byte.to_N y).
+
+Definition compare (x y : byte) := 
+  N.compare (Byte.to_N x) (Byte.to_N y).
diff --git a/template-coq/theories/utils/ByteCompareSpec.v b/template-coq/theories/utils/ByteCompareSpec.v
new file mode 100644
index 000000000..1159c5e63
--- /dev/null
+++ b/template-coq/theories/utils/ByteCompareSpec.v
@@ -0,0 +1,104 @@
+From Coq Require Import Byte NArith.
+From MetaCoq.Template Require Import ReflectEq ByteCompare.
+From Equations Require Import Equations.
+
+Derive NoConfusion for comparison.
+
+Section ByteNoConf.
+  Local Ltac solve_noconf ::= idtac.
+  Derive NoConfusion for byte.
+  Next Obligation.
+    destruct a; abstract (destruct b; try exact (False_ind _ H); exact eq_refl).
+  Defined.
+  Next Obligation.
+    destruct b; cbn; exact I.
+  Defined.
+  Next Obligation.
+    destruct a; abstract (destruct b; try (exact (False_ind _ e)); destruct e; exact eq_refl).
+  Defined.
+  Next Obligation.
+    destruct b; cbn; exact eq_refl.
+  Defined.
+End ByteNoConf.
+
+Lemma reflect_equiv P Q b : P <-> Q -> Bool.reflect P b -> Bool.reflect Q b.
+Proof.
+  intros eq r. destruct r.
+  - now constructor; apply eq.
+  - constructor. now rewrite <- eq.
+Qed.
+
+Require Import MCCompare.
+
+Definition lt x y := compare x y = Lt.
+
+Lemma compare_equiv x y : compare x y = N.compare (Byte.to_N x) (Byte.to_N y).
+Proof.
+  reflexivity.
+Qed.
+(* 
+Proof.
+  destruct x; abstract (destruct y; exact eq_refl).
+Qed. *)
+
+Lemma compare_opp x y : compare x y = CompOpp (compare y x).
+Proof.
+  rewrite !compare_equiv.
+  apply N.compare_antisym.
+Qed.
+
+Lemma compare_eq x y : compare x y = Eq -> x = y.
+Proof.
+  rewrite compare_equiv.
+  intros Hcomp.
+  eapply N.compare_eq in Hcomp.
+  eapply (f_equal of_N) in Hcomp.
+  rewrite !of_to_N in Hcomp. now noconf Hcomp.
+Qed.
+
+Lemma compare_spec x y : CompareSpec (x = y) (lt x y) (lt y x) (compare x y).
+Proof.
+  destruct (compare x y) eqn:comp.
+  - constructor. now apply compare_eq in comp.
+  - constructor. exact comp.
+  - constructor. red. now rewrite compare_opp, comp.
+Qed.
+
+From Coq Require Import Lia.
+
+Lemma lt_trans x y z : lt x y -> lt y z -> lt x z.
+Proof.
+  unfold lt.
+  rewrite !compare_equiv.
+  rewrite !N.compare_lt_iff. lia.
+Qed.
+
+Lemma lt_not_eq x y : lt x y -> x <> y.
+Proof.
+  unfold lt.
+  rewrite !compare_equiv.
+  rewrite !N.compare_lt_iff. intros Hlt Heq. subst. lia.
+Qed.
+
+Lemma compare_eq_refl x : compare x x = Eq.
+Proof.
+  rewrite compare_equiv.
+  eapply N.compare_refl.
+Qed.
+
+Definition eqb_compare x y : eqb x y = match compare x y with Eq => true | _ => false end.
+Proof.
+  unfold eqb.
+  apply N.eqb_compare.
+  (* destruct x; cbn; abstract (destruct y; cbn; exact eq_refl). *)
+Qed.
+
+Global Program Instance byte_reflect_eq : ReflectEq byte := 
+  {| ReflectEq.eqb := eqb |}.
+Next Obligation.
+  rewrite eqb_compare.
+  destruct (compare_spec x y); constructor; auto.
+  all:apply lt_not_eq in H.
+  - assumption.
+  - now apply not_eq_sym.
+Qed.
\ No newline at end of file
diff --git a/template-coq/theories/utils/ByteCompare_opt.v b/template-coq/theories/utils/ByteCompare_opt.v
new file mode 100644
index 000000000..9502d44dd
--- /dev/null
+++ b/template-coq/theories/utils/ByteCompare_opt.v
@@ -0,0 +1,2310 @@
+From Coq Require Import Byte.
+
+Definition is_byte_x00 (b : byte) := match b with | x00 => true | _ => false end.
+Definition is_byte_x01 (b : byte) := match b with | x01 => true | _ => false end.
+Definition is_byte_x02 (b : byte) := match b with | x02 => true | _ => false end.
+Definition is_byte_x03 (b : byte) := match b with | x03 => true | _ => false end.
+Definition is_byte_x04 (b : byte) := match b with | x04 => true | _ => false end.
+Definition is_byte_x05 (b : byte) := match b with | x05 => true | _ => false end.
+Definition is_byte_x06 (b : byte) := match b with | x06 => true | _ => false end.
+Definition is_byte_x07 (b : byte) := match b with | x07 => true | _ => false end.
+Definition is_byte_x08 (b : byte) := match b with | x08 => true | _ => false end.
+Definition is_byte_x09 (b : byte) := match b with | x09 => true | _ => false end.
+Definition is_byte_x0a (b : byte) := match b with | x0a => true | _ => false end.
+Definition is_byte_x0b (b : byte) := match b with | x0b => true | _ => false end.
+Definition is_byte_x0c (b : byte) := match b with | x0c => true | _ => false end.
+Definition is_byte_x0d (b : byte) := match b with | x0d => true | _ => false end.
+Definition is_byte_x0e (b : byte) := match b with | x0e => true | _ => false end.
+Definition is_byte_x0f (b : byte) := match b with | x0f => true | _ => false end.
+Definition is_byte_x10 (b : byte) := match b with | x10 => true | _ => false end.
+Definition is_byte_x11 (b : byte) := match b with | x11 => true | _ => false end.
+Definition is_byte_x12 (b : byte) := match b with | x12 => true | _ => false end.
+Definition is_byte_x13 (b : byte) := match b with | x13 => true | _ => false end.
+Definition is_byte_x14 (b : byte) := match b with | x14 => true | _ => false end.
+Definition is_byte_x15 (b : byte) := match b with | x15 => true | _ => false end.
+Definition is_byte_x16 (b : byte) := match b with | x16 => true | _ => false end.
+Definition is_byte_x17 (b : byte) := match b with | x17 => true | _ => false end.
+Definition is_byte_x18 (b : byte) := match b with | x18 => true | _ => false end.
+Definition is_byte_x19 (b : byte) := match b with | x19 => true | _ => false end.
+Definition is_byte_x1a (b : byte) := match b with | x1a => true | _ => false end.
+Definition is_byte_x1b (b : byte) := match b with | x1b => true | _ => false end.
+Definition is_byte_x1c (b : byte) := match b with | x1c => true | _ => false end.
+Definition is_byte_x1d (b : byte) := match b with | x1d => true | _ => false end.
+Definition is_byte_x1e (b : byte) := match b with | x1e => true | _ => false end.
+Definition is_byte_x1f (b : byte) := match b with | x1f => true | _ => false end.
+Definition is_byte_x20 (b : byte) := match b with | x20 => true | _ => false end.
+Definition is_byte_x21 (b : byte) := match b with | x21 => true | _ => false end.
+Definition is_byte_x22 (b : byte) := match b with | x22 => true | _ => false end.
+Definition is_byte_x23 (b : byte) := match b with | x23 => true | _ => false end.
+Definition is_byte_x24 (b : byte) := match b with | x24 => true | _ => false end.
+Definition is_byte_x25 (b : byte) := match b with | x25 => true | _ => false end.
+Definition is_byte_x26 (b : byte) := match b with | x26 => true | _ => false end.
+Definition is_byte_x27 (b : byte) := match b with | x27 => true | _ => false end.
+Definition is_byte_x28 (b : byte) := match b with | x28 => true | _ => false end.
+Definition is_byte_x29 (b : byte) := match b with | x29 => true | _ => false end.
+Definition is_byte_x2a (b : byte) := match b with | x2a => true | _ => false end.
+Definition is_byte_x2b (b : byte) := match b with | x2b => true | _ => false end.
+Definition is_byte_x2c (b : byte) := match b with | x2c => true | _ => false end.
+Definition is_byte_x2d (b : byte) := match b with | x2d => true | _ => false end.
+Definition is_byte_x2e (b : byte) := match b with | x2e => true | _ => false end.
+Definition is_byte_x2f (b : byte) := match b with | x2f => true | _ => false end.
+Definition is_byte_x30 (b : byte) := match b with | x30 => true | _ => false end.
+Definition is_byte_x31 (b : byte) := match b with | x31 => true | _ => false end.
+Definition is_byte_x32 (b : byte) := match b with | x32 => true | _ => false end.
+Definition is_byte_x33 (b : byte) := match b with | x33 => true | _ => false end.
+Definition is_byte_x34 (b : byte) := match b with | x34 => true | _ => false end.
+Definition is_byte_x35 (b : byte) := match b with | x35 => true | _ => false end.
+Definition is_byte_x36 (b : byte) := match b with | x36 => true | _ => false end.
+Definition is_byte_x37 (b : byte) := match b with | x37 => true | _ => false end.
+Definition is_byte_x38 (b : byte) := match b with | x38 => true | _ => false end.
+Definition is_byte_x39 (b : byte) := match b with | x39 => true | _ => false end.
+Definition is_byte_x3a (b : byte) := match b with | x3a => true | _ => false end.
+Definition is_byte_x3b (b : byte) := match b with | x3b => true | _ => false end.
+Definition is_byte_x3c (b : byte) := match b with | x3c => true | _ => false end.
+Definition is_byte_x3d (b : byte) := match b with | x3d => true | _ => false end.
+Definition is_byte_x3e (b : byte) := match b with | x3e => true | _ => false end.
+Definition is_byte_x3f (b : byte) := match b with | x3f => true | _ => false end.
+Definition is_byte_x40 (b : byte) := match b with | x40 => true | _ => false end.
+Definition is_byte_x41 (b : byte) := match b with | x41 => true | _ => false end.
+Definition is_byte_x42 (b : byte) := match b with | x42 => true | _ => false end.
+Definition is_byte_x43 (b : byte) := match b with | x43 => true | _ => false end.
+Definition is_byte_x44 (b : byte) := match b with | x44 => true | _ => false end.
+Definition is_byte_x45 (b : byte) := match b with | x45 => true | _ => false end.
+Definition is_byte_x46 (b : byte) := match b with | x46 => true | _ => false end.
+Definition is_byte_x47 (b : byte) := match b with | x47 => true | _ => false end.
+Definition is_byte_x48 (b : byte) := match b with | x48 => true | _ => false end.
+Definition is_byte_x49 (b : byte) := match b with | x49 => true | _ => false end.
+Definition is_byte_x4a (b : byte) := match b with | x4a => true | _ => false end.
+Definition is_byte_x4b (b : byte) := match b with | x4b => true | _ => false end.
+Definition is_byte_x4c (b : byte) := match b with | x4c => true | _ => false end.
+Definition is_byte_x4d (b : byte) := match b with | x4d => true | _ => false end.
+Definition is_byte_x4e (b : byte) := match b with | x4e => true | _ => false end.
+Definition is_byte_x4f (b : byte) := match b with | x4f => true | _ => false end.
+Definition is_byte_x50 (b : byte) := match b with | x50 => true | _ => false end.
+Definition is_byte_x51 (b : byte) := match b with | x51 => true | _ => false end.
+Definition is_byte_x52 (b : byte) := match b with | x52 => true | _ => false end.
+Definition is_byte_x53 (b : byte) := match b with | x53 => true | _ => false end.
+Definition is_byte_x54 (b : byte) := match b with | x54 => true | _ => false end.
+Definition is_byte_x55 (b : byte) := match b with | x55 => true | _ => false end.
+Definition is_byte_x56 (b : byte) := match b with | x56 => true | _ => false end.
+Definition is_byte_x57 (b : byte) := match b with | x57 => true | _ => false end.
+Definition is_byte_x58 (b : byte) := match b with | x58 => true | _ => false end.
+Definition is_byte_x59 (b : byte) := match b with | x59 => true | _ => false end.
+Definition is_byte_x5a (b : byte) := match b with | x5a => true | _ => false end.
+Definition is_byte_x5b (b : byte) := match b with | x5b => true | _ => false end.
+Definition is_byte_x5c (b : byte) := match b with | x5c => true | _ => false end.
+Definition is_byte_x5d (b : byte) := match b with | x5d => true | _ => false end.
+Definition is_byte_x5e (b : byte) := match b with | x5e => true | _ => false end.
+Definition is_byte_x5f (b : byte) := match b with | x5f => true | _ => false end.
+Definition is_byte_x60 (b : byte) := match b with | x60 => true | _ => false end.
+Definition is_byte_x61 (b : byte) := match b with | x61 => true | _ => false end.
+Definition is_byte_x62 (b : byte) := match b with | x62 => true | _ => false end.
+Definition is_byte_x63 (b : byte) := match b with | x63 => true | _ => false end.
+Definition is_byte_x64 (b : byte) := match b with | x64 => true | _ => false end.
+Definition is_byte_x65 (b : byte) := match b with | x65 => true | _ => false end.
+Definition is_byte_x66 (b : byte) := match b with | x66 => true | _ => false end.
+Definition is_byte_x67 (b : byte) := match b with | x67 => true | _ => false end.
+Definition is_byte_x68 (b : byte) := match b with | x68 => true | _ => false end.
+Definition is_byte_x69 (b : byte) := match b with | x69 => true | _ => false end.
+Definition is_byte_x6a (b : byte) := match b with | x6a => true | _ => false end.
+Definition is_byte_x6b (b : byte) := match b with | x6b => true | _ => false end.
+Definition is_byte_x6c (b : byte) := match b with | x6c => true | _ => false end.
+Definition is_byte_x6d (b : byte) := match b with | x6d => true | _ => false end.
+Definition is_byte_x6e (b : byte) := match b with | x6e => true | _ => false end.
+Definition is_byte_x6f (b : byte) := match b with | x6f => true | _ => false end.
+Definition is_byte_x70 (b : byte) := match b with | x70 => true | _ => false end.
+Definition is_byte_x71 (b : byte) := match b with | x71 => true | _ => false end.
+Definition is_byte_x72 (b : byte) := match b with | x72 => true | _ => false end.
+Definition is_byte_x73 (b : byte) := match b with | x73 => true | _ => false end.
+Definition is_byte_x74 (b : byte) := match b with | x74 => true | _ => false end.
+Definition is_byte_x75 (b : byte) := match b with | x75 => true | _ => false end.
+Definition is_byte_x76 (b : byte) := match b with | x76 => true | _ => false end.
+Definition is_byte_x77 (b : byte) := match b with | x77 => true | _ => false end.
+Definition is_byte_x78 (b : byte) := match b with | x78 => true | _ => false end.
+Definition is_byte_x79 (b : byte) := match b with | x79 => true | _ => false end.
+Definition is_byte_x7a (b : byte) := match b with | x7a => true | _ => false end.
+Definition is_byte_x7b (b : byte) := match b with | x7b => true | _ => false end.
+Definition is_byte_x7c (b : byte) := match b with | x7c => true | _ => false end.
+Definition is_byte_x7d (b : byte) := match b with | x7d => true | _ => false end.
+Definition is_byte_x7e (b : byte) := match b with | x7e => true | _ => false end.
+Definition is_byte_x7f (b : byte) := match b with | x7f => true | _ => false end.
+Definition is_byte_x80 (b : byte) := match b with | x80 => true | _ => false end.
+Definition is_byte_x81 (b : byte) := match b with | x81 => true | _ => false end.
+Definition is_byte_x82 (b : byte) := match b with | x82 => true | _ => false end.
+Definition is_byte_x83 (b : byte) := match b with | x83 => true | _ => false end.
+Definition is_byte_x84 (b : byte) := match b with | x84 => true | _ => false end.
+Definition is_byte_x85 (b : byte) := match b with | x85 => true | _ => false end.
+Definition is_byte_x86 (b : byte) := match b with | x86 => true | _ => false end.
+Definition is_byte_x87 (b : byte) := match b with | x87 => true | _ => false end.
+Definition is_byte_x88 (b : byte) := match b with | x88 => true | _ => false end.
+Definition is_byte_x89 (b : byte) := match b with | x89 => true | _ => false end.
+Definition is_byte_x8a (b : byte) := match b with | x8a => true | _ => false end.
+Definition is_byte_x8b (b : byte) := match b with | x8b => true | _ => false end.
+Definition is_byte_x8c (b : byte) := match b with | x8c => true | _ => false end.
+Definition is_byte_x8d (b : byte) := match b with | x8d => true | _ => false end.
+Definition is_byte_x8e (b : byte) := match b with | x8e => true | _ => false end.
+Definition is_byte_x8f (b : byte) := match b with | x8f => true | _ => false end.
+Definition is_byte_x90 (b : byte) := match b with | x90 => true | _ => false end.
+Definition is_byte_x91 (b : byte) := match b with | x91 => true | _ => false end.
+Definition is_byte_x92 (b : byte) := match b with | x92 => true | _ => false end.
+Definition is_byte_x93 (b : byte) := match b with | x93 => true | _ => false end.
+Definition is_byte_x94 (b : byte) := match b with | x94 => true | _ => false end.
+Definition is_byte_x95 (b : byte) := match b with | x95 => true | _ => false end.
+Definition is_byte_x96 (b : byte) := match b with | x96 => true | _ => false end.
+Definition is_byte_x97 (b : byte) := match b with | x97 => true | _ => false end.
+Definition is_byte_x98 (b : byte) := match b with | x98 => true | _ => false end.
+Definition is_byte_x99 (b : byte) := match b with | x99 => true | _ => false end.
+Definition is_byte_x9a (b : byte) := match b with | x9a => true | _ => false end.
+Definition is_byte_x9b (b : byte) := match b with | x9b => true | _ => false end.
+Definition is_byte_x9c (b : byte) := match b with | x9c => true | _ => false end.
+Definition is_byte_x9d (b : byte) := match b with | x9d => true | _ => false end.
+Definition is_byte_x9e (b : byte) := match b with | x9e => true | _ => false end.
+Definition is_byte_x9f (b : byte) := match b with | x9f => true | _ => false end.
+Definition is_byte_xa0 (b : byte) := match b with | xa0 => true | _ => false end.
+Definition is_byte_xa1 (b : byte) := match b with | xa1 => true | _ => false end.
+Definition is_byte_xa2 (b : byte) := match b with | xa2 => true | _ => false end.
+Definition is_byte_xa3 (b : byte) := match b with | xa3 => true | _ => false end.
+Definition is_byte_xa4 (b : byte) := match b with | xa4 => true | _ => false end.
+Definition is_byte_xa5 (b : byte) := match b with | xa5 => true | _ => false end.
+Definition is_byte_xa6 (b : byte) := match b with | xa6 => true | _ => false end.
+Definition is_byte_xa7 (b : byte) := match b with | xa7 => true | _ => false end.
+Definition is_byte_xa8 (b : byte) := match b with | xa8 => true | _ => false end.
+Definition is_byte_xa9 (b : byte) := match b with | xa9 => true | _ => false end.
+Definition is_byte_xaa (b : byte) := match b with | xaa => true | _ => false end.
+Definition is_byte_xab (b : byte) := match b with | xab => true | _ => false end.
+Definition is_byte_xac (b : byte) := match b with | xac => true | _ => false end.
+Definition is_byte_xad (b : byte) := match b with | xad => true | _ => false end.
+Definition is_byte_xae (b : byte) := match b with | xae => true | _ => false end.
+Definition is_byte_xaf (b : byte) := match b with | xaf => true | _ => false end.
+Definition is_byte_xb0 (b : byte) := match b with | xb0 => true | _ => false end.
+Definition is_byte_xb1 (b : byte) := match b with | xb1 => true | _ => false end.
+Definition is_byte_xb2 (b : byte) := match b with | xb2 => true | _ => false end.
+Definition is_byte_xb3 (b : byte) := match b with | xb3 => true | _ => false end.
+Definition is_byte_xb4 (b : byte) := match b with | xb4 => true | _ => false end.
+Definition is_byte_xb5 (b : byte) := match b with | xb5 => true | _ => false end.
+Definition is_byte_xb6 (b : byte) := match b with | xb6 => true | _ => false end.
+Definition is_byte_xb7 (b : byte) := match b with | xb7 => true | _ => false end.
+Definition is_byte_xb8 (b : byte) := match b with | xb8 => true | _ => false end.
+Definition is_byte_xb9 (b : byte) := match b with | xb9 => true | _ => false end.
+Definition is_byte_xba (b : byte) := match b with | xba => true | _ => false end.
+Definition is_byte_xbb (b : byte) := match b with | xbb => true | _ => false end.
+Definition is_byte_xbc (b : byte) := match b with | xbc => true | _ => false end.
+Definition is_byte_xbd (b : byte) := match b with | xbd => true | _ => false end.
+Definition is_byte_xbe (b : byte) := match b with | xbe => true | _ => false end.
+Definition is_byte_xbf (b : byte) := match b with | xbf => true | _ => false end.
+Definition is_byte_xc0 (b : byte) := match b with | xc0 => true | _ => false end.
+Definition is_byte_xc1 (b : byte) := match b with | xc1 => true | _ => false end.
+Definition is_byte_xc2 (b : byte) := match b with | xc2 => true | _ => false end.
+Definition is_byte_xc3 (b : byte) := match b with | xc3 => true | _ => false end.
+Definition is_byte_xc4 (b : byte) := match b with | xc4 => true | _ => false end.
+Definition is_byte_xc5 (b : byte) := match b with | xc5 => true | _ => false end.
+Definition is_byte_xc6 (b : byte) := match b with | xc6 => true | _ => false end.
+Definition is_byte_xc7 (b : byte) := match b with | xc7 => true | _ => false end.
+Definition is_byte_xc8 (b : byte) := match b with | xc8 => true | _ => false end.
+Definition is_byte_xc9 (b : byte) := match b with | xc9 => true | _ => false end.
+Definition is_byte_xca (b : byte) := match b with | xca => true | _ => false end.
+Definition is_byte_xcb (b : byte) := match b with | xcb => true | _ => false end.
+Definition is_byte_xcc (b : byte) := match b with | xcc => true | _ => false end.
+Definition is_byte_xcd (b : byte) := match b with | xcd => true | _ => false end.
+Definition is_byte_xce (b : byte) := match b with | xce => true | _ => false end.
+Definition is_byte_xcf (b : byte) := match b with | xcf => true | _ => false end.
+Definition is_byte_xd0 (b : byte) := match b with | xd0 => true | _ => false end.
+Definition is_byte_xd1 (b : byte) := match b with | xd1 => true | _ => false end.
+Definition is_byte_xd2 (b : byte) := match b with | xd2 => true | _ => false end.
+Definition is_byte_xd3 (b : byte) := match b with | xd3 => true | _ => false end.
+Definition is_byte_xd4 (b : byte) := match b with | xd4 => true | _ => false end.
+Definition is_byte_xd5 (b : byte) := match b with | xd5 => true | _ => false end.
+Definition is_byte_xd6 (b : byte) := match b with | xd6 => true | _ => false end.
+Definition is_byte_xd7 (b : byte) := match b with | xd7 => true | _ => false end.
+Definition is_byte_xd8 (b : byte) := match b with | xd8 => true | _ => false end.
+Definition is_byte_xd9 (b : byte) := match b with | xd9 => true | _ => false end.
+Definition is_byte_xda (b : byte) := match b with | xda => true | _ => false end.
+Definition is_byte_xdb (b : byte) := match b with | xdb => true | _ => false end.
+Definition is_byte_xdc (b : byte) := match b with | xdc => true | _ => false end.
+Definition is_byte_xdd (b : byte) := match b with | xdd => true | _ => false end.
+Definition is_byte_xde (b : byte) := match b with | xde => true | _ => false end.
+Definition is_byte_xdf (b : byte) := match b with | xdf => true | _ => false end.
+Definition is_byte_xe0 (b : byte) := match b with | xe0 => true | _ => false end.
+Definition is_byte_xe1 (b : byte) := match b with | xe1 => true | _ => false end.
+Definition is_byte_xe2 (b : byte) := match b with | xe2 => true | _ => false end.
+Definition is_byte_xe3 (b : byte) := match b with | xe3 => true | _ => false end.
+Definition is_byte_xe4 (b : byte) := match b with | xe4 => true | _ => false end.
+Definition is_byte_xe5 (b : byte) := match b with | xe5 => true | _ => false end.
+Definition is_byte_xe6 (b : byte) := match b with | xe6 => true | _ => false end.
+Definition is_byte_xe7 (b : byte) := match b with | xe7 => true | _ => false end.
+Definition is_byte_xe8 (b : byte) := match b with | xe8 => true | _ => false end.
+Definition is_byte_xe9 (b : byte) := match b with | xe9 => true | _ => false end.
+Definition is_byte_xea (b : byte) := match b with | xea => true | _ => false end.
+Definition is_byte_xeb (b : byte) := match b with | xeb => true | _ => false end.
+Definition is_byte_xec (b : byte) := match b with | xec => true | _ => false end.
+Definition is_byte_xed (b : byte) := match b with | xed => true | _ => false end.
+Definition is_byte_xee (b : byte) := match b with | xee => true | _ => false end.
+Definition is_byte_xef (b : byte) := match b with | xef => true | _ => false end.
+Definition is_byte_xf0 (b : byte) := match b with | xf0 => true | _ => false end.
+Definition is_byte_xf1 (b : byte) := match b with | xf1 => true | _ => false end.
+Definition is_byte_xf2 (b : byte) := match b with | xf2 => true | _ => false end.
+Definition is_byte_xf3 (b : byte) := match b with | xf3 => true | _ => false end.
+Definition is_byte_xf4 (b : byte) := match b with | xf4 => true | _ => false end.
+Definition is_byte_xf5 (b : byte) := match b with | xf5 => true | _ => false end.
+Definition is_byte_xf6 (b : byte) := match b with | xf6 => true | _ => false end.
+Definition is_byte_xf7 (b : byte) := match b with | xf7 => true | _ => false end.
+Definition is_byte_xf8 (b : byte) := match b with | xf8 => true | _ => false end.
+Definition is_byte_xf9 (b : byte) := match b with | xf9 => true | _ => false end.
+Definition is_byte_xfa (b : byte) := match b with | xfa => true | _ => false end.
+Definition is_byte_xfb (b : byte) := match b with | xfb => true | _ => false end.
+Definition is_byte_xfc (b : byte) := match b with | xfc => true | _ => false end.
+Definition is_byte_xfd (b : byte) := match b with | xfd => true | _ => false end.
+Definition is_byte_xfe (b : byte) := match b with | xfe => true | _ => false end.
+Definition is_byte_xff (b : byte) := match b with | xff => true | _ => false end.
+Definition eqb (b b' : byte) :=
+  match b with
+  | x00 => is_byte_x00 b'
+  | x01 => is_byte_x01 b'
+  | x02 => is_byte_x02 b'
+  | x03 => is_byte_x03 b'
+  | x04 => is_byte_x04 b'
+  | x05 => is_byte_x05 b'
+  | x06 => is_byte_x06 b'
+  | x07 => is_byte_x07 b'
+  | x08 => is_byte_x08 b'
+  | x09 => is_byte_x09 b'
+  | x0a => is_byte_x0a b'
+  | x0b => is_byte_x0b b'
+  | x0c => is_byte_x0c b'
+  | x0d => is_byte_x0d b'
+  | x0e => is_byte_x0e b'
+  | x0f => is_byte_x0f b'
+  | x10 => is_byte_x10 b'
+  | x11 => is_byte_x11 b'
+  | x12 => is_byte_x12 b'
+  | x13 => is_byte_x13 b'
+  | x14 => is_byte_x14 b'
+  | x15 => is_byte_x15 b'
+  | x16 => is_byte_x16 b'
+  | x17 => is_byte_x17 b'
+  | x18 => is_byte_x18 b'
+  | x19 => is_byte_x19 b'
+  | x1a => is_byte_x1a b'
+  | x1b => is_byte_x1b b'
+  | x1c => is_byte_x1c b'
+  | x1d => is_byte_x1d b'
+  | x1e => is_byte_x1e b'
+  | x1f => is_byte_x1f b'
+  | x20 => is_byte_x20 b'
+  | x21 => is_byte_x21 b'
+  | x22 => is_byte_x22 b'
+  | x23 => is_byte_x23 b'
+  | x24 => is_byte_x24 b'
+  | x25 => is_byte_x25 b'
+  | x26 => is_byte_x26 b'
+  | x27 => is_byte_x27 b'
+  | x28 => is_byte_x28 b'
+  | x29 => is_byte_x29 b'
+  | x2a => is_byte_x2a b'
+  | x2b => is_byte_x2b b'
+  | x2c => is_byte_x2c b'
+  | x2d => is_byte_x2d b'
+  | x2e => is_byte_x2e b'
+  | x2f => is_byte_x2f b'
+  | x30 => is_byte_x30 b'
+  | x31 => is_byte_x31 b'
+  | x32 => is_byte_x32 b'
+  | x33 => is_byte_x33 b'
+  | x34 => is_byte_x34 b'
+  | x35 => is_byte_x35 b'
+  | x36 => is_byte_x36 b'
+  | x37 => is_byte_x37 b'
+  | x38 => is_byte_x38 b'
+  | x39 => is_byte_x39 b'
+  | x3a => is_byte_x3a b'
+  | x3b => is_byte_x3b b'
+  | x3c => is_byte_x3c b'
+  | x3d => is_byte_x3d b'
+  | x3e => is_byte_x3e b'
+  | x3f => is_byte_x3f b'
+  | x40 => is_byte_x40 b'
+  | x41 => is_byte_x41 b'
+  | x42 => is_byte_x42 b'
+  | x43 => is_byte_x43 b'
+  | x44 => is_byte_x44 b'
+  | x45 => is_byte_x45 b'
+  | x46 => is_byte_x46 b'
+  | x47 => is_byte_x47 b'
+  | x48 => is_byte_x48 b'
+  | x49 => is_byte_x49 b'
+  | x4a => is_byte_x4a b'
+  | x4b => is_byte_x4b b'
+  | x4c => is_byte_x4c b'
+  | x4d => is_byte_x4d b'
+  | x4e => is_byte_x4e b'
+  | x4f => is_byte_x4f b'
+  | x50 => is_byte_x50 b'
+  | x51 => is_byte_x51 b'
+  | x52 => is_byte_x52 b'
+  | x53 => is_byte_x53 b'
+  | x54 => is_byte_x54 b'
+  | x55 => is_byte_x55 b'
+  | x56 => is_byte_x56 b'
+  | x57 => is_byte_x57 b'
+  | x58 => is_byte_x58 b'
+  | x59 => is_byte_x59 b'
+  | x5a => is_byte_x5a b'
+  | x5b => is_byte_x5b b'
+  | x5c => is_byte_x5c b'
+  | x5d => is_byte_x5d b'
+  | x5e => is_byte_x5e b'
+  | x5f => is_byte_x5f b'
+  | x60 => is_byte_x60 b'
+  | x61 => is_byte_x61 b'
+  | x62 => is_byte_x62 b'
+  | x63 => is_byte_x63 b'
+  | x64 => is_byte_x64 b'
+  | x65 => is_byte_x65 b'
+  | x66 => is_byte_x66 b'
+  | x67 => is_byte_x67 b'
+  | x68 => is_byte_x68 b'
+  | x69 => is_byte_x69 b'
+  | x6a => is_byte_x6a b'
+  | x6b => is_byte_x6b b'
+  | x6c => is_byte_x6c b'
+  | x6d => is_byte_x6d b'
+  | x6e => is_byte_x6e b'
+  | x6f => is_byte_x6f b'
+  | x70 => is_byte_x70 b'
+  | x71 => is_byte_x71 b'
+  | x72 => is_byte_x72 b'
+  | x73 => is_byte_x73 b'
+  | x74 => is_byte_x74 b'
+  | x75 => is_byte_x75 b'
+  | x76 => is_byte_x76 b'
+  | x77 => is_byte_x77 b'
+  | x78 => is_byte_x78 b'
+  | x79 => is_byte_x79 b'
+  | x7a => is_byte_x7a b'
+  | x7b => is_byte_x7b b'
+  | x7c => is_byte_x7c b'
+  | x7d => is_byte_x7d b'
+  | x7e => is_byte_x7e b'
+  | x7f => is_byte_x7f b'
+  | x80 => is_byte_x80 b'
+  | x81 => is_byte_x81 b'
+  | x82 => is_byte_x82 b'
+  | x83 => is_byte_x83 b'
+  | x84 => is_byte_x84 b'
+  | x85 => is_byte_x85 b'
+  | x86 => is_byte_x86 b'
+  | x87 => is_byte_x87 b'
+  | x88 => is_byte_x88 b'
+  | x89 => is_byte_x89 b'
+  | x8a => is_byte_x8a b'
+  | x8b => is_byte_x8b b'
+  | x8c => is_byte_x8c b'
+  | x8d => is_byte_x8d b'
+  | x8e => is_byte_x8e b'
+  | x8f => is_byte_x8f b'
+  | x90 => is_byte_x90 b'
+  | x91 => is_byte_x91 b'
+  | x92 => is_byte_x92 b'
+  | x93 => is_byte_x93 b'
+  | x94 => is_byte_x94 b'
+  | x95 => is_byte_x95 b'
+  | x96 => is_byte_x96 b'
+  | x97 => is_byte_x97 b'
+  | x98 => is_byte_x98 b'
+  | x99 => is_byte_x99 b'
+  | x9a => is_byte_x9a b'
+  | x9b => is_byte_x9b b'
+  | x9c => is_byte_x9c b'
+  | x9d => is_byte_x9d b'
+  | x9e => is_byte_x9e b'
+  | x9f => is_byte_x9f b'
+  | xa0 => is_byte_xa0 b'
+  | xa1 => is_byte_xa1 b'
+  | xa2 => is_byte_xa2 b'
+  | xa3 => is_byte_xa3 b'
+  | xa4 => is_byte_xa4 b'
+  | xa5 => is_byte_xa5 b'
+  | xa6 => is_byte_xa6 b'
+  | xa7 => is_byte_xa7 b'
+  | xa8 => is_byte_xa8 b'
+  | xa9 => is_byte_xa9 b'
+  | xaa => is_byte_xaa b'
+  | xab => is_byte_xab b'
+  | xac => is_byte_xac b'
+  | xad => is_byte_xad b'
+  | xae => is_byte_xae b'
+  | xaf => is_byte_xaf b'
+  | xb0 => is_byte_xb0 b'
+  | xb1 => is_byte_xb1 b'
+  | xb2 => is_byte_xb2 b'
+  | xb3 => is_byte_xb3 b'
+  | xb4 => is_byte_xb4 b'
+  | xb5 => is_byte_xb5 b'
+  | xb6 => is_byte_xb6 b'
+  | xb7 => is_byte_xb7 b'
+  | xb8 => is_byte_xb8 b'
+  | xb9 => is_byte_xb9 b'
+  | xba => is_byte_xba b'
+  | xbb => is_byte_xbb b'
+  | xbc => is_byte_xbc b'
+  | xbd => is_byte_xbd b'
+  | xbe => is_byte_xbe b'
+  | xbf => is_byte_xbf b'
+  | xc0 => is_byte_xc0 b'
+  | xc1 => is_byte_xc1 b'
+  | xc2 => is_byte_xc2 b'
+  | xc3 => is_byte_xc3 b'
+  | xc4 => is_byte_xc4 b'
+  | xc5 => is_byte_xc5 b'
+  | xc6 => is_byte_xc6 b'
+  | xc7 => is_byte_xc7 b'
+  | xc8 => is_byte_xc8 b'
+  | xc9 => is_byte_xc9 b'
+  | xca => is_byte_xca b'
+  | xcb => is_byte_xcb b'
+  | xcc => is_byte_xcc b'
+  | xcd => is_byte_xcd b'
+  | xce => is_byte_xce b'
+  | xcf => is_byte_xcf b'
+  | xd0 => is_byte_xd0 b'
+  | xd1 => is_byte_xd1 b'
+  | xd2 => is_byte_xd2 b'
+  | xd3 => is_byte_xd3 b'
+  | xd4 => is_byte_xd4 b'
+  | xd5 => is_byte_xd5 b'
+  | xd6 => is_byte_xd6 b'
+  | xd7 => is_byte_xd7 b'
+  | xd8 => is_byte_xd8 b'
+  | xd9 => is_byte_xd9 b'
+  | xda => is_byte_xda b'
+  | xdb => is_byte_xdb b'
+  | xdc => is_byte_xdc b'
+  | xdd => is_byte_xdd b'
+  | xde => is_byte_xde b'
+  | xdf => is_byte_xdf b'
+  | xe0 => is_byte_xe0 b'
+  | xe1 => is_byte_xe1 b'
+  | xe2 => is_byte_xe2 b'
+  | xe3 => is_byte_xe3 b'
+  | xe4 => is_byte_xe4 b'
+  | xe5 => is_byte_xe5 b'
+  | xe6 => is_byte_xe6 b'
+  | xe7 => is_byte_xe7 b'
+  | xe8 => is_byte_xe8 b'
+  | xe9 => is_byte_xe9 b'
+  | xea => is_byte_xea b'
+  | xeb => is_byte_xeb b'
+  | xec => is_byte_xec b'
+  | xed => is_byte_xed b'
+  | xee => is_byte_xee b'
+  | xef => is_byte_xef b'
+  | xf0 => is_byte_xf0 b'
+  | xf1 => is_byte_xf1 b'
+  | xf2 => is_byte_xf2 b'
+  | xf3 => is_byte_xf3 b'
+  | xf4 => is_byte_xf4 b'
+  | xf5 => is_byte_xf5 b'
+  | xf6 => is_byte_xf6 b'
+  | xf7 => is_byte_xf7 b'
+  | xf8 => is_byte_xf8 b'
+  | xf9 => is_byte_xf9 b'
+  | xfa => is_byte_xfa b'
+  | xfb => is_byte_xfb b'
+  | xfc => is_byte_xfc b'
+  | xfd => is_byte_xfd b'
+  | xfe => is_byte_xfe b'
+  | xff => is_byte_xff b'
+  end.
+Definition compare_byte_x00 (b : byte) :=
+  match b with
+  | x00 => Eq
+  | _ => Lt
+  end.
+Definition compare_byte_x01 (b : byte) :=
+  match b with
+  | x00 => Gt
+  | x01 => Eq
+  | _ => Lt
+  end.
+Definition compare_byte_x02 (b : byte) :=
+  match b with
+  | x00 | x01 => Gt
+  | x02 => Eq
+  | _ => Lt
+  end.
+Definition compare_byte_x03 (b : byte) :=
+  match b with
+  | x00 | x01 | x02 => Gt
+  | x03 => Eq
+  | _ => Lt
+  end.
+Definition compare_byte_x04 (b : byte) :=
+  match b with
+  | x00 | x01 | x02 | x03 => Gt
+  | x04 => Eq
+  | _ => Lt
+  end.
+Definition compare_byte_x05 (b : byte) :=
+  match b with
+  | x00 | x01 | x02 | x03 | x04 => Gt
+  | x05 => Eq
+  | _ => Lt
+  end.
+Definition compare_byte_x06 (b : byte) :=
+  match b with
+  | x00 | x01 | x02 | x03 | x04 | x05 => Gt
+  | x06 => Eq
+  | _ => Lt
+  end.
+Definition compare_byte_x07 (b : byte) :=
+  match b with
+  | x00 | x01 | x02 | x03 | x04 | x05 | x06 => Gt
+  | x07 => Eq
+  | _ => Lt
+  end.
+Definition compare_byte_x08 (b : byte) :=
+  match b with
+  | x00 | x01 | x02 | x03 | x04 | x05 | x06 | x07 => Gt
+  | x08 => Eq
+  | _ => Lt
+  end.
+Definition compare_byte_x09 (b : byte) :=
+  match b with
+  | x00 | x01 | x02 | x03 | x04 | x05 | x06 | x07 | x08 => Gt
+  | x09 => Eq
+  | _ => Lt
+  end.
+Definition compare_byte_x0a (b : byte) :=
+  match b with
+  | x00 | x01 | x02 | x03 | x04 | x05 | x06 | x07 | x08 | x09 => Gt
+  | x0a => Eq
+  | _ => Lt
+  end.
+Definition compare_byte_x0b (b : byte) :=
+  match b with
+  | x00 | x01 | x02 | x03 | x04 | x05 | x06 | x07 | x08 | x09 | x0a => Gt
+  | x0b => Eq
+  | _ => Lt
+  end.
+Definition compare_byte_x0c (b : byte) :=
+  match b with
+  | x00 | x01 | x02 | x03 | x04 | x05 | x06 | x07 | x08 | x09 | x0a | x0b => Gt
+  | x0c => Eq
+  | _ => Lt
+  end.
+Definition compare_byte_x0d (b : byte) :=
+  match b with
+  | x00 | x01 | x02 | x03 | x04 | x05 | x06 | x07 | x08 | x09 | x0a | x0b | x0c => Gt
+  | x0d => Eq
+  | _ => Lt
+  end.
+Definition compare_byte_x0e (b : byte) :=
+  match b with
+  | x00 | x01 | x02 | x03 | x04 | x05 | x06 | x07 | x08 | x09 | x0a | x0b | x0c | x0d => Gt
+  | x0e => Eq
+  | _ => Lt
+  end.
+Definition compare_byte_x0f (b : byte) :=
+  match b with
+  | x00 | x01 | x02 | x03 | x04 | x05 | x06 | x07 | x08 | x09 | x0a | x0b | x0c | x0d | x0e => Gt
+  | x0f => Eq
+  | _ => Lt
+  end.
+Definition compare_byte_x10 (b : byte) :=
+  match b with
+  | x00 | x01 | x02 | x03 | x04 | x05 | x06 | x07 | x08 | x09 | x0a | x0b | x0c | x0d | x0e | x0f => Gt
+  | x10 => Eq
+  | _ => Lt
+  end.
+Definition compare_byte_x11 (b : byte) :=
+  match b with
+  | x00 | x01 | x02 | x03 | x04 | x05 | x06 | x07 | x08 | x09 | x0a | x0b | x0c | x0d | x0e | x0f | x10 => Gt
+  | x11 => Eq
+  | _ => Lt
+  end.
+Definition compare_byte_x12 (b : byte) :=
+  match b with
+  | x00 | x01 | x02 | x03 | x04 | x05 | x06 | x07 | x08 | x09 | x0a | x0b | x0c | x0d | x0e | x0f | x10 | x11 => Gt
+  | x12 => Eq
+  | _ => Lt
+  end.
+Definition compare_byte_x13 (b : byte) :=
+  match b with
+  | x00 | x01 | x02 | x03 | x04 | x05 | x06 | x07 | x08 | x09 | x0a | x0b | x0c | x0d | x0e | x0f | x10 | x11 | x12 => Gt
+  | x13 => Eq
+  | _ => Lt
+  end.
+Definition compare_byte_x14 (b : byte) :=
+  match b with
+  | x00 | x01 | x02 | x03 | x04 | x05 | x06 | x07 | x08 | x09 | x0a | x0b | x0c | x0d | x0e | x0f | x10 | x11 | x12 | x13 => Gt
+  | x14 => Eq
+  | _ => Lt
+  end.
+Definition compare_byte_x15 (b : byte) :=
+  match b with
+  | x00 | x01 | x02 | x03 | x04 | x05 | x06 | x07 | x08 | x09 | x0a | x0b | x0c | x0d | x0e | x0f | x10 | x11 | x12 | x13 | x14 => Gt
+  | x15 => Eq
+  | _ => Lt
+  end.
+Definition compare_byte_x16 (b : byte) :=
+  match b with
+  | x00 | x01 | x02 | x03 | x04 | x05 | x06 | x07 | x08 | x09 | x0a | x0b | x0c | x0d | x0e | x0f | x10 | x11 | x12 | x13 | x14 | x15 => Gt
+  | x16 => Eq
+  | _ => Lt
+  end.
+Definition compare_byte_x17 (b : byte) :=
+  match b with
+  | x00 | x01 | x02 | x03 | x04 | x05 | x06 | x07 | x08 | x09 | x0a | x0b | x0c | x0d | x0e | x0f | x10 | x11 | x12 | x13 | x14 | x15 | x16 => Gt
+  | x17 => Eq
+  | _ => Lt
+  end.
+Definition compare_byte_x18 (b : byte) :=
+  match b with
+  | x00 | x01 | x02 | x03 | x04 | x05 | x06 | x07 | x08 | x09 | x0a | x0b | x0c | x0d | x0e | x0f | x10 | x11 | x12 | x13 | x14 | x15 | x16 | x17 => Gt
+  | x18 => Eq
+  | _ => Lt
+  end.
+Definition compare_byte_x19 (b : byte) :=
+  match b with
+  | x00 | x01 | x02 | x03 | x04 | x05 | x06 | x07 | x08 | x09 | x0a | x0b | x0c | x0d | x0e | x0f | x10 | x11 | x12 | x13 | x14 | x15 | x16 | x17 | x18 => Gt
+  | x19 => Eq
+  | _ => Lt
+  end.
+Definition compare_byte_x1a (b : byte) :=
+  match b with
+  | x00 | x01 | x02 | x03 | x04 | x05 | x06 | x07 | x08 | x09 | x0a | x0b | x0c | x0d | x0e | x0f | x10 | x11 | x12 | x13 | x14 | x15 | x16 | x17 | x18 | x19 => Gt
+  | x1a => Eq
+  | _ => Lt
+  end.
+Definition compare_byte_x1b (b : byte) :=
+  match b with
+  | x00 | x01 | x02 | x03 | x04 | x05 | x06 | x07 | x08 | x09 | x0a | x0b | x0c | x0d | x0e | x0f | x10 | x11 | x12 | x13 | x14 | x15 | x16 | x17 | x18 | x19 | x1a => Gt
+  | x1b => Eq
+  | _ => Lt
+  end.
+Definition compare_byte_x1c (b : byte) :=
+  match b with
+  | x00 | x01 | x02 | x03 | x04 | x05 | x06 | x07 | x08 | x09 | x0a | x0b | x0c | x0d | x0e | x0f | x10 | x11 | x12 | x13 | x14 | x15 | x16 | x17 | x18 | x19 | x1a | x1b => Gt
+  | x1c => Eq
+  | _ => Lt
+  end.
+Definition compare_byte_x1d (b : byte) :=
+  match b with
+  | x00 | x01 | x02 | x03 | x04 | x05 | x06 | x07 | x08 | x09 | x0a | x0b | x0c | x0d | x0e | x0f | x10 | x11 | x12 | x13 | x14 | x15 | x16 | x17 | x18 | x19 | x1a | x1b | x1c => Gt
+  | x1d => Eq
+  | _ => Lt
+  end.
+Definition compare_byte_x1e (b : byte) :=
+  match b with
+  | x00 | x01 | x02 | x03 | x04 | x05 | x06 | x07 | x08 | x09 | x0a | x0b | x0c | x0d | x0e | x0f | x10 | x11 | x12 | x13 | x14 | x15 | x16 | x17 | x18 | x19 | x1a | x1b | x1c | x1d => Gt
+  | x1e => Eq
+  | _ => Lt
+  end.
+Definition compare_byte_x1f (b : byte) :=
+  match b with
+  | x00 | x01 | x02 | x03 | x04 | x05 | x06 | x07 | x08 | x09 | x0a | x0b | x0c | x0d | x0e | x0f | x10 | x11 | x12 | x13 | x14 | x15 | x16 | x17 | x18 | x19 | x1a | x1b | x1c | x1d | x1e => Gt
+  | x1f => Eq
+  | _ => Lt
+  end.
+Definition compare_byte_x20 (b : byte) :=
+  match b with
+  | x00 | x01 | x02 | x03 | x04 | x05 | x06 | x07 | x08 | x09 | x0a | x0b | x0c | x0d | x0e | x0f | x10 | x11 | x12 | x13 | x14 | x15 | x16 | x17 | x18 | x19 | x1a | x1b | x1c | x1d | x1e | x1f => Gt
+  | x20 => Eq
+  | _ => Lt
+  end.
+Definition compare_byte_x21 (b : byte) :=
+  match b with
+  | x00 | x01 | x02 | x03 | x04 | x05 | x06 | x07 | x08 | x09 | x0a | x0b | x0c | x0d | x0e | x0f | x10 | x11 | x12 | x13 | x14 | x15 | x16 | x17 | x18 | x19 | x1a | x1b | x1c | x1d | x1e | x1f | x20 => Gt
+  | x21 => Eq
+  | _ => Lt
+  end.
+Definition compare_byte_x22 (b : byte) :=
+  match b with
+  | x00 | x01 | x02 | x03 | x04 | x05 | x06 | x07 | x08 | x09 | x0a | x0b | x0c | x0d | x0e | x0f | x10 | x11 | x12 | x13 | x14 | x15 | x16 | x17 | x18 | x19 | x1a | x1b | x1c | x1d | x1e | x1f | x20 | x21 => Gt
+  | x22 => Eq
+  | _ => Lt
+  end.
+Definition compare_byte_x23 (b : byte) :=
+  match b with
+  | x00 | x01 | x02 | x03 | x04 | x05 | x06 | x07 | x08 | x09 | x0a | x0b | x0c | x0d | x0e | x0f | x10 | x11 | x12 | x13 | x14 | x15 | x16 | x17 | x18 | x19 | x1a | x1b | x1c | x1d | x1e | x1f | x20 | x21 | x22 => Gt
+  | x23 => Eq
+  | _ => Lt
+  end.
+Definition compare_byte_x24 (b : byte) :=
+  match b with
+  | x00 | x01 | x02 | x03 | x04 | x05 | x06 | x07 | x08 | x09 | x0a | x0b | x0c | x0d | x0e | x0f | x10 | x11 | x12 | x13 | x14 | x15 | x16 | x17 | x18 | x19 | x1a | x1b | x1c | x1d | x1e | x1f | x20 | x21 | x22 | x23 => Gt
+  | x24 => Eq
+  | _ => Lt
+  end.
+Definition compare_byte_x25 (b : byte) :=
+  match b with
+  | x00 | x01 | x02 | x03 | x04 | x05 | x06 | x07 | x08 | x09 | x0a | x0b | x0c | x0d | x0e | x0f | x10 | x11 | x12 | x13 | x14 | x15 | x16 | x17 | x18 | x19 | x1a | x1b | x1c | x1d | x1e | x1f | x20 | x21 | x22 | x23 | x24 => Gt
+  | x25 => Eq
+  | _ => Lt
+  end.
+Definition compare_byte_x26 (b : byte) :=
+  match b with
+  | x00 | x01 | x02 | x03 | x04 | x05 | x06 | x07 | x08 | x09 | x0a | x0b | x0c | x0d | x0e | x0f | x10 | x11 | x12 | x13 | x14 | x15 | x16 | x17 | x18 | x19 | x1a | x1b | x1c | x1d | x1e | x1f | x20 | x21 | x22 | x23 | x24 | x25 => Gt
+  | x26 => Eq
+  | _ => Lt
+  end.
+Definition compare_byte_x27 (b : byte) :=
+  match b with
+  | x00 | x01 | x02 | x03 | x04 | x05 | x06 | x07 | x08 | x09 | x0a | x0b | x0c | x0d | x0e | x0f | x10 | x11 | x12 | x13 | x14 | x15 | x16 | x17 | x18 | x19 | x1a | x1b | x1c | x1d | x1e | x1f | x20 | x21 | x22 | x23 | x24 | x25 | x26 => Gt
+  | x27 => Eq
+  | _ => Lt
+  end.
+Definition compare_byte_x28 (b : byte) :=
+  match b with
+  | x00 | x01 | x02 | x03 | x04 | x05 | x06 | x07 | x08 | x09 | x0a | x0b | x0c | x0d | x0e | x0f | x10 | x11 | x12 | x13 | x14 | x15 | x16 | x17 | x18 | x19 | x1a | x1b | x1c | x1d | x1e | x1f | x20 | x21 | x22 | x23 | x24 | x25 | x26 | x27 => Gt
+  | x28 => Eq
+  | _ => Lt
+  end.
+Definition compare_byte_x29 (b : byte) :=
+  match b with
+  | x00 | x01 | x02 | x03 | x04 | x05 | x06 | x07 | x08 | x09 | x0a | x0b | x0c | x0d | x0e | x0f | x10 | x11 | x12 | x13 | x14 | x15 | x16 | x17 | x18 | x19 | x1a | x1b | x1c | x1d | x1e | x1f | x20 | x21 | x22 | x23 | x24 | x25 | x26 | x27 | x28 => Gt
+  | x29 => Eq
+  | _ => Lt
+  end.
+Definition compare_byte_x2a (b : byte) :=
+  match b with
+  | x00 | x01 | x02 | x03 | x04 | x05 | x06 | x07 | x08 | x09 | x0a | x0b | x0c | x0d | x0e | x0f | x10 | x11 | x12 | x13 | x14 | x15 | x16 | x17 | x18 | x19 | x1a | x1b | x1c | x1d | x1e | x1f | x20 | x21 | x22 | x23 | x24 | x25 | x26 | x27 | x28 | x29 => Gt
+  | x2a => Eq
+  | _ => Lt
+  end.
+Definition compare_byte_x2b (b : byte) :=
+  match b with
+  | x00 | x01 | x02 | x03 | x04 | x05 | x06 | x07 | x08 | x09 | x0a | x0b | x0c | x0d | x0e | x0f | x10 | x11 | x12 | x13 | x14 | x15 | x16 | x17 | x18 | x19 | x1a | x1b | x1c | x1d | x1e | x1f | x20 | x21 | x22 | x23 | x24 | x25 | x26 | x27 | x28 | x29 | x2a => Gt
+  | x2b => Eq
+  | _ => Lt
+  end.
+Definition compare_byte_x2c (b : byte) :=
+  match b with
+  | x00 | x01 | x02 | x03 | x04 | x05 | x06 | x07 | x08 | x09 | x0a | x0b | x0c | x0d | x0e | x0f | x10 | x11 | x12 | x13 | x14 | x15 | x16 | x17 | x18 | x19 | x1a | x1b | x1c | x1d | x1e | x1f | x20 | x21 | x22 | x23 | x24 | x25 | x26 | x27 | x28 | x29 | x2a | x2b => Gt
+  | x2c => Eq
+  | _ => Lt
+  end.
+Definition compare_byte_x2d (b : byte) :=
+  match b with
+  | x00 | x01 | x02 | x03 | x04 | x05 | x06 | x07 | x08 | x09 | x0a | x0b | x0c | x0d | x0e | x0f | x10 | x11 | x12 | x13 | x14 | x15 | x16 | x17 | x18 | x19 | x1a | x1b | x1c | x1d | x1e | x1f | x20 | x21 | x22 | x23 | x24 | x25 | x26 | x27 | x28 | x29 | x2a | x2b | x2c => Gt
+  | x2d => Eq
+  | _ => Lt
+  end.
+Definition compare_byte_x2e (b : byte) :=
+  match b with
+  | x00 | x01 | x02 | x03 | x04 | x05 | x06 | x07 | x08 | x09 | x0a | x0b | x0c | x0d | x0e | x0f | x10 | x11 | x12 | x13 | x14 | x15 | x16 | x17 | x18 | x19 | x1a | x1b | x1c | x1d | x1e | x1f | x20 | x21 | x22 | x23 | x24 | x25 | x26 | x27 | x28 | x29 | x2a | x2b | x2c | x2d => Gt
+  | x2e => Eq
+  | _ => Lt
+  end.
+Definition compare_byte_x2f (b : byte) :=
+  match b with
+  | x00 | x01 | x02 | x03 | x04 | x05 | x06 | x07 | x08 | x09 | x0a | x0b | x0c | x0d | x0e | x0f | x10 | x11 | x12 | x13 | x14 | x15 | x16 | x17 | x18 | x19 | x1a | x1b | x1c | x1d | x1e | x1f | x20 | x21 | x22 | x23 | x24 | x25 | x26 | x27 | x28 | x29 | x2a | x2b | x2c | x2d | x2e => Gt
+  | x2f => Eq
+  | _ => Lt
+  end.
+Definition compare_byte_x30 (b : byte) :=
+  match b with
+  | x00 | x01 | x02 | x03 | x04 | x05 | x06 | x07 | x08 | x09 | x0a | x0b | x0c | x0d | x0e | x0f | x10 | x11 | x12 | x13 | x14 | x15 | x16 | x17 | x18 | x19 | x1a | x1b | x1c | x1d | x1e | x1f | x20 | x21 | x22 | x23 | x24 | x25 | x26 | x27 | x28 | x29 | x2a | x2b | x2c | x2d | x2e | x2f => Gt
+  | x30 => Eq
+  | _ => Lt
+  end.
+Definition compare_byte_x31 (b : byte) :=
+  match b with
+  | x00 | x01 | x02 | x03 | x04 | x05 | x06 | x07 | x08 | x09 | x0a | x0b | x0c | x0d | x0e | x0f | x10 | x11 | x12 | x13 | x14 | x15 | x16 | x17 | x18 | x19 | x1a | x1b | x1c | x1d | x1e | x1f | x20 | x21 | x22 | x23 | x24 | x25 | x26 | x27 | x28 | x29 | x2a | x2b | x2c | x2d | x2e | x2f | x30 => Gt
+  | x31 => Eq
+  | _ => Lt
+  end.
+Definition compare_byte_x32 (b : byte) :=
+  match b with
+  | x00 | x01 | x02 | x03 | x04 | x05 | x06 | x07 | x08 | x09 | x0a | x0b | x0c | x0d | x0e | x0f | x10 | x11 | x12 | x13 | x14 | x15 | x16 | x17 | x18 | x19 | x1a | x1b | x1c | x1d | x1e | x1f | x20 | x21 | x22 | x23 | x24 | x25 | x26 | x27 | x28 | x29 | x2a | x2b | x2c | x2d | x2e | x2f | x30 | x31 => Gt
+  | x32 => Eq
+  | _ => Lt
+  end.
+Definition compare_byte_x33 (b : byte) :=
+  match b with
+  | x00 | x01 | x02 | x03 | x04 | x05 | x06 | x07 | x08 | x09 | x0a | x0b | x0c | x0d | x0e | x0f | x10 | x11 | x12 | x13 | x14 | x15 | x16 | x17 | x18 | x19 | x1a | x1b | x1c | x1d | x1e | x1f | x20 | x21 | x22 | x23 | x24 | x25 | x26 | x27 | x28 | x29 | x2a | x2b | x2c | x2d | x2e | x2f | x30 | x31 | x32 => Gt
+  | x33 => Eq
+  | _ => Lt
+  end.
+Definition compare_byte_x34 (b : byte) :=
+  match b with
+  | x00 | x01 | x02 | x03 | x04 | x05 | x06 | x07 | x08 | x09 | x0a | x0b | x0c | x0d | x0e | x0f | x10 | x11 | x12 | x13 | x14 | x15 | x16 | x17 | x18 | x19 | x1a | x1b | x1c | x1d | x1e | x1f | x20 | x21 | x22 | x23 | x24 | x25 | x26 | x27 | x28 | x29 | x2a | x2b | x2c | x2d | x2e | x2f | x30 | x31 | x32 | x33 => Gt
+  | x34 => Eq
+  | _ => Lt
+  end.
+Definition compare_byte_x35 (b : byte) :=
+  match b with
+  | x00 | x01 | x02 | x03 | x04 | x05 | x06 | x07 | x08 | x09 | x0a | x0b | x0c | x0d | x0e | x0f | x10 | x11 | x12 | x13 | x14 | x15 | x16 | x17 | x18 | x19 | x1a | x1b | x1c | x1d | x1e | x1f | x20 | x21 | x22 | x23 | x24 | x25 | x26 | x27 | x28 | x29 | x2a | x2b | x2c | x2d | x2e | x2f | x30 | x31 | x32 | x33 | x34 => Gt
+  | x35 => Eq
+  | _ => Lt
+  end.
+Definition compare_byte_x36 (b : byte) :=
+  match b with
+  | x00 | x01 | x02 | x03 | x04 | x05 | x06 | x07 | x08 | x09 | x0a | x0b | x0c | x0d | x0e | x0f | x10 | x11 | x12 | x13 | x14 | x15 | x16 | x17 | x18 | x19 | x1a | x1b | x1c | x1d | x1e | x1f | x20 | x21 | x22 | x23 | x24 | x25 | x26 | x27 | x28 | x29 | x2a | x2b | x2c | x2d | x2e | x2f | x30 | x31 | x32 | x33 | x34 | x35 => Gt
+  | x36 => Eq
+  | _ => Lt
+  end.
+Definition compare_byte_x37 (b : byte) :=
+  match b with
+  | x00 | x01 | x02 | x03 | x04 | x05 | x06 | x07 | x08 | x09 | x0a | x0b | x0c | x0d | x0e | x0f | x10 | x11 | x12 | x13 | x14 | x15 | x16 | x17 | x18 | x19 | x1a | x1b | x1c | x1d | x1e | x1f | x20 | x21 | x22 | x23 | x24 | x25 | x26 | x27 | x28 | x29 | x2a | x2b | x2c | x2d | x2e | x2f | x30 | x31 | x32 | x33 | x34 | x35 | x36 => Gt
+  | x37 => Eq
+  | _ => Lt
+  end.
+Definition compare_byte_x38 (b : byte) :=
+  match b with
+  | x00 | x01 | x02 | x03 | x04 | x05 | x06 | x07 | x08 | x09 | x0a | x0b | x0c | x0d | x0e | x0f | x10 | x11 | x12 | x13 | x14 | x15 | x16 | x17 | x18 | x19 | x1a | x1b | x1c | x1d | x1e | x1f | x20 | x21 | x22 | x23 | x24 | x25 | x26 | x27 | x28 | x29 | x2a | x2b | x2c | x2d | x2e | x2f | x30 | x31 | x32 | x33 | x34 | x35 | x36 | x37 => Gt
+  | x38 => Eq
+  | _ => Lt
+  end.
+Definition compare_byte_x39 (b : byte) :=
+  match b with
+  | x00 | x01 | x02 | x03 | x04 | x05 | x06 | x07 | x08 | x09 | x0a | x0b | x0c | x0d | x0e | x0f | x10 | x11 | x12 | x13 | x14 | x15 | x16 | x17 | x18 | x19 | x1a | x1b | x1c | x1d | x1e | x1f | x20 | x21 | x22 | x23 | x24 | x25 | x26 | x27 | x28 | x29 | x2a | x2b | x2c | x2d | x2e | x2f | x30 | x31 | x32 | x33 | x34 | x35 | x36 | x37 | x38 => Gt
+  | x39 => Eq
+  | _ => Lt
+  end.
+Definition compare_byte_x3a (b : byte) :=
+  match b with
+  | x00 | x01 | x02 | x03 | x04 | x05 | x06 | x07 | x08 | x09 | x0a | x0b | x0c | x0d | x0e | x0f | x10 | x11 | x12 | x13 | x14 | x15 | x16 | x17 | x18 | x19 | x1a | x1b | x1c | x1d | x1e | x1f | x20 | x21 | x22 | x23 | x24 | x25 | x26 | x27 | x28 | x29 | x2a | x2b | x2c | x2d | x2e | x2f | x30 | x31 | x32 | x33 | x34 | x35 | x36 | x37 | x38 | x39 => Gt
+  | x3a => Eq
+  | _ => Lt
+  end.
+Definition compare_byte_x3b (b : byte) :=
+  match b with
+  | x00 | x01 | x02 | x03 | x04 | x05 | x06 | x07 | x08 | x09 | x0a | x0b | x0c | x0d | x0e | x0f | x10 | x11 | x12 | x13 | x14 | x15 | x16 | x17 | x18 | x19 | x1a | x1b | x1c | x1d | x1e | x1f | x20 | x21 | x22 | x23 | x24 | x25 | x26 | x27 | x28 | x29 | x2a | x2b | x2c | x2d | x2e | x2f | x30 | x31 | x32 | x33 | x34 | x35 | x36 | x37 | x38 | x39 | x3a => Gt
+  | x3b => Eq
+  | _ => Lt
+  end.
+Definition compare_byte_x3c (b : byte) :=
+  match b with
+  | x00 | x01 | x02 | x03 | x04 | x05 | x06 | x07 | x08 | x09 | x0a | x0b | x0c | x0d | x0e | x0f | x10 | x11 | x12 | x13 | x14 | x15 | x16 | x17 | x18 | x19 | x1a | x1b | x1c | x1d | x1e | x1f | x20 | x21 | x22 | x23 | x24 | x25 | x26 | x27 | x28 | x29 | x2a | x2b | x2c | x2d | x2e | x2f | x30 | x31 | x32 | x33 | x34 | x35 | x36 | x37 | x38 | x39 | x3a | x3b => Gt
+  | x3c => Eq
+  | _ => Lt
+  end.
+Definition compare_byte_x3d (b : byte) :=
+  match b with
+  | x00 | x01 | x02 | x03 | x04 | x05 | x06 | x07 | x08 | x09 | x0a | x0b | x0c | x0d | x0e | x0f | x10 | x11 | x12 | x13 | x14 | x15 | x16 | x17 | x18 | x19 | x1a | x1b | x1c | x1d | x1e | x1f | x20 | x21 | x22 | x23 | x24 | x25 | x26 | x27 | x28 | x29 | x2a | x2b | x2c | x2d | x2e | x2f | x30 | x31 | x32 | x33 | x34 | x35 | x36 | x37 | x38 | x39 | x3a | x3b | x3c => Gt
+  | x3d => Eq
+  | _ => Lt
+  end.
+Definition compare_byte_x3e (b : byte) :=
+  match b with
+  | x00 | x01 | x02 | x03 | x04 | x05 | x06 | x07 | x08 | x09 | x0a | x0b | x0c | x0d | x0e | x0f | x10 | x11 | x12 | x13 | x14 | x15 | x16 | x17 | x18 | x19 | x1a | x1b | x1c | x1d | x1e | x1f | x20 | x21 | x22 | x23 | x24 | x25 | x26 | x27 | x28 | x29 | x2a | x2b | x2c | x2d | x2e | x2f | x30 | x31 | x32 | x33 | x34 | x35 | x36 | x37 | x38 | x39 | x3a | x3b | x3c | x3d => Gt
+  | x3e => Eq
+  | _ => Lt
+  end.
+Definition compare_byte_x3f (b : byte) :=
+  match b with
+  | x00 | x01 | x02 | x03 | x04 | x05 | x06 | x07 | x08 | x09 | x0a | x0b | x0c | x0d | x0e | x0f | x10 | x11 | x12 | x13 | x14 | x15 | x16 | x17 | x18 | x19 | x1a | x1b | x1c | x1d | x1e | x1f | x20 | x21 | x22 | x23 | x24 | x25 | x26 | x27 | x28 | x29 | x2a | x2b | x2c | x2d | x2e | x2f | x30 | x31 | x32 | x33 | x34 | x35 | x36 | x37 | x38 | x39 | x3a | x3b | x3c | x3d | x3e => Gt
+  | x3f => Eq
+  | _ => Lt
+  end.
+Definition compare_byte_x40 (b : byte) :=
+  match b with
+  | x00 | x01 | x02 | x03 | x04 | x05 | x06 | x07 | x08 | x09 | x0a | x0b | x0c | x0d | x0e | x0f | x10 | x11 | x12 | x13 | x14 | x15 | x16 | x17 | x18 | x19 | x1a | x1b | x1c | x1d | x1e | x1f | x20 | x21 | x22 | x23 | x24 | x25 | x26 | x27 | x28 | x29 | x2a | x2b | x2c | x2d | x2e | x2f | x30 | x31 | x32 | x33 | x34 | x35 | x36 | x37 | x38 | x39 | x3a | x3b | x3c | x3d | x3e | x3f => Gt
+  | x40 => Eq
+  | _ => Lt
+  end.
+Definition compare_byte_x41 (b : byte) :=
+  match b with
+  | x00 | x01 | x02 | x03 | x04 | x05 | x06 | x07 | x08 | x09 | x0a | x0b | x0c | x0d | x0e | x0f | x10 | x11 | x12 | x13 | x14 | x15 | x16 | x17 | x18 | x19 | x1a | x1b | x1c | x1d | x1e | x1f | x20 | x21 | x22 | x23 | x24 | x25 | x26 | x27 | x28 | x29 | x2a | x2b | x2c | x2d | x2e | x2f | x30 | x31 | x32 | x33 | x34 | x35 | x36 | x37 | x38 | x39 | x3a | x3b | x3c | x3d | x3e | x3f | x40 => Gt
+  | x41 => Eq
+  | _ => Lt
+  end.
+Definition compare_byte_x42 (b : byte) :=
+  match b with
+  | x00 | x01 | x02 | x03 | x04 | x05 | x06 | x07 | x08 | x09 | x0a | x0b | x0c | x0d | x0e | x0f | x10 | x11 | x12 | x13 | x14 | x15 | x16 | x17 | x18 | x19 | x1a | x1b | x1c | x1d | x1e | x1f | x20 | x21 | x22 | x23 | x24 | x25 | x26 | x27 | x28 | x29 | x2a | x2b | x2c | x2d | x2e | x2f | x30 | x31 | x32 | x33 | x34 | x35 | x36 | x37 | x38 | x39 | x3a | x3b | x3c | x3d | x3e | x3f | x40 | x41 => Gt
+  | x42 => Eq
+  | _ => Lt
+  end.
+Definition compare_byte_x43 (b : byte) :=
+  match b with
+  | x00 | x01 | x02 | x03 | x04 | x05 | x06 | x07 | x08 | x09 | x0a | x0b | x0c | x0d | x0e | x0f | x10 | x11 | x12 | x13 | x14 | x15 | x16 | x17 | x18 | x19 | x1a | x1b | x1c | x1d | x1e | x1f | x20 | x21 | x22 | x23 | x24 | x25 | x26 | x27 | x28 | x29 | x2a | x2b | x2c | x2d | x2e | x2f | x30 | x31 | x32 | x33 | x34 | x35 | x36 | x37 | x38 | x39 | x3a | x3b | x3c | x3d | x3e | x3f | x40 | x41 | x42 => Gt
+  | x43 => Eq
+  | _ => Lt
+  end.
+Definition compare_byte_x44 (b : byte) :=
+  match b with
+  | x00 | x01 | x02 | x03 | x04 | x05 | x06 | x07 | x08 | x09 | x0a | x0b | x0c | x0d | x0e | x0f | x10 | x11 | x12 | x13 | x14 | x15 | x16 | x17 | x18 | x19 | x1a | x1b | x1c | x1d | x1e | x1f | x20 | x21 | x22 | x23 | x24 | x25 | x26 | x27 | x28 | x29 | x2a | x2b | x2c | x2d | x2e | x2f | x30 | x31 | x32 | x33 | x34 | x35 | x36 | x37 | x38 | x39 | x3a | x3b | x3c | x3d | x3e | x3f | x40 | x41 | x42 | x43 => Gt
+  | x44 => Eq
+  | _ => Lt
+  end.
+Definition compare_byte_x45 (b : byte) :=
+  match b with
+  | x00 | x01 | x02 | x03 | x04 | x05 | x06 | x07 | x08 | x09 | x0a | x0b | x0c | x0d | x0e | x0f | x10 | x11 | x12 | x13 | x14 | x15 | x16 | x17 | x18 | x19 | x1a | x1b | x1c | x1d | x1e | x1f | x20 | x21 | x22 | x23 | x24 | x25 | x26 | x27 | x28 | x29 | x2a | x2b | x2c | x2d | x2e | x2f | x30 | x31 | x32 | x33 | x34 | x35 | x36 | x37 | x38 | x39 | x3a | x3b | x3c | x3d | x3e | x3f | x40 | x41 | x42 | x43 | x44 => Gt
+  | x45 => Eq
+  | _ => Lt
+  end.
+Definition compare_byte_x46 (b : byte) :=
+  match b with
+  | x00 | x01 | x02 | x03 | x04 | x05 | x06 | x07 | x08 | x09 | x0a | x0b | x0c | x0d | x0e | x0f | x10 | x11 | x12 | x13 | x14 | x15 | x16 | x17 | x18 | x19 | x1a | x1b | x1c | x1d | x1e | x1f | x20 | x21 | x22 | x23 | x24 | x25 | x26 | x27 | x28 | x29 | x2a | x2b | x2c | x2d | x2e | x2f | x30 | x31 | x32 | x33 | x34 | x35 | x36 | x37 | x38 | x39 | x3a | x3b | x3c | x3d | x3e | x3f | x40 | x41 | x42 | x43 | x44 | x45 => Gt
+  | x46 => Eq
+  | _ => Lt
+  end.
+Definition compare_byte_x47 (b : byte) :=
+  match b with
+  | x00 | x01 | x02 | x03 | x04 | x05 | x06 | x07 | x08 | x09 | x0a | x0b | x0c | x0d | x0e | x0f | x10 | x11 | x12 | x13 | x14 | x15 | x16 | x17 | x18 | x19 | x1a | x1b | x1c | x1d | x1e | x1f | x20 | x21 | x22 | x23 | x24 | x25 | x26 | x27 | x28 | x29 | x2a | x2b | x2c | x2d | x2e | x2f | x30 | x31 | x32 | x33 | x34 | x35 | x36 | x37 | x38 | x39 | x3a | x3b | x3c | x3d | x3e | x3f | x40 | x41 | x42 | x43 | x44 | x45 | x46 => Gt
+  | x47 => Eq
+  | _ => Lt
+  end.
+Definition compare_byte_x48 (b : byte) :=
+  match b with
+  | x00 | x01 | x02 | x03 | x04 | x05 | x06 | x07 | x08 | x09 | x0a | x0b | x0c | x0d | x0e | x0f | x10 | x11 | x12 | x13 | x14 | x15 | x16 | x17 | x18 | x19 | x1a | x1b | x1c | x1d | x1e | x1f | x20 | x21 | x22 | x23 | x24 | x25 | x26 | x27 | x28 | x29 | x2a | x2b | x2c | x2d | x2e | x2f | x30 | x31 | x32 | x33 | x34 | x35 | x36 | x37 | x38 | x39 | x3a | x3b | x3c | x3d | x3e | x3f | x40 | x41 | x42 | x43 | x44 | x45 | x46 | x47 => Gt
+  | x48 => Eq
+  | _ => Lt
+  end.
+Definition compare_byte_x49 (b : byte) :=
+  match b with
+  | x00 | x01 | x02 | x03 | x04 | x05 | x06 | x07 | x08 | x09 | x0a | x0b | x0c | x0d | x0e | x0f | x10 | x11 | x12 | x13 | x14 | x15 | x16 | x17 | x18 | x19 | x1a | x1b | x1c | x1d | x1e | x1f | x20 | x21 | x22 | x23 | x24 | x25 | x26 | x27 | x28 | x29 | x2a | x2b | x2c | x2d | x2e | x2f | x30 | x31 | x32 | x33 | x34 | x35 | x36 | x37 | x38 | x39 | x3a | x3b | x3c | x3d | x3e | x3f | x40 | x41 | x42 | x43 | x44 | x45 | x46 | x47 | x48 => Gt
+  | x49 => Eq
+  | _ => Lt
+  end.
+Definition compare_byte_x4a (b : byte) :=
+  match b with
+  | x00 | x01 | x02 | x03 | x04 | x05 | x06 | x07 | x08 | x09 | x0a | x0b | x0c | x0d | x0e | x0f | x10 | x11 | x12 | x13 | x14 | x15 | x16 | x17 | x18 | x19 | x1a | x1b | x1c | x1d | x1e | x1f | x20 | x21 | x22 | x23 | x24 | x25 | x26 | x27 | x28 | x29 | x2a | x2b | x2c | x2d | x2e | x2f | x30 | x31 | x32 | x33 | x34 | x35 | x36 | x37 | x38 | x39 | x3a | x3b | x3c | x3d | x3e | x3f | x40 | x41 | x42 | x43 | x44 | x45 | x46 | x47 | x48 | x49 => Gt
+  | x4a => Eq
+  | _ => Lt
+  end.
+Definition compare_byte_x4b (b : byte) :=
+  match b with
+  | x00 | x01 | x02 | x03 | x04 | x05 | x06 | x07 | x08 | x09 | x0a | x0b | x0c | x0d | x0e | x0f | x10 | x11 | x12 | x13 | x14 | x15 | x16 | x17 | x18 | x19 | x1a | x1b | x1c | x1d | x1e | x1f | x20 | x21 | x22 | x23 | x24 | x25 | x26 | x27 | x28 | x29 | x2a | x2b | x2c | x2d | x2e | x2f | x30 | x31 | x32 | x33 | x34 | x35 | x36 | x37 | x38 | x39 | x3a | x3b | x3c | x3d | x3e | x3f | x40 | x41 | x42 | x43 | x44 | x45 | x46 | x47 | x48 | x49 | x4a => Gt
+  | x4b => Eq
+  | _ => Lt
+  end.
+Definition compare_byte_x4c (b : byte) :=
+  match b with
+  | x00 | x01 | x02 | x03 | x04 | x05 | x06 | x07 | x08 | x09 | x0a | x0b | x0c | x0d | x0e | x0f | x10 | x11 | x12 | x13 | x14 | x15 | x16 | x17 | x18 | x19 | x1a | x1b | x1c | x1d | x1e | x1f | x20 | x21 | x22 | x23 | x24 | x25 | x26 | x27 | x28 | x29 | x2a | x2b | x2c | x2d | x2e | x2f | x30 | x31 | x32 | x33 | x34 | x35 | x36 | x37 | x38 | x39 | x3a | x3b | x3c | x3d | x3e | x3f | x40 | x41 | x42 | x43 | x44 | x45 | x46 | x47 | x48 | x49 | x4a | x4b => Gt
+  | x4c => Eq
+  | _ => Lt
+  end.
+Definition compare_byte_x4d (b : byte) :=
+  match b with
+  | x00 | x01 | x02 | x03 | x04 | x05 | x06 | x07 | x08 | x09 | x0a | x0b | x0c | x0d | x0e | x0f | x10 | x11 | x12 | x13 | x14 | x15 | x16 | x17 | x18 | x19 | x1a | x1b | x1c | x1d | x1e | x1f | x20 | x21 | x22 | x23 | x24 | x25 | x26 | x27 | x28 | x29 | x2a | x2b | x2c | x2d | x2e | x2f | x30 | x31 | x32 | x33 | x34 | x35 | x36 | x37 | x38 | x39 | x3a | x3b | x3c | x3d | x3e | x3f | x40 | x41 | x42 | x43 | x44 | x45 | x46 | x47 | x48 | x49 | x4a | x4b | x4c => Gt
+  | x4d => Eq
+  | _ => Lt
+  end.
+Definition compare_byte_x4e (b : byte) :=
+  match b with
+  | x00 | x01 | x02 | x03 | x04 | x05 | x06 | x07 | x08 | x09 | x0a | x0b | x0c | x0d | x0e | x0f | x10 | x11 | x12 | x13 | x14 | x15 | x16 | x17 | x18 | x19 | x1a | x1b | x1c | x1d | x1e | x1f | x20 | x21 | x22 | x23 | x24 | x25 | x26 | x27 | x28 | x29 | x2a | x2b | x2c | x2d | x2e | x2f | x30 | x31 | x32 | x33 | x34 | x35 | x36 | x37 | x38 | x39 | x3a | x3b | x3c | x3d | x3e | x3f | x40 | x41 | x42 | x43 | x44 | x45 | x46 | x47 | x48 | x49 | x4a | x4b | x4c | x4d => Gt
+  | x4e => Eq
+  | _ => Lt
+  end.
+Definition compare_byte_x4f (b : byte) :=
+  match b with
+  | x00 | x01 | x02 | x03 | x04 | x05 | x06 | x07 | x08 | x09 | x0a | x0b | x0c | x0d | x0e | x0f | x10 | x11 | x12 | x13 | x14 | x15 | x16 | x17 | x18 | x19 | x1a | x1b | x1c | x1d | x1e | x1f | x20 | x21 | x22 | x23 | x24 | x25 | x26 | x27 | x28 | x29 | x2a | x2b | x2c | x2d | x2e | x2f | x30 | x31 | x32 | x33 | x34 | x35 | x36 | x37 | x38 | x39 | x3a | x3b | x3c | x3d | x3e | x3f | x40 | x41 | x42 | x43 | x44 | x45 | x46 | x47 | x48 | x49 | x4a | x4b | x4c | x4d | x4e => Gt
+  | x4f => Eq
+  | _ => Lt
+  end.
+Definition compare_byte_x50 (b : byte) :=
+  match b with
+  | x00 | x01 | x02 | x03 | x04 | x05 | x06 | x07 | x08 | x09 | x0a | x0b | x0c | x0d | x0e | x0f | x10 | x11 | x12 | x13 | x14 | x15 | x16 | x17 | x18 | x19 | x1a | x1b | x1c | x1d | x1e | x1f | x20 | x21 | x22 | x23 | x24 | x25 | x26 | x27 | x28 | x29 | x2a | x2b | x2c | x2d | x2e | x2f | x30 | x31 | x32 | x33 | x34 | x35 | x36 | x37 | x38 | x39 | x3a | x3b | x3c | x3d | x3e | x3f | x40 | x41 | x42 | x43 | x44 | x45 | x46 | x47 | x48 | x49 | x4a | x4b | x4c | x4d | x4e | x4f => Gt
+  | x50 => Eq
+  | _ => Lt
+  end.
+Definition compare_byte_x51 (b : byte) :=
+  match b with
+  | x00 | x01 | x02 | x03 | x04 | x05 | x06 | x07 | x08 | x09 | x0a | x0b | x0c | x0d | x0e | x0f | x10 | x11 | x12 | x13 | x14 | x15 | x16 | x17 | x18 | x19 | x1a | x1b | x1c | x1d | x1e | x1f | x20 | x21 | x22 | x23 | x24 | x25 | x26 | x27 | x28 | x29 | x2a | x2b | x2c | x2d | x2e | x2f | x30 | x31 | x32 | x33 | x34 | x35 | x36 | x37 | x38 | x39 | x3a | x3b | x3c | x3d | x3e | x3f | x40 | x41 | x42 | x43 | x44 | x45 | x46 | x47 | x48 | x49 | x4a | x4b | x4c | x4d | x4e | x4f | x50 => Gt
+  | x51 => Eq
+  | _ => Lt
+  end.
+Definition compare_byte_x52 (b : byte) :=
+  match b with
+  | x00 | x01 | x02 | x03 | x04 | x05 | x06 | x07 | x08 | x09 | x0a | x0b | x0c | x0d | x0e | x0f | x10 | x11 | x12 | x13 | x14 | x15 | x16 | x17 | x18 | x19 | x1a | x1b | x1c | x1d | x1e | x1f | x20 | x21 | x22 | x23 | x24 | x25 | x26 | x27 | x28 | x29 | x2a | x2b | x2c | x2d | x2e | x2f | x30 | x31 | x32 | x33 | x34 | x35 | x36 | x37 | x38 | x39 | x3a | x3b | x3c | x3d | x3e | x3f | x40 | x41 | x42 | x43 | x44 | x45 | x46 | x47 | x48 | x49 | x4a | x4b | x4c | x4d | x4e | x4f | x50 | x51 => Gt
+  | x52 => Eq
+  | _ => Lt
+  end.
+Definition compare_byte_x53 (b : byte) :=
+  match b with
+  | x00 | x01 | x02 | x03 | x04 | x05 | x06 | x07 | x08 | x09 | x0a | x0b | x0c | x0d | x0e | x0f | x10 | x11 | x12 | x13 | x14 | x15 | x16 | x17 | x18 | x19 | x1a | x1b | x1c | x1d | x1e | x1f | x20 | x21 | x22 | x23 | x24 | x25 | x26 | x27 | x28 | x29 | x2a | x2b | x2c | x2d | x2e | x2f | x30 | x31 | x32 | x33 | x34 | x35 | x36 | x37 | x38 | x39 | x3a | x3b | x3c | x3d | x3e | x3f | x40 | x41 | x42 | x43 | x44 | x45 | x46 | x47 | x48 | x49 | x4a | x4b | x4c | x4d | x4e | x4f | x50 | x51 | x52 => Gt
+  | x53 => Eq
+  | _ => Lt
+  end.
+Definition compare_byte_x54 (b : byte) :=
+  match b with
+  | x00 | x01 | x02 | x03 | x04 | x05 | x06 | x07 | x08 | x09 | x0a | x0b | x0c | x0d | x0e | x0f | x10 | x11 | x12 | x13 | x14 | x15 | x16 | x17 | x18 | x19 | x1a | x1b | x1c | x1d | x1e | x1f | x20 | x21 | x22 | x23 | x24 | x25 | x26 | x27 | x28 | x29 | x2a | x2b | x2c | x2d | x2e | x2f | x30 | x31 | x32 | x33 | x34 | x35 | x36 | x37 | x38 | x39 | x3a | x3b | x3c | x3d | x3e | x3f | x40 | x41 | x42 | x43 | x44 | x45 | x46 | x47 | x48 | x49 | x4a | x4b | x4c | x4d | x4e | x4f | x50 | x51 | x52 | x53 => Gt
+  | x54 => Eq
+  | _ => Lt
+  end.
+Definition compare_byte_x55 (b : byte) :=
+  match b with
+  | x00 | x01 | x02 | x03 | x04 | x05 | x06 | x07 | x08 | x09 | x0a | x0b | x0c | x0d | x0e | x0f | x10 | x11 | x12 | x13 | x14 | x15 | x16 | x17 | x18 | x19 | x1a | x1b | x1c | x1d | x1e | x1f | x20 | x21 | x22 | x23 | x24 | x25 | x26 | x27 | x28 | x29 | x2a | x2b | x2c | x2d | x2e | x2f | x30 | x31 | x32 | x33 | x34 | x35 | x36 | x37 | x38 | x39 | x3a | x3b | x3c | x3d | x3e | x3f | x40 | x41 | x42 | x43 | x44 | x45 | x46 | x47 | x48 | x49 | x4a | x4b | x4c | x4d | x4e | x4f | x50 | x51 | x52 | x53 | x54 => Gt
+  | x55 => Eq
+  | _ => Lt
+  end.
+Definition compare_byte_x56 (b : byte) :=
+  match b with
+  | x00 | x01 | x02 | x03 | x04 | x05 | x06 | x07 | x08 | x09 | x0a | x0b | x0c | x0d | x0e | x0f | x10 | x11 | x12 | x13 | x14 | x15 | x16 | x17 | x18 | x19 | x1a | x1b | x1c | x1d | x1e | x1f | x20 | x21 | x22 | x23 | x24 | x25 | x26 | x27 | x28 | x29 | x2a | x2b | x2c | x2d | x2e | x2f | x30 | x31 | x32 | x33 | x34 | x35 | x36 | x37 | x38 | x39 | x3a | x3b | x3c | x3d | x3e | x3f | x40 | x41 | x42 | x43 | x44 | x45 | x46 | x47 | x48 | x49 | x4a | x4b | x4c | x4d | x4e | x4f | x50 | x51 | x52 | x53 | x54 | x55 => Gt
+  | x56 => Eq
+  | _ => Lt
+  end.
+Definition compare_byte_x57 (b : byte) :=
+  match b with
+  | x00 | x01 | x02 | x03 | x04 | x05 | x06 | x07 | x08 | x09 | x0a | x0b | x0c | x0d | x0e | x0f | x10 | x11 | x12 | x13 | x14 | x15 | x16 | x17 | x18 | x19 | x1a | x1b | x1c | x1d | x1e | x1f | x20 | x21 | x22 | x23 | x24 | x25 | x26 | x27 | x28 | x29 | x2a | x2b | x2c | x2d | x2e | x2f | x30 | x31 | x32 | x33 | x34 | x35 | x36 | x37 | x38 | x39 | x3a | x3b | x3c | x3d | x3e | x3f | x40 | x41 | x42 | x43 | x44 | x45 | x46 | x47 | x48 | x49 | x4a | x4b | x4c | x4d | x4e | x4f | x50 | x51 | x52 | x53 | x54 | x55 | x56 => Gt
+  | x57 => Eq
+  | _ => Lt
+  end.
+Definition compare_byte_x58 (b : byte) :=
+  match b with
+  | x00 | x01 | x02 | x03 | x04 | x05 | x06 | x07 | x08 | x09 | x0a | x0b | x0c | x0d | x0e | x0f | x10 | x11 | x12 | x13 | x14 | x15 | x16 | x17 | x18 | x19 | x1a | x1b | x1c | x1d | x1e | x1f | x20 | x21 | x22 | x23 | x24 | x25 | x26 | x27 | x28 | x29 | x2a | x2b | x2c | x2d | x2e | x2f | x30 | x31 | x32 | x33 | x34 | x35 | x36 | x37 | x38 | x39 | x3a | x3b | x3c | x3d | x3e | x3f | x40 | x41 | x42 | x43 | x44 | x45 | x46 | x47 | x48 | x49 | x4a | x4b | x4c | x4d | x4e | x4f | x50 | x51 | x52 | x53 | x54 | x55 | x56 | x57 => Gt
+  | x58 => Eq
+  | _ => Lt
+  end.
+Definition compare_byte_x59 (b : byte) :=
+  match b with
+  | x00 | x01 | x02 | x03 | x04 | x05 | x06 | x07 | x08 | x09 | x0a | x0b | x0c | x0d | x0e | x0f | x10 | x11 | x12 | x13 | x14 | x15 | x16 | x17 | x18 | x19 | x1a | x1b | x1c | x1d | x1e | x1f | x20 | x21 | x22 | x23 | x24 | x25 | x26 | x27 | x28 | x29 | x2a | x2b | x2c | x2d | x2e | x2f | x30 | x31 | x32 | x33 | x34 | x35 | x36 | x37 | x38 | x39 | x3a | x3b | x3c | x3d | x3e | x3f | x40 | x41 | x42 | x43 | x44 | x45 | x46 | x47 | x48 | x49 | x4a | x4b | x4c | x4d | x4e | x4f | x50 | x51 | x52 | x53 | x54 | x55 | x56 | x57 | x58 => Gt
+  | x59 => Eq
+  | _ => Lt
+  end.
+Definition compare_byte_x5a (b : byte) :=
+  match b with
+  | x00 | x01 | x02 | x03 | x04 | x05 | x06 | x07 | x08 | x09 | x0a | x0b | x0c | x0d | x0e | x0f | x10 | x11 | x12 | x13 | x14 | x15 | x16 | x17 | x18 | x19 | x1a | x1b | x1c | x1d | x1e | x1f | x20 | x21 | x22 | x23 | x24 | x25 | x26 | x27 | x28 | x29 | x2a | x2b | x2c | x2d | x2e | x2f | x30 | x31 | x32 | x33 | x34 | x35 | x36 | x37 | x38 | x39 | x3a | x3b | x3c | x3d | x3e | x3f | x40 | x41 | x42 | x43 | x44 | x45 | x46 | x47 | x48 | x49 | x4a | x4b | x4c | x4d | x4e | x4f | x50 | x51 | x52 | x53 | x54 | x55 | x56 | x57 | x58 | x59 => Gt
+  | x5a => Eq
+  | _ => Lt
+  end.
+Definition compare_byte_x5b (b : byte) :=
+  match b with
+  | x00 | x01 | x02 | x03 | x04 | x05 | x06 | x07 | x08 | x09 | x0a | x0b | x0c | x0d | x0e | x0f | x10 | x11 | x12 | x13 | x14 | x15 | x16 | x17 | x18 | x19 | x1a | x1b | x1c | x1d | x1e | x1f | x20 | x21 | x22 | x23 | x24 | x25 | x26 | x27 | x28 | x29 | x2a | x2b | x2c | x2d | x2e | x2f | x30 | x31 | x32 | x33 | x34 | x35 | x36 | x37 | x38 | x39 | x3a | x3b | x3c | x3d | x3e | x3f | x40 | x41 | x42 | x43 | x44 | x45 | x46 | x47 | x48 | x49 | x4a | x4b | x4c | x4d | x4e | x4f | x50 | x51 | x52 | x53 | x54 | x55 | x56 | x57 | x58 | x59 | x5a => Gt
+  | x5b => Eq
+  | _ => Lt
+  end.
+Definition compare_byte_x5c (b : byte) :=
+  match b with
+  | x00 | x01 | x02 | x03 | x04 | x05 | x06 | x07 | x08 | x09 | x0a | x0b | x0c | x0d | x0e | x0f | x10 | x11 | x12 | x13 | x14 | x15 | x16 | x17 | x18 | x19 | x1a | x1b | x1c | x1d | x1e | x1f | x20 | x21 | x22 | x23 | x24 | x25 | x26 | x27 | x28 | x29 | x2a | x2b | x2c | x2d | x2e | x2f | x30 | x31 | x32 | x33 | x34 | x35 | x36 | x37 | x38 | x39 | x3a | x3b | x3c | x3d | x3e | x3f | x40 | x41 | x42 | x43 | x44 | x45 | x46 | x47 | x48 | x49 | x4a | x4b | x4c | x4d | x4e | x4f | x50 | x51 | x52 | x53 | x54 | x55 | x56 | x57 | x58 | x59 | x5a | x5b => Gt
+  | x5c => Eq
+  | _ => Lt
+  end.
+Definition compare_byte_x5d (b : byte) :=
+  match b with
+  | x00 | x01 | x02 | x03 | x04 | x05 | x06 | x07 | x08 | x09 | x0a | x0b | x0c | x0d | x0e | x0f | x10 | x11 | x12 | x13 | x14 | x15 | x16 | x17 | x18 | x19 | x1a | x1b | x1c | x1d | x1e | x1f | x20 | x21 | x22 | x23 | x24 | x25 | x26 | x27 | x28 | x29 | x2a | x2b | x2c | x2d | x2e | x2f | x30 | x31 | x32 | x33 | x34 | x35 | x36 | x37 | x38 | x39 | x3a | x3b | x3c | x3d | x3e | x3f | x40 | x41 | x42 | x43 | x44 | x45 | x46 | x47 | x48 | x49 | x4a | x4b | x4c | x4d | x4e | x4f | x50 | x51 | x52 | x53 | x54 | x55 | x56 | x57 | x58 | x59 | x5a | x5b | x5c => Gt
+  | x5d => Eq
+  | _ => Lt
+  end.
+Definition compare_byte_x5e (b : byte) :=
+  match b with
+  | x00 | x01 | x02 | x03 | x04 | x05 | x06 | x07 | x08 | x09 | x0a | x0b | x0c | x0d | x0e | x0f | x10 | x11 | x12 | x13 | x14 | x15 | x16 | x17 | x18 | x19 | x1a | x1b | x1c | x1d | x1e | x1f | x20 | x21 | x22 | x23 | x24 | x25 | x26 | x27 | x28 | x29 | x2a | x2b | x2c | x2d | x2e | x2f | x30 | x31 | x32 | x33 | x34 | x35 | x36 | x37 | x38 | x39 | x3a | x3b | x3c | x3d | x3e | x3f | x40 | x41 | x42 | x43 | x44 | x45 | x46 | x47 | x48 | x49 | x4a | x4b | x4c | x4d | x4e | x4f | x50 | x51 | x52 | x53 | x54 | x55 | x56 | x57 | x58 | x59 | x5a | x5b | x5c | x5d => Gt
+  | x5e => Eq
+  | _ => Lt
+  end.
+Definition compare_byte_x5f (b : byte) :=
+  match b with
+  | x00 | x01 | x02 | x03 | x04 | x05 | x06 | x07 | x08 | x09 | x0a | x0b | x0c | x0d | x0e | x0f | x10 | x11 | x12 | x13 | x14 | x15 | x16 | x17 | x18 | x19 | x1a | x1b | x1c | x1d | x1e | x1f | x20 | x21 | x22 | x23 | x24 | x25 | x26 | x27 | x28 | x29 | x2a | x2b | x2c | x2d | x2e | x2f | x30 | x31 | x32 | x33 | x34 | x35 | x36 | x37 | x38 | x39 | x3a | x3b | x3c | x3d | x3e | x3f | x40 | x41 | x42 | x43 | x44 | x45 | x46 | x47 | x48 | x49 | x4a | x4b | x4c | x4d | x4e | x4f | x50 | x51 | x52 | x53 | x54 | x55 | x56 | x57 | x58 | x59 | x5a | x5b | x5c | x5d | x5e => Gt
+  | x5f => Eq
+  | _ => Lt
+  end.
+Definition compare_byte_x60 (b : byte) :=
+  match b with
+  | x00 | x01 | x02 | x03 | x04 | x05 | x06 | x07 | x08 | x09 | x0a | x0b | x0c | x0d | x0e | x0f | x10 | x11 | x12 | x13 | x14 | x15 | x16 | x17 | x18 | x19 | x1a | x1b | x1c | x1d | x1e | x1f | x20 | x21 | x22 | x23 | x24 | x25 | x26 | x27 | x28 | x29 | x2a | x2b | x2c | x2d | x2e | x2f | x30 | x31 | x32 | x33 | x34 | x35 | x36 | x37 | x38 | x39 | x3a | x3b | x3c | x3d | x3e | x3f | x40 | x41 | x42 | x43 | x44 | x45 | x46 | x47 | x48 | x49 | x4a | x4b | x4c | x4d | x4e | x4f | x50 | x51 | x52 | x53 | x54 | x55 | x56 | x57 | x58 | x59 | x5a | x5b | x5c | x5d | x5e | x5f => Gt
+  | x60 => Eq
+  | _ => Lt
+  end.
+Definition compare_byte_x61 (b : byte) :=
+  match b with
+  | x00 | x01 | x02 | x03 | x04 | x05 | x06 | x07 | x08 | x09 | x0a | x0b | x0c | x0d | x0e | x0f | x10 | x11 | x12 | x13 | x14 | x15 | x16 | x17 | x18 | x19 | x1a | x1b | x1c | x1d | x1e | x1f | x20 | x21 | x22 | x23 | x24 | x25 | x26 | x27 | x28 | x29 | x2a | x2b | x2c | x2d | x2e | x2f | x30 | x31 | x32 | x33 | x34 | x35 | x36 | x37 | x38 | x39 | x3a | x3b | x3c | x3d | x3e | x3f | x40 | x41 | x42 | x43 | x44 | x45 | x46 | x47 | x48 | x49 | x4a | x4b | x4c | x4d | x4e | x4f | x50 | x51 | x52 | x53 | x54 | x55 | x56 | x57 | x58 | x59 | x5a | x5b | x5c | x5d | x5e | x5f | x60 => Gt
+  | x61 => Eq
+  | _ => Lt
+  end.
+Definition compare_byte_x62 (b : byte) :=
+  match b with
+  | x00 | x01 | x02 | x03 | x04 | x05 | x06 | x07 | x08 | x09 | x0a | x0b | x0c | x0d | x0e | x0f | x10 | x11 | x12 | x13 | x14 | x15 | x16 | x17 | x18 | x19 | x1a | x1b | x1c | x1d | x1e | x1f | x20 | x21 | x22 | x23 | x24 | x25 | x26 | x27 | x28 | x29 | x2a | x2b | x2c | x2d | x2e | x2f | x30 | x31 | x32 | x33 | x34 | x35 | x36 | x37 | x38 | x39 | x3a | x3b | x3c | x3d | x3e | x3f | x40 | x41 | x42 | x43 | x44 | x45 | x46 | x47 | x48 | x49 | x4a | x4b | x4c | x4d | x4e | x4f | x50 | x51 | x52 | x53 | x54 | x55 | x56 | x57 | x58 | x59 | x5a | x5b | x5c | x5d | x5e | x5f | x60 | x61 => Gt
+  | x62 => Eq
+  | _ => Lt
+  end.
+Definition compare_byte_x63 (b : byte) :=
+  match b with
+  | x00 | x01 | x02 | x03 | x04 | x05 | x06 | x07 | x08 | x09 | x0a | x0b | x0c | x0d | x0e | x0f | x10 | x11 | x12 | x13 | x14 | x15 | x16 | x17 | x18 | x19 | x1a | x1b | x1c | x1d | x1e | x1f | x20 | x21 | x22 | x23 | x24 | x25 | x26 | x27 | x28 | x29 | x2a | x2b | x2c | x2d | x2e | x2f | x30 | x31 | x32 | x33 | x34 | x35 | x36 | x37 | x38 | x39 | x3a | x3b | x3c | x3d | x3e | x3f | x40 | x41 | x42 | x43 | x44 | x45 | x46 | x47 | x48 | x49 | x4a | x4b | x4c | x4d | x4e | x4f | x50 | x51 | x52 | x53 | x54 | x55 | x56 | x57 | x58 | x59 | x5a | x5b | x5c | x5d | x5e | x5f | x60 | x61 | x62 => Gt
+  | x63 => Eq
+  | _ => Lt
+  end.
+Definition compare_byte_x64 (b : byte) :=
+  match b with
+  | x00 | x01 | x02 | x03 | x04 | x05 | x06 | x07 | x08 | x09 | x0a | x0b | x0c | x0d | x0e | x0f | x10 | x11 | x12 | x13 | x14 | x15 | x16 | x17 | x18 | x19 | x1a | x1b | x1c | x1d | x1e | x1f | x20 | x21 | x22 | x23 | x24 | x25 | x26 | x27 | x28 | x29 | x2a | x2b | x2c | x2d | x2e | x2f | x30 | x31 | x32 | x33 | x34 | x35 | x36 | x37 | x38 | x39 | x3a | x3b | x3c | x3d | x3e | x3f | x40 | x41 | x42 | x43 | x44 | x45 | x46 | x47 | x48 | x49 | x4a | x4b | x4c | x4d | x4e | x4f | x50 | x51 | x52 | x53 | x54 | x55 | x56 | x57 | x58 | x59 | x5a | x5b | x5c | x5d | x5e | x5f | x60 | x61 | x62 | x63 => Gt
+  | x64 => Eq
+  | _ => Lt
+  end.
+Definition compare_byte_x65 (b : byte) :=
+  match b with
+  | x00 | x01 | x02 | x03 | x04 | x05 | x06 | x07 | x08 | x09 | x0a | x0b | x0c | x0d | x0e | x0f | x10 | x11 | x12 | x13 | x14 | x15 | x16 | x17 | x18 | x19 | x1a | x1b | x1c | x1d | x1e | x1f | x20 | x21 | x22 | x23 | x24 | x25 | x26 | x27 | x28 | x29 | x2a | x2b | x2c | x2d | x2e | x2f | x30 | x31 | x32 | x33 | x34 | x35 | x36 | x37 | x38 | x39 | x3a | x3b | x3c | x3d | x3e | x3f | x40 | x41 | x42 | x43 | x44 | x45 | x46 | x47 | x48 | x49 | x4a | x4b | x4c | x4d | x4e | x4f | x50 | x51 | x52 | x53 | x54 | x55 | x56 | x57 | x58 | x59 | x5a | x5b | x5c | x5d | x5e | x5f | x60 | x61 | x62 | x63 | x64 => Gt
+  | x65 => Eq
+  | _ => Lt
+  end.
+Definition compare_byte_x66 (b : byte) :=
+  match b with
+  | x00 | x01 | x02 | x03 | x04 | x05 | x06 | x07 | x08 | x09 | x0a | x0b | x0c | x0d | x0e | x0f | x10 | x11 | x12 | x13 | x14 | x15 | x16 | x17 | x18 | x19 | x1a | x1b | x1c | x1d | x1e | x1f | x20 | x21 | x22 | x23 | x24 | x25 | x26 | x27 | x28 | x29 | x2a | x2b | x2c | x2d | x2e | x2f | x30 | x31 | x32 | x33 | x34 | x35 | x36 | x37 | x38 | x39 | x3a | x3b | x3c | x3d | x3e | x3f | x40 | x41 | x42 | x43 | x44 | x45 | x46 | x47 | x48 | x49 | x4a | x4b | x4c | x4d | x4e | x4f | x50 | x51 | x52 | x53 | x54 | x55 | x56 | x57 | x58 | x59 | x5a | x5b | x5c | x5d | x5e | x5f | x60 | x61 | x62 | x63 | x64 | x65 => Gt
+  | x66 => Eq
+  | _ => Lt
+  end.
+Definition compare_byte_x67 (b : byte) :=
+  match b with
+  | x00 | x01 | x02 | x03 | x04 | x05 | x06 | x07 | x08 | x09 | x0a | x0b | x0c | x0d | x0e | x0f | x10 | x11 | x12 | x13 | x14 | x15 | x16 | x17 | x18 | x19 | x1a | x1b | x1c | x1d | x1e | x1f | x20 | x21 | x22 | x23 | x24 | x25 | x26 | x27 | x28 | x29 | x2a | x2b | x2c | x2d | x2e | x2f | x30 | x31 | x32 | x33 | x34 | x35 | x36 | x37 | x38 | x39 | x3a | x3b | x3c | x3d | x3e | x3f | x40 | x41 | x42 | x43 | x44 | x45 | x46 | x47 | x48 | x49 | x4a | x4b | x4c | x4d | x4e | x4f | x50 | x51 | x52 | x53 | x54 | x55 | x56 | x57 | x58 | x59 | x5a | x5b | x5c | x5d | x5e | x5f | x60 | x61 | x62 | x63 | x64 | x65 | x66 => Gt
+  | x67 => Eq
+  | _ => Lt
+  end.
+Definition compare_byte_x68 (b : byte) :=
+  match b with
+  | x00 | x01 | x02 | x03 | x04 | x05 | x06 | x07 | x08 | x09 | x0a | x0b | x0c | x0d | x0e | x0f | x10 | x11 | x12 | x13 | x14 | x15 | x16 | x17 | x18 | x19 | x1a | x1b | x1c | x1d | x1e | x1f | x20 | x21 | x22 | x23 | x24 | x25 | x26 | x27 | x28 | x29 | x2a | x2b | x2c | x2d | x2e | x2f | x30 | x31 | x32 | x33 | x34 | x35 | x36 | x37 | x38 | x39 | x3a | x3b | x3c | x3d | x3e | x3f | x40 | x41 | x42 | x43 | x44 | x45 | x46 | x47 | x48 | x49 | x4a | x4b | x4c | x4d | x4e | x4f | x50 | x51 | x52 | x53 | x54 | x55 | x56 | x57 | x58 | x59 | x5a | x5b | x5c | x5d | x5e | x5f | x60 | x61 | x62 | x63 | x64 | x65 | x66 | x67 => Gt
+  | x68 => Eq
+  | _ => Lt
+  end.
+Definition compare_byte_x69 (b : byte) :=
+  match b with
+  | x00 | x01 | x02 | x03 | x04 | x05 | x06 | x07 | x08 | x09 | x0a | x0b | x0c | x0d | x0e | x0f | x10 | x11 | x12 | x13 | x14 | x15 | x16 | x17 | x18 | x19 | x1a | x1b | x1c | x1d | x1e | x1f | x20 | x21 | x22 | x23 | x24 | x25 | x26 | x27 | x28 | x29 | x2a | x2b | x2c | x2d | x2e | x2f | x30 | x31 | x32 | x33 | x34 | x35 | x36 | x37 | x38 | x39 | x3a | x3b | x3c | x3d | x3e | x3f | x40 | x41 | x42 | x43 | x44 | x45 | x46 | x47 | x48 | x49 | x4a | x4b | x4c | x4d | x4e | x4f | x50 | x51 | x52 | x53 | x54 | x55 | x56 | x57 | x58 | x59 | x5a | x5b | x5c | x5d | x5e | x5f | x60 | x61 | x62 | x63 | x64 | x65 | x66 | x67 | x68 => Gt
+  | x69 => Eq
+  | _ => Lt
+  end.
+Definition compare_byte_x6a (b : byte) :=
+  match b with
+  | x00 | x01 | x02 | x03 | x04 | x05 | x06 | x07 | x08 | x09 | x0a | x0b | x0c | x0d | x0e | x0f | x10 | x11 | x12 | x13 | x14 | x15 | x16 | x17 | x18 | x19 | x1a | x1b | x1c | x1d | x1e | x1f | x20 | x21 | x22 | x23 | x24 | x25 | x26 | x27 | x28 | x29 | x2a | x2b | x2c | x2d | x2e | x2f | x30 | x31 | x32 | x33 | x34 | x35 | x36 | x37 | x38 | x39 | x3a | x3b | x3c | x3d | x3e | x3f | x40 | x41 | x42 | x43 | x44 | x45 | x46 | x47 | x48 | x49 | x4a | x4b | x4c | x4d | x4e | x4f | x50 | x51 | x52 | x53 | x54 | x55 | x56 | x57 | x58 | x59 | x5a | x5b | x5c | x5d | x5e | x5f | x60 | x61 | x62 | x63 | x64 | x65 | x66 | x67 | x68 | x69 => Gt
+  | x6a => Eq
+  | _ => Lt
+  end.
+Definition compare_byte_x6b (b : byte) :=
+  match b with
+  | x00 | x01 | x02 | x03 | x04 | x05 | x06 | x07 | x08 | x09 | x0a | x0b | x0c | x0d | x0e | x0f | x10 | x11 | x12 | x13 | x14 | x15 | x16 | x17 | x18 | x19 | x1a | x1b | x1c | x1d | x1e | x1f | x20 | x21 | x22 | x23 | x24 | x25 | x26 | x27 | x28 | x29 | x2a | x2b | x2c | x2d | x2e | x2f | x30 | x31 | x32 | x33 | x34 | x35 | x36 | x37 | x38 | x39 | x3a | x3b | x3c | x3d | x3e | x3f | x40 | x41 | x42 | x43 | x44 | x45 | x46 | x47 | x48 | x49 | x4a | x4b | x4c | x4d | x4e | x4f | x50 | x51 | x52 | x53 | x54 | x55 | x56 | x57 | x58 | x59 | x5a | x5b | x5c | x5d | x5e | x5f | x60 | x61 | x62 | x63 | x64 | x65 | x66 | x67 | x68 | x69 | x6a => Gt
+  | x6b => Eq
+  | _ => Lt
+  end.
+Definition compare_byte_x6c (b : byte) :=
+  match b with
+  | x00 | x01 | x02 | x03 | x04 | x05 | x06 | x07 | x08 | x09 | x0a | x0b | x0c | x0d | x0e | x0f | x10 | x11 | x12 | x13 | x14 | x15 | x16 | x17 | x18 | x19 | x1a | x1b | x1c | x1d | x1e | x1f | x20 | x21 | x22 | x23 | x24 | x25 | x26 | x27 | x28 | x29 | x2a | x2b | x2c | x2d | x2e | x2f | x30 | x31 | x32 | x33 | x34 | x35 | x36 | x37 | x38 | x39 | x3a | x3b | x3c | x3d | x3e | x3f | x40 | x41 | x42 | x43 | x44 | x45 | x46 | x47 | x48 | x49 | x4a | x4b | x4c | x4d | x4e | x4f | x50 | x51 | x52 | x53 | x54 | x55 | x56 | x57 | x58 | x59 | x5a | x5b | x5c | x5d | x5e | x5f | x60 | x61 | x62 | x63 | x64 | x65 | x66 | x67 | x68 | x69 | x6a | x6b => Gt
+  | x6c => Eq
+  | _ => Lt
+  end.
+Definition compare_byte_x6d (b : byte) :=
+  match b with
+  | x00 | x01 | x02 | x03 | x04 | x05 | x06 | x07 | x08 | x09 | x0a | x0b | x0c | x0d | x0e | x0f | x10 | x11 | x12 | x13 | x14 | x15 | x16 | x17 | x18 | x19 | x1a | x1b | x1c | x1d | x1e | x1f | x20 | x21 | x22 | x23 | x24 | x25 | x26 | x27 | x28 | x29 | x2a | x2b | x2c | x2d | x2e | x2f | x30 | x31 | x32 | x33 | x34 | x35 | x36 | x37 | x38 | x39 | x3a | x3b | x3c | x3d | x3e | x3f | x40 | x41 | x42 | x43 | x44 | x45 | x46 | x47 | x48 | x49 | x4a | x4b | x4c | x4d | x4e | x4f | x50 | x51 | x52 | x53 | x54 | x55 | x56 | x57 | x58 | x59 | x5a | x5b | x5c | x5d | x5e | x5f | x60 | x61 | x62 | x63 | x64 | x65 | x66 | x67 | x68 | x69 | x6a | x6b | x6c => Gt
+  | x6d => Eq
+  | _ => Lt
+  end.
+Definition compare_byte_x6e (b : byte) :=
+  match b with
+  | x00 | x01 | x02 | x03 | x04 | x05 | x06 | x07 | x08 | x09 | x0a | x0b | x0c | x0d | x0e | x0f | x10 | x11 | x12 | x13 | x14 | x15 | x16 | x17 | x18 | x19 | x1a | x1b | x1c | x1d | x1e | x1f | x20 | x21 | x22 | x23 | x24 | x25 | x26 | x27 | x28 | x29 | x2a | x2b | x2c | x2d | x2e | x2f | x30 | x31 | x32 | x33 | x34 | x35 | x36 | x37 | x38 | x39 | x3a | x3b | x3c | x3d | x3e | x3f | x40 | x41 | x42 | x43 | x44 | x45 | x46 | x47 | x48 | x49 | x4a | x4b | x4c | x4d | x4e | x4f | x50 | x51 | x52 | x53 | x54 | x55 | x56 | x57 | x58 | x59 | x5a | x5b | x5c | x5d | x5e | x5f | x60 | x61 | x62 | x63 | x64 | x65 | x66 | x67 | x68 | x69 | x6a | x6b | x6c | x6d => Gt
+  | x6e => Eq
+  | _ => Lt
+  end.
+Definition compare_byte_x6f (b : byte) :=
+  match b with
+  | x00 | x01 | x02 | x03 | x04 | x05 | x06 | x07 | x08 | x09 | x0a | x0b | x0c | x0d | x0e | x0f | x10 | x11 | x12 | x13 | x14 | x15 | x16 | x17 | x18 | x19 | x1a | x1b | x1c | x1d | x1e | x1f | x20 | x21 | x22 | x23 | x24 | x25 | x26 | x27 | x28 | x29 | x2a | x2b | x2c | x2d | x2e | x2f | x30 | x31 | x32 | x33 | x34 | x35 | x36 | x37 | x38 | x39 | x3a | x3b | x3c | x3d | x3e | x3f | x40 | x41 | x42 | x43 | x44 | x45 | x46 | x47 | x48 | x49 | x4a | x4b | x4c | x4d | x4e | x4f | x50 | x51 | x52 | x53 | x54 | x55 | x56 | x57 | x58 | x59 | x5a | x5b | x5c | x5d | x5e | x5f | x60 | x61 | x62 | x63 | x64 | x65 | x66 | x67 | x68 | x69 | x6a | x6b | x6c | x6d | x6e => Gt
+  | x6f => Eq
+  | _ => Lt
+  end.
+Definition compare_byte_x70 (b : byte) :=
+  match b with
+  | x00 | x01 | x02 | x03 | x04 | x05 | x06 | x07 | x08 | x09 | x0a | x0b | x0c | x0d | x0e | x0f | x10 | x11 | x12 | x13 | x14 | x15 | x16 | x17 | x18 | x19 | x1a | x1b | x1c | x1d | x1e | x1f | x20 | x21 | x22 | x23 | x24 | x25 | x26 | x27 | x28 | x29 | x2a | x2b | x2c | x2d | x2e | x2f | x30 | x31 | x32 | x33 | x34 | x35 | x36 | x37 | x38 | x39 | x3a | x3b | x3c | x3d | x3e | x3f | x40 | x41 | x42 | x43 | x44 | x45 | x46 | x47 | x48 | x49 | x4a | x4b | x4c | x4d | x4e | x4f | x50 | x51 | x52 | x53 | x54 | x55 | x56 | x57 | x58 | x59 | x5a | x5b | x5c | x5d | x5e | x5f | x60 | x61 | x62 | x63 | x64 | x65 | x66 | x67 | x68 | x69 | x6a | x6b | x6c | x6d | x6e | x6f => Gt
+  | x70 => Eq
+  | _ => Lt
+  end.
+Definition compare_byte_x71 (b : byte) :=
+  match b with
+  | x00 | x01 | x02 | x03 | x04 | x05 | x06 | x07 | x08 | x09 | x0a | x0b | x0c | x0d | x0e | x0f | x10 | x11 | x12 | x13 | x14 | x15 | x16 | x17 | x18 | x19 | x1a | x1b | x1c | x1d | x1e | x1f | x20 | x21 | x22 | x23 | x24 | x25 | x26 | x27 | x28 | x29 | x2a | x2b | x2c | x2d | x2e | x2f | x30 | x31 | x32 | x33 | x34 | x35 | x36 | x37 | x38 | x39 | x3a | x3b | x3c | x3d | x3e | x3f | x40 | x41 | x42 | x43 | x44 | x45 | x46 | x47 | x48 | x49 | x4a | x4b | x4c | x4d | x4e | x4f | x50 | x51 | x52 | x53 | x54 | x55 | x56 | x57 | x58 | x59 | x5a | x5b | x5c | x5d | x5e | x5f | x60 | x61 | x62 | x63 | x64 | x65 | x66 | x67 | x68 | x69 | x6a | x6b | x6c | x6d | x6e | x6f | x70 => Gt
+  | x71 => Eq
+  | _ => Lt
+  end.
+Definition compare_byte_x72 (b : byte) :=
+  match b with
+  | x00 | x01 | x02 | x03 | x04 | x05 | x06 | x07 | x08 | x09 | x0a | x0b | x0c | x0d | x0e | x0f | x10 | x11 | x12 | x13 | x14 | x15 | x16 | x17 | x18 | x19 | x1a | x1b | x1c | x1d | x1e | x1f | x20 | x21 | x22 | x23 | x24 | x25 | x26 | x27 | x28 | x29 | x2a | x2b | x2c | x2d | x2e | x2f | x30 | x31 | x32 | x33 | x34 | x35 | x36 | x37 | x38 | x39 | x3a | x3b | x3c | x3d | x3e | x3f | x40 | x41 | x42 | x43 | x44 | x45 | x46 | x47 | x48 | x49 | x4a | x4b | x4c | x4d | x4e | x4f | x50 | x51 | x52 | x53 | x54 | x55 | x56 | x57 | x58 | x59 | x5a | x5b | x5c | x5d | x5e | x5f | x60 | x61 | x62 | x63 | x64 | x65 | x66 | x67 | x68 | x69 | x6a | x6b | x6c | x6d | x6e | x6f | x70 | x71 => Gt
+  | x72 => Eq
+  | _ => Lt
+  end.
+Definition compare_byte_x73 (b : byte) :=
+  match b with
+  | x00 | x01 | x02 | x03 | x04 | x05 | x06 | x07 | x08 | x09 | x0a | x0b | x0c | x0d | x0e | x0f | x10 | x11 | x12 | x13 | x14 | x15 | x16 | x17 | x18 | x19 | x1a | x1b | x1c | x1d | x1e | x1f | x20 | x21 | x22 | x23 | x24 | x25 | x26 | x27 | x28 | x29 | x2a | x2b | x2c | x2d | x2e | x2f | x30 | x31 | x32 | x33 | x34 | x35 | x36 | x37 | x38 | x39 | x3a | x3b | x3c | x3d | x3e | x3f | x40 | x41 | x42 | x43 | x44 | x45 | x46 | x47 | x48 | x49 | x4a | x4b | x4c | x4d | x4e | x4f | x50 | x51 | x52 | x53 | x54 | x55 | x56 | x57 | x58 | x59 | x5a | x5b | x5c | x5d | x5e | x5f | x60 | x61 | x62 | x63 | x64 | x65 | x66 | x67 | x68 | x69 | x6a | x6b | x6c | x6d | x6e | x6f | x70 | x71 | x72 => Gt
+  | x73 => Eq
+  | _ => Lt
+  end.
+Definition compare_byte_x74 (b : byte) :=
+  match b with
+  | x00 | x01 | x02 | x03 | x04 | x05 | x06 | x07 | x08 | x09 | x0a | x0b | x0c | x0d | x0e | x0f | x10 | x11 | x12 | x13 | x14 | x15 | x16 | x17 | x18 | x19 | x1a | x1b | x1c | x1d | x1e | x1f | x20 | x21 | x22 | x23 | x24 | x25 | x26 | x27 | x28 | x29 | x2a | x2b | x2c | x2d | x2e | x2f | x30 | x31 | x32 | x33 | x34 | x35 | x36 | x37 | x38 | x39 | x3a | x3b | x3c | x3d | x3e | x3f | x40 | x41 | x42 | x43 | x44 | x45 | x46 | x47 | x48 | x49 | x4a | x4b | x4c | x4d | x4e | x4f | x50 | x51 | x52 | x53 | x54 | x55 | x56 | x57 | x58 | x59 | x5a | x5b | x5c | x5d | x5e | x5f | x60 | x61 | x62 | x63 | x64 | x65 | x66 | x67 | x68 | x69 | x6a | x6b | x6c | x6d | x6e | x6f | x70 | x71 | x72 | x73 => Gt
+  | x74 => Eq
+  | _ => Lt
+  end.
+Definition compare_byte_x75 (b : byte) :=
+  match b with
+  | x00 | x01 | x02 | x03 | x04 | x05 | x06 | x07 | x08 | x09 | x0a | x0b | x0c | x0d | x0e | x0f | x10 | x11 | x12 | x13 | x14 | x15 | x16 | x17 | x18 | x19 | x1a | x1b | x1c | x1d | x1e | x1f | x20 | x21 | x22 | x23 | x24 | x25 | x26 | x27 | x28 | x29 | x2a | x2b | x2c | x2d | x2e | x2f | x30 | x31 | x32 | x33 | x34 | x35 | x36 | x37 | x38 | x39 | x3a | x3b | x3c | x3d | x3e | x3f | x40 | x41 | x42 | x43 | x44 | x45 | x46 | x47 | x48 | x49 | x4a | x4b | x4c | x4d | x4e | x4f | x50 | x51 | x52 | x53 | x54 | x55 | x56 | x57 | x58 | x59 | x5a | x5b | x5c | x5d | x5e | x5f | x60 | x61 | x62 | x63 | x64 | x65 | x66 | x67 | x68 | x69 | x6a | x6b | x6c | x6d | x6e | x6f | x70 | x71 | x72 | x73 | x74 => Gt
+  | x75 => Eq
+  | _ => Lt
+  end.
+Definition compare_byte_x76 (b : byte) :=
+  match b with
+  | x00 | x01 | x02 | x03 | x04 | x05 | x06 | x07 | x08 | x09 | x0a | x0b | x0c | x0d | x0e | x0f | x10 | x11 | x12 | x13 | x14 | x15 | x16 | x17 | x18 | x19 | x1a | x1b | x1c | x1d | x1e | x1f | x20 | x21 | x22 | x23 | x24 | x25 | x26 | x27 | x28 | x29 | x2a | x2b | x2c | x2d | x2e | x2f | x30 | x31 | x32 | x33 | x34 | x35 | x36 | x37 | x38 | x39 | x3a | x3b | x3c | x3d | x3e | x3f | x40 | x41 | x42 | x43 | x44 | x45 | x46 | x47 | x48 | x49 | x4a | x4b | x4c | x4d | x4e | x4f | x50 | x51 | x52 | x53 | x54 | x55 | x56 | x57 | x58 | x59 | x5a | x5b | x5c | x5d | x5e | x5f | x60 | x61 | x62 | x63 | x64 | x65 | x66 | x67 | x68 | x69 | x6a | x6b | x6c | x6d | x6e | x6f | x70 | x71 | x72 | x73 | x74 | x75 => Gt
+  | x76 => Eq
+  | _ => Lt
+  end.
+Definition compare_byte_x77 (b : byte) :=
+  match b with
+  | x00 | x01 | x02 | x03 | x04 | x05 | x06 | x07 | x08 | x09 | x0a | x0b | x0c | x0d | x0e | x0f | x10 | x11 | x12 | x13 | x14 | x15 | x16 | x17 | x18 | x19 | x1a | x1b | x1c | x1d | x1e | x1f | x20 | x21 | x22 | x23 | x24 | x25 | x26 | x27 | x28 | x29 | x2a | x2b | x2c | x2d | x2e | x2f | x30 | x31 | x32 | x33 | x34 | x35 | x36 | x37 | x38 | x39 | x3a | x3b | x3c | x3d | x3e | x3f | x40 | x41 | x42 | x43 | x44 | x45 | x46 | x47 | x48 | x49 | x4a | x4b | x4c | x4d | x4e | x4f | x50 | x51 | x52 | x53 | x54 | x55 | x56 | x57 | x58 | x59 | x5a | x5b | x5c | x5d | x5e | x5f | x60 | x61 | x62 | x63 | x64 | x65 | x66 | x67 | x68 | x69 | x6a | x6b | x6c | x6d | x6e | x6f | x70 | x71 | x72 | x73 | x74 | x75 | x76 => Gt
+  | x77 => Eq
+  | _ => Lt
+  end.
+Definition compare_byte_x78 (b : byte) :=
+  match b with
+  | x00 | x01 | x02 | x03 | x04 | x05 | x06 | x07 | x08 | x09 | x0a | x0b | x0c | x0d | x0e | x0f | x10 | x11 | x12 | x13 | x14 | x15 | x16 | x17 | x18 | x19 | x1a | x1b | x1c | x1d | x1e | x1f | x20 | x21 | x22 | x23 | x24 | x25 | x26 | x27 | x28 | x29 | x2a | x2b | x2c | x2d | x2e | x2f | x30 | x31 | x32 | x33 | x34 | x35 | x36 | x37 | x38 | x39 | x3a | x3b | x3c | x3d | x3e | x3f | x40 | x41 | x42 | x43 | x44 | x45 | x46 | x47 | x48 | x49 | x4a | x4b | x4c | x4d | x4e | x4f | x50 | x51 | x52 | x53 | x54 | x55 | x56 | x57 | x58 | x59 | x5a | x5b | x5c | x5d | x5e | x5f | x60 | x61 | x62 | x63 | x64 | x65 | x66 | x67 | x68 | x69 | x6a | x6b | x6c | x6d | x6e | x6f | x70 | x71 | x72 | x73 | x74 | x75 | x76 | x77 => Gt
+  | x78 => Eq
+  | _ => Lt
+  end.
+Definition compare_byte_x79 (b : byte) :=
+  match b with
+  | x00 | x01 | x02 | x03 | x04 | x05 | x06 | x07 | x08 | x09 | x0a | x0b | x0c | x0d | x0e | x0f | x10 | x11 | x12 | x13 | x14 | x15 | x16 | x17 | x18 | x19 | x1a | x1b | x1c | x1d | x1e | x1f | x20 | x21 | x22 | x23 | x24 | x25 | x26 | x27 | x28 | x29 | x2a | x2b | x2c | x2d | x2e | x2f | x30 | x31 | x32 | x33 | x34 | x35 | x36 | x37 | x38 | x39 | x3a | x3b | x3c | x3d | x3e | x3f | x40 | x41 | x42 | x43 | x44 | x45 | x46 | x47 | x48 | x49 | x4a | x4b | x4c | x4d | x4e | x4f | x50 | x51 | x52 | x53 | x54 | x55 | x56 | x57 | x58 | x59 | x5a | x5b | x5c | x5d | x5e | x5f | x60 | x61 | x62 | x63 | x64 | x65 | x66 | x67 | x68 | x69 | x6a | x6b | x6c | x6d | x6e | x6f | x70 | x71 | x72 | x73 | x74 | x75 | x76 | x77 | x78 => Gt
+  | x79 => Eq
+  | _ => Lt
+  end.
+Definition compare_byte_x7a (b : byte) :=
+  match b with
+  | x00 | x01 | x02 | x03 | x04 | x05 | x06 | x07 | x08 | x09 | x0a | x0b | x0c | x0d | x0e | x0f | x10 | x11 | x12 | x13 | x14 | x15 | x16 | x17 | x18 | x19 | x1a | x1b | x1c | x1d | x1e | x1f | x20 | x21 | x22 | x23 | x24 | x25 | x26 | x27 | x28 | x29 | x2a | x2b | x2c | x2d | x2e | x2f | x30 | x31 | x32 | x33 | x34 | x35 | x36 | x37 | x38 | x39 | x3a | x3b | x3c | x3d | x3e | x3f | x40 | x41 | x42 | x43 | x44 | x45 | x46 | x47 | x48 | x49 | x4a | x4b | x4c | x4d | x4e | x4f | x50 | x51 | x52 | x53 | x54 | x55 | x56 | x57 | x58 | x59 | x5a | x5b | x5c | x5d | x5e | x5f | x60 | x61 | x62 | x63 | x64 | x65 | x66 | x67 | x68 | x69 | x6a | x6b | x6c | x6d | x6e | x6f | x70 | x71 | x72 | x73 | x74 | x75 | x76 | x77 | x78 | x79 => Gt
+  | x7a => Eq
+  | _ => Lt
+  end.
+Definition compare_byte_x7b (b : byte) :=
+  match b with
+  | x00 | x01 | x02 | x03 | x04 | x05 | x06 | x07 | x08 | x09 | x0a | x0b | x0c | x0d | x0e | x0f | x10 | x11 | x12 | x13 | x14 | x15 | x16 | x17 | x18 | x19 | x1a | x1b | x1c | x1d | x1e | x1f | x20 | x21 | x22 | x23 | x24 | x25 | x26 | x27 | x28 | x29 | x2a | x2b | x2c | x2d | x2e | x2f | x30 | x31 | x32 | x33 | x34 | x35 | x36 | x37 | x38 | x39 | x3a | x3b | x3c | x3d | x3e | x3f | x40 | x41 | x42 | x43 | x44 | x45 | x46 | x47 | x48 | x49 | x4a | x4b | x4c | x4d | x4e | x4f | x50 | x51 | x52 | x53 | x54 | x55 | x56 | x57 | x58 | x59 | x5a | x5b | x5c | x5d | x5e | x5f | x60 | x61 | x62 | x63 | x64 | x65 | x66 | x67 | x68 | x69 | x6a | x6b | x6c | x6d | x6e | x6f | x70 | x71 | x72 | x73 | x74 | x75 | x76 | x77 | x78 | x79 | x7a => Gt
+  | x7b => Eq
+  | _ => Lt
+  end.
+Definition compare_byte_x7c (b : byte) :=
+  match b with
+  | x00 | x01 | x02 | x03 | x04 | x05 | x06 | x07 | x08 | x09 | x0a | x0b | x0c | x0d | x0e | x0f | x10 | x11 | x12 | x13 | x14 | x15 | x16 | x17 | x18 | x19 | x1a | x1b | x1c | x1d | x1e | x1f | x20 | x21 | x22 | x23 | x24 | x25 | x26 | x27 | x28 | x29 | x2a | x2b | x2c | x2d | x2e | x2f | x30 | x31 | x32 | x33 | x34 | x35 | x36 | x37 | x38 | x39 | x3a | x3b | x3c | x3d | x3e | x3f | x40 | x41 | x42 | x43 | x44 | x45 | x46 | x47 | x48 | x49 | x4a | x4b | x4c | x4d | x4e | x4f | x50 | x51 | x52 | x53 | x54 | x55 | x56 | x57 | x58 | x59 | x5a | x5b | x5c | x5d | x5e | x5f | x60 | x61 | x62 | x63 | x64 | x65 | x66 | x67 | x68 | x69 | x6a | x6b | x6c | x6d | x6e | x6f | x70 | x71 | x72 | x73 | x74 | x75 | x76 | x77 | x78 | x79 | x7a | x7b => Gt
+  | x7c => Eq
+  | _ => Lt
+  end.
+Definition compare_byte_x7d (b : byte) :=
+  match b with
+  | x00 | x01 | x02 | x03 | x04 | x05 | x06 | x07 | x08 | x09 | x0a | x0b | x0c | x0d | x0e | x0f | x10 | x11 | x12 | x13 | x14 | x15 | x16 | x17 | x18 | x19 | x1a | x1b | x1c | x1d | x1e | x1f | x20 | x21 | x22 | x23 | x24 | x25 | x26 | x27 | x28 | x29 | x2a | x2b | x2c | x2d | x2e | x2f | x30 | x31 | x32 | x33 | x34 | x35 | x36 | x37 | x38 | x39 | x3a | x3b | x3c | x3d | x3e | x3f | x40 | x41 | x42 | x43 | x44 | x45 | x46 | x47 | x48 | x49 | x4a | x4b | x4c | x4d | x4e | x4f | x50 | x51 | x52 | x53 | x54 | x55 | x56 | x57 | x58 | x59 | x5a | x5b | x5c | x5d | x5e | x5f | x60 | x61 | x62 | x63 | x64 | x65 | x66 | x67 | x68 | x69 | x6a | x6b | x6c | x6d | x6e | x6f | x70 | x71 | x72 | x73 | x74 | x75 | x76 | x77 | x78 | x79 | x7a | x7b | x7c => Gt
+  | x7d => Eq
+  | _ => Lt
+  end.
+Definition compare_byte_x7e (b : byte) :=
+  match b with
+  | x00 | x01 | x02 | x03 | x04 | x05 | x06 | x07 | x08 | x09 | x0a | x0b | x0c | x0d | x0e | x0f | x10 | x11 | x12 | x13 | x14 | x15 | x16 | x17 | x18 | x19 | x1a | x1b | x1c | x1d | x1e | x1f | x20 | x21 | x22 | x23 | x24 | x25 | x26 | x27 | x28 | x29 | x2a | x2b | x2c | x2d | x2e | x2f | x30 | x31 | x32 | x33 | x34 | x35 | x36 | x37 | x38 | x39 | x3a | x3b | x3c | x3d | x3e | x3f | x40 | x41 | x42 | x43 | x44 | x45 | x46 | x47 | x48 | x49 | x4a | x4b | x4c | x4d | x4e | x4f | x50 | x51 | x52 | x53 | x54 | x55 | x56 | x57 | x58 | x59 | x5a | x5b | x5c | x5d | x5e | x5f | x60 | x61 | x62 | x63 | x64 | x65 | x66 | x67 | x68 | x69 | x6a | x6b | x6c | x6d | x6e | x6f | x70 | x71 | x72 | x73 | x74 | x75 | x76 | x77 | x78 | x79 | x7a | x7b | x7c | x7d => Gt
+  | x7e => Eq
+  | _ => Lt
+  end.
+Definition compare_byte_x7f (b : byte) :=
+  match b with
+  | x00 | x01 | x02 | x03 | x04 | x05 | x06 | x07 | x08 | x09 | x0a | x0b | x0c | x0d | x0e | x0f | x10 | x11 | x12 | x13 | x14 | x15 | x16 | x17 | x18 | x19 | x1a | x1b | x1c | x1d | x1e | x1f | x20 | x21 | x22 | x23 | x24 | x25 | x26 | x27 | x28 | x29 | x2a | x2b | x2c | x2d | x2e | x2f | x30 | x31 | x32 | x33 | x34 | x35 | x36 | x37 | x38 | x39 | x3a | x3b | x3c | x3d | x3e | x3f | x40 | x41 | x42 | x43 | x44 | x45 | x46 | x47 | x48 | x49 | x4a | x4b | x4c | x4d | x4e | x4f | x50 | x51 | x52 | x53 | x54 | x55 | x56 | x57 | x58 | x59 | x5a | x5b | x5c | x5d | x5e | x5f | x60 | x61 | x62 | x63 | x64 | x65 | x66 | x67 | x68 | x69 | x6a | x6b | x6c | x6d | x6e | x6f | x70 | x71 | x72 | x73 | x74 | x75 | x76 | x77 | x78 | x79 | x7a | x7b | x7c | x7d | x7e => Gt
+  | x7f => Eq
+  | _ => Lt
+  end.
+Definition compare_byte_x80 (b : byte) :=
+  match b with
+  | x00 | x01 | x02 | x03 | x04 | x05 | x06 | x07 | x08 | x09 | x0a | x0b | x0c | x0d | x0e | x0f | x10 | x11 | x12 | x13 | x14 | x15 | x16 | x17 | x18 | x19 | x1a | x1b | x1c | x1d | x1e | x1f | x20 | x21 | x22 | x23 | x24 | x25 | x26 | x27 | x28 | x29 | x2a | x2b | x2c | x2d | x2e | x2f | x30 | x31 | x32 | x33 | x34 | x35 | x36 | x37 | x38 | x39 | x3a | x3b | x3c | x3d | x3e | x3f | x40 | x41 | x42 | x43 | x44 | x45 | x46 | x47 | x48 | x49 | x4a | x4b | x4c | x4d | x4e | x4f | x50 | x51 | x52 | x53 | x54 | x55 | x56 | x57 | x58 | x59 | x5a | x5b | x5c | x5d | x5e | x5f | x60 | x61 | x62 | x63 | x64 | x65 | x66 | x67 | x68 | x69 | x6a | x6b | x6c | x6d | x6e | x6f | x70 | x71 | x72 | x73 | x74 | x75 | x76 | x77 | x78 | x79 | x7a | x7b | x7c | x7d | x7e | x7f => Gt
+  | x80 => Eq
+  | _ => Lt
+  end.
+Definition compare_byte_x81 (b : byte) :=
+  match b with
+  | x00 | x01 | x02 | x03 | x04 | x05 | x06 | x07 | x08 | x09 | x0a | x0b | x0c | x0d | x0e | x0f | x10 | x11 | x12 | x13 | x14 | x15 | x16 | x17 | x18 | x19 | x1a | x1b | x1c | x1d | x1e | x1f | x20 | x21 | x22 | x23 | x24 | x25 | x26 | x27 | x28 | x29 | x2a | x2b | x2c | x2d | x2e | x2f | x30 | x31 | x32 | x33 | x34 | x35 | x36 | x37 | x38 | x39 | x3a | x3b | x3c | x3d | x3e | x3f | x40 | x41 | x42 | x43 | x44 | x45 | x46 | x47 | x48 | x49 | x4a | x4b | x4c | x4d | x4e | x4f | x50 | x51 | x52 | x53 | x54 | x55 | x56 | x57 | x58 | x59 | x5a | x5b | x5c | x5d | x5e | x5f | x60 | x61 | x62 | x63 | x64 | x65 | x66 | x67 | x68 | x69 | x6a | x6b | x6c | x6d | x6e | x6f | x70 | x71 | x72 | x73 | x74 | x75 | x76 | x77 | x78 | x79 | x7a | x7b | x7c | x7d | x7e | x7f | x80 => Gt
+  | x81 => Eq
+  | _ => Lt
+  end.
+Definition compare_byte_x82 (b : byte) :=
+  match b with
+  | x00 | x01 | x02 | x03 | x04 | x05 | x06 | x07 | x08 | x09 | x0a | x0b | x0c | x0d | x0e | x0f | x10 | x11 | x12 | x13 | x14 | x15 | x16 | x17 | x18 | x19 | x1a | x1b | x1c | x1d | x1e | x1f | x20 | x21 | x22 | x23 | x24 | x25 | x26 | x27 | x28 | x29 | x2a | x2b | x2c | x2d | x2e | x2f | x30 | x31 | x32 | x33 | x34 | x35 | x36 | x37 | x38 | x39 | x3a | x3b | x3c | x3d | x3e | x3f | x40 | x41 | x42 | x43 | x44 | x45 | x46 | x47 | x48 | x49 | x4a | x4b | x4c | x4d | x4e | x4f | x50 | x51 | x52 | x53 | x54 | x55 | x56 | x57 | x58 | x59 | x5a | x5b | x5c | x5d | x5e | x5f | x60 | x61 | x62 | x63 | x64 | x65 | x66 | x67 | x68 | x69 | x6a | x6b | x6c | x6d | x6e | x6f | x70 | x71 | x72 | x73 | x74 | x75 | x76 | x77 | x78 | x79 | x7a | x7b | x7c | x7d | x7e | x7f | x80 | x81 => Gt
+  | x82 => Eq
+  | _ => Lt
+  end.
+Definition compare_byte_x83 (b : byte) :=
+  match b with
+  | x00 | x01 | x02 | x03 | x04 | x05 | x06 | x07 | x08 | x09 | x0a | x0b | x0c | x0d | x0e | x0f | x10 | x11 | x12 | x13 | x14 | x15 | x16 | x17 | x18 | x19 | x1a | x1b | x1c | x1d | x1e | x1f | x20 | x21 | x22 | x23 | x24 | x25 | x26 | x27 | x28 | x29 | x2a | x2b | x2c | x2d | x2e | x2f | x30 | x31 | x32 | x33 | x34 | x35 | x36 | x37 | x38 | x39 | x3a | x3b | x3c | x3d | x3e | x3f | x40 | x41 | x42 | x43 | x44 | x45 | x46 | x47 | x48 | x49 | x4a | x4b | x4c | x4d | x4e | x4f | x50 | x51 | x52 | x53 | x54 | x55 | x56 | x57 | x58 | x59 | x5a | x5b | x5c | x5d | x5e | x5f | x60 | x61 | x62 | x63 | x64 | x65 | x66 | x67 | x68 | x69 | x6a | x6b | x6c | x6d | x6e | x6f | x70 | x71 | x72 | x73 | x74 | x75 | x76 | x77 | x78 | x79 | x7a | x7b | x7c | x7d | x7e | x7f | x80 | x81 | x82 => Gt
+  | x83 => Eq
+  | _ => Lt
+  end.
+Definition compare_byte_x84 (b : byte) :=
+  match b with
+  | x00 | x01 | x02 | x03 | x04 | x05 | x06 | x07 | x08 | x09 | x0a | x0b | x0c | x0d | x0e | x0f | x10 | x11 | x12 | x13 | x14 | x15 | x16 | x17 | x18 | x19 | x1a | x1b | x1c | x1d | x1e | x1f | x20 | x21 | x22 | x23 | x24 | x25 | x26 | x27 | x28 | x29 | x2a | x2b | x2c | x2d | x2e | x2f | x30 | x31 | x32 | x33 | x34 | x35 | x36 | x37 | x38 | x39 | x3a | x3b | x3c | x3d | x3e | x3f | x40 | x41 | x42 | x43 | x44 | x45 | x46 | x47 | x48 | x49 | x4a | x4b | x4c | x4d | x4e | x4f | x50 | x51 | x52 | x53 | x54 | x55 | x56 | x57 | x58 | x59 | x5a | x5b | x5c | x5d | x5e | x5f | x60 | x61 | x62 | x63 | x64 | x65 | x66 | x67 | x68 | x69 | x6a | x6b | x6c | x6d | x6e | x6f | x70 | x71 | x72 | x73 | x74 | x75 | x76 | x77 | x78 | x79 | x7a | x7b | x7c | x7d | x7e | x7f | x80 | x81 | x82 | x83 => Gt
+  | x84 => Eq
+  | _ => Lt
+  end.
+Definition compare_byte_x85 (b : byte) :=
+  match b with
+  | x00 | x01 | x02 | x03 | x04 | x05 | x06 | x07 | x08 | x09 | x0a | x0b | x0c | x0d | x0e | x0f | x10 | x11 | x12 | x13 | x14 | x15 | x16 | x17 | x18 | x19 | x1a | x1b | x1c | x1d | x1e | x1f | x20 | x21 | x22 | x23 | x24 | x25 | x26 | x27 | x28 | x29 | x2a | x2b | x2c | x2d | x2e | x2f | x30 | x31 | x32 | x33 | x34 | x35 | x36 | x37 | x38 | x39 | x3a | x3b | x3c | x3d | x3e | x3f | x40 | x41 | x42 | x43 | x44 | x45 | x46 | x47 | x48 | x49 | x4a | x4b | x4c | x4d | x4e | x4f | x50 | x51 | x52 | x53 | x54 | x55 | x56 | x57 | x58 | x59 | x5a | x5b | x5c | x5d | x5e | x5f | x60 | x61 | x62 | x63 | x64 | x65 | x66 | x67 | x68 | x69 | x6a | x6b | x6c | x6d | x6e | x6f | x70 | x71 | x72 | x73 | x74 | x75 | x76 | x77 | x78 | x79 | x7a | x7b | x7c | x7d | x7e | x7f | x80 | x81 | x82 | x83 | x84 => Gt
+  | x85 => Eq
+  | _ => Lt
+  end.
+Definition compare_byte_x86 (b : byte) :=
+  match b with
+  | x00 | x01 | x02 | x03 | x04 | x05 | x06 | x07 | x08 | x09 | x0a | x0b | x0c | x0d | x0e | x0f | x10 | x11 | x12 | x13 | x14 | x15 | x16 | x17 | x18 | x19 | x1a | x1b | x1c | x1d | x1e | x1f | x20 | x21 | x22 | x23 | x24 | x25 | x26 | x27 | x28 | x29 | x2a | x2b | x2c | x2d | x2e | x2f | x30 | x31 | x32 | x33 | x34 | x35 | x36 | x37 | x38 | x39 | x3a | x3b | x3c | x3d | x3e | x3f | x40 | x41 | x42 | x43 | x44 | x45 | x46 | x47 | x48 | x49 | x4a | x4b | x4c | x4d | x4e | x4f | x50 | x51 | x52 | x53 | x54 | x55 | x56 | x57 | x58 | x59 | x5a | x5b | x5c | x5d | x5e | x5f | x60 | x61 | x62 | x63 | x64 | x65 | x66 | x67 | x68 | x69 | x6a | x6b | x6c | x6d | x6e | x6f | x70 | x71 | x72 | x73 | x74 | x75 | x76 | x77 | x78 | x79 | x7a | x7b | x7c | x7d | x7e | x7f | x80 | x81 | x82 | x83 | x84 | x85 => Gt
+  | x86 => Eq
+  | _ => Lt
+  end.
+Definition compare_byte_x87 (b : byte) :=
+  match b with
+  | x00 | x01 | x02 | x03 | x04 | x05 | x06 | x07 | x08 | x09 | x0a | x0b | x0c | x0d | x0e | x0f | x10 | x11 | x12 | x13 | x14 | x15 | x16 | x17 | x18 | x19 | x1a | x1b | x1c | x1d | x1e | x1f | x20 | x21 | x22 | x23 | x24 | x25 | x26 | x27 | x28 | x29 | x2a | x2b | x2c | x2d | x2e | x2f | x30 | x31 | x32 | x33 | x34 | x35 | x36 | x37 | x38 | x39 | x3a | x3b | x3c | x3d | x3e | x3f | x40 | x41 | x42 | x43 | x44 | x45 | x46 | x47 | x48 | x49 | x4a | x4b | x4c | x4d | x4e | x4f | x50 | x51 | x52 | x53 | x54 | x55 | x56 | x57 | x58 | x59 | x5a | x5b | x5c | x5d | x5e | x5f | x60 | x61 | x62 | x63 | x64 | x65 | x66 | x67 | x68 | x69 | x6a | x6b | x6c | x6d | x6e | x6f | x70 | x71 | x72 | x73 | x74 | x75 | x76 | x77 | x78 | x79 | x7a | x7b | x7c | x7d | x7e | x7f | x80 | x81 | x82 | x83 | x84 | x85 | x86 => Gt
+  | x87 => Eq
+  | _ => Lt
+  end.
+Definition compare_byte_x88 (b : byte) :=
+  match b with
+  | x00 | x01 | x02 | x03 | x04 | x05 | x06 | x07 | x08 | x09 | x0a | x0b | x0c | x0d | x0e | x0f | x10 | x11 | x12 | x13 | x14 | x15 | x16 | x17 | x18 | x19 | x1a | x1b | x1c | x1d | x1e | x1f | x20 | x21 | x22 | x23 | x24 | x25 | x26 | x27 | x28 | x29 | x2a | x2b | x2c | x2d | x2e | x2f | x30 | x31 | x32 | x33 | x34 | x35 | x36 | x37 | x38 | x39 | x3a | x3b | x3c | x3d | x3e | x3f | x40 | x41 | x42 | x43 | x44 | x45 | x46 | x47 | x48 | x49 | x4a | x4b | x4c | x4d | x4e | x4f | x50 | x51 | x52 | x53 | x54 | x55 | x56 | x57 | x58 | x59 | x5a | x5b | x5c | x5d | x5e | x5f | x60 | x61 | x62 | x63 | x64 | x65 | x66 | x67 | x68 | x69 | x6a | x6b | x6c | x6d | x6e | x6f | x70 | x71 | x72 | x73 | x74 | x75 | x76 | x77 | x78 | x79 | x7a | x7b | x7c | x7d | x7e | x7f | x80 | x81 | x82 | x83 | x84 | x85 | x86 | x87 => Gt
+  | x88 => Eq
+  | _ => Lt
+  end.
+Definition compare_byte_x89 (b : byte) :=
+  match b with
+  | x00 | x01 | x02 | x03 | x04 | x05 | x06 | x07 | x08 | x09 | x0a | x0b | x0c | x0d | x0e | x0f | x10 | x11 | x12 | x13 | x14 | x15 | x16 | x17 | x18 | x19 | x1a | x1b | x1c | x1d | x1e | x1f | x20 | x21 | x22 | x23 | x24 | x25 | x26 | x27 | x28 | x29 | x2a | x2b | x2c | x2d | x2e | x2f | x30 | x31 | x32 | x33 | x34 | x35 | x36 | x37 | x38 | x39 | x3a | x3b | x3c | x3d | x3e | x3f | x40 | x41 | x42 | x43 | x44 | x45 | x46 | x47 | x48 | x49 | x4a | x4b | x4c | x4d | x4e | x4f | x50 | x51 | x52 | x53 | x54 | x55 | x56 | x57 | x58 | x59 | x5a | x5b | x5c | x5d | x5e | x5f | x60 | x61 | x62 | x63 | x64 | x65 | x66 | x67 | x68 | x69 | x6a | x6b | x6c | x6d | x6e | x6f | x70 | x71 | x72 | x73 | x74 | x75 | x76 | x77 | x78 | x79 | x7a | x7b | x7c | x7d | x7e | x7f | x80 | x81 | x82 | x83 | x84 | x85 | x86 | x87 | x88 => Gt
+  | x89 => Eq
+  | _ => Lt
+  end.
+Definition compare_byte_x8a (b : byte) :=
+  match b with
+  | x00 | x01 | x02 | x03 | x04 | x05 | x06 | x07 | x08 | x09 | x0a | x0b | x0c | x0d | x0e | x0f | x10 | x11 | x12 | x13 | x14 | x15 | x16 | x17 | x18 | x19 | x1a | x1b | x1c | x1d | x1e | x1f | x20 | x21 | x22 | x23 | x24 | x25 | x26 | x27 | x28 | x29 | x2a | x2b | x2c | x2d | x2e | x2f | x30 | x31 | x32 | x33 | x34 | x35 | x36 | x37 | x38 | x39 | x3a | x3b | x3c | x3d | x3e | x3f | x40 | x41 | x42 | x43 | x44 | x45 | x46 | x47 | x48 | x49 | x4a | x4b | x4c | x4d | x4e | x4f | x50 | x51 | x52 | x53 | x54 | x55 | x56 | x57 | x58 | x59 | x5a | x5b | x5c | x5d | x5e | x5f | x60 | x61 | x62 | x63 | x64 | x65 | x66 | x67 | x68 | x69 | x6a | x6b | x6c | x6d | x6e | x6f | x70 | x71 | x72 | x73 | x74 | x75 | x76 | x77 | x78 | x79 | x7a | x7b | x7c | x7d | x7e | x7f | x80 | x81 | x82 | x83 | x84 | x85 | x86 | x87 | x88 | x89 => Gt
+  | x8a => Eq
+  | _ => Lt
+  end.
+Definition compare_byte_x8b (b : byte) :=
+  match b with
+  | x00 | x01 | x02 | x03 | x04 | x05 | x06 | x07 | x08 | x09 | x0a | x0b | x0c | x0d | x0e | x0f | x10 | x11 | x12 | x13 | x14 | x15 | x16 | x17 | x18 | x19 | x1a | x1b | x1c | x1d | x1e | x1f | x20 | x21 | x22 | x23 | x24 | x25 | x26 | x27 | x28 | x29 | x2a | x2b | x2c | x2d | x2e | x2f | x30 | x31 | x32 | x33 | x34 | x35 | x36 | x37 | x38 | x39 | x3a | x3b | x3c | x3d | x3e | x3f | x40 | x41 | x42 | x43 | x44 | x45 | x46 | x47 | x48 | x49 | x4a | x4b | x4c | x4d | x4e | x4f | x50 | x51 | x52 | x53 | x54 | x55 | x56 | x57 | x58 | x59 | x5a | x5b | x5c | x5d | x5e | x5f | x60 | x61 | x62 | x63 | x64 | x65 | x66 | x67 | x68 | x69 | x6a | x6b | x6c | x6d | x6e | x6f | x70 | x71 | x72 | x73 | x74 | x75 | x76 | x77 | x78 | x79 | x7a | x7b | x7c | x7d | x7e | x7f | x80 | x81 | x82 | x83 | x84 | x85 | x86 | x87 | x88 | x89 | x8a => Gt
+  | x8b => Eq
+  | _ => Lt
+  end.
+Definition compare_byte_x8c (b : byte) :=
+  match b with
+  | x00 | x01 | x02 | x03 | x04 | x05 | x06 | x07 | x08 | x09 | x0a | x0b | x0c | x0d | x0e | x0f | x10 | x11 | x12 | x13 | x14 | x15 | x16 | x17 | x18 | x19 | x1a | x1b | x1c | x1d | x1e | x1f | x20 | x21 | x22 | x23 | x24 | x25 | x26 | x27 | x28 | x29 | x2a | x2b | x2c | x2d | x2e | x2f | x30 | x31 | x32 | x33 | x34 | x35 | x36 | x37 | x38 | x39 | x3a | x3b | x3c | x3d | x3e | x3f | x40 | x41 | x42 | x43 | x44 | x45 | x46 | x47 | x48 | x49 | x4a | x4b | x4c | x4d | x4e | x4f | x50 | x51 | x52 | x53 | x54 | x55 | x56 | x57 | x58 | x59 | x5a | x5b | x5c | x5d | x5e | x5f | x60 | x61 | x62 | x63 | x64 | x65 | x66 | x67 | x68 | x69 | x6a | x6b | x6c | x6d | x6e | x6f | x70 | x71 | x72 | x73 | x74 | x75 | x76 | x77 | x78 | x79 | x7a | x7b | x7c | x7d | x7e | x7f | x80 | x81 | x82 | x83 | x84 | x85 | x86 | x87 | x88 | x89 | x8a | x8b => Gt
+  | x8c => Eq
+  | _ => Lt
+  end.
+Definition compare_byte_x8d (b : byte) :=
+  match b with
+  | x00 | x01 | x02 | x03 | x04 | x05 | x06 | x07 | x08 | x09 | x0a | x0b | x0c | x0d | x0e | x0f | x10 | x11 | x12 | x13 | x14 | x15 | x16 | x17 | x18 | x19 | x1a | x1b | x1c | x1d | x1e | x1f | x20 | x21 | x22 | x23 | x24 | x25 | x26 | x27 | x28 | x29 | x2a | x2b | x2c | x2d | x2e | x2f | x30 | x31 | x32 | x33 | x34 | x35 | x36 | x37 | x38 | x39 | x3a | x3b | x3c | x3d | x3e | x3f | x40 | x41 | x42 | x43 | x44 | x45 | x46 | x47 | x48 | x49 | x4a | x4b | x4c | x4d | x4e | x4f | x50 | x51 | x52 | x53 | x54 | x55 | x56 | x57 | x58 | x59 | x5a | x5b | x5c | x5d | x5e | x5f | x60 | x61 | x62 | x63 | x64 | x65 | x66 | x67 | x68 | x69 | x6a | x6b | x6c | x6d | x6e | x6f | x70 | x71 | x72 | x73 | x74 | x75 | x76 | x77 | x78 | x79 | x7a | x7b | x7c | x7d | x7e | x7f | x80 | x81 | x82 | x83 | x84 | x85 | x86 | x87 | x88 | x89 | x8a | x8b | x8c => Gt
+  | x8d => Eq
+  | _ => Lt
+  end.
+Definition compare_byte_x8e (b : byte) :=
+  match b with
+  | x00 | x01 | x02 | x03 | x04 | x05 | x06 | x07 | x08 | x09 | x0a | x0b | x0c | x0d | x0e | x0f | x10 | x11 | x12 | x13 | x14 | x15 | x16 | x17 | x18 | x19 | x1a | x1b | x1c | x1d | x1e | x1f | x20 | x21 | x22 | x23 | x24 | x25 | x26 | x27 | x28 | x29 | x2a | x2b | x2c | x2d | x2e | x2f | x30 | x31 | x32 | x33 | x34 | x35 | x36 | x37 | x38 | x39 | x3a | x3b | x3c | x3d | x3e | x3f | x40 | x41 | x42 | x43 | x44 | x45 | x46 | x47 | x48 | x49 | x4a | x4b | x4c | x4d | x4e | x4f | x50 | x51 | x52 | x53 | x54 | x55 | x56 | x57 | x58 | x59 | x5a | x5b | x5c | x5d | x5e | x5f | x60 | x61 | x62 | x63 | x64 | x65 | x66 | x67 | x68 | x69 | x6a | x6b | x6c | x6d | x6e | x6f | x70 | x71 | x72 | x73 | x74 | x75 | x76 | x77 | x78 | x79 | x7a | x7b | x7c | x7d | x7e | x7f | x80 | x81 | x82 | x83 | x84 | x85 | x86 | x87 | x88 | x89 | x8a | x8b | x8c | x8d => Gt
+  | x8e => Eq
+  | _ => Lt
+  end.
+Definition compare_byte_x8f (b : byte) :=
+  match b with
+  | x00 | x01 | x02 | x03 | x04 | x05 | x06 | x07 | x08 | x09 | x0a | x0b | x0c | x0d | x0e | x0f | x10 | x11 | x12 | x13 | x14 | x15 | x16 | x17 | x18 | x19 | x1a | x1b | x1c | x1d | x1e | x1f | x20 | x21 | x22 | x23 | x24 | x25 | x26 | x27 | x28 | x29 | x2a | x2b | x2c | x2d | x2e | x2f | x30 | x31 | x32 | x33 | x34 | x35 | x36 | x37 | x38 | x39 | x3a | x3b | x3c | x3d | x3e | x3f | x40 | x41 | x42 | x43 | x44 | x45 | x46 | x47 | x48 | x49 | x4a | x4b | x4c | x4d | x4e | x4f | x50 | x51 | x52 | x53 | x54 | x55 | x56 | x57 | x58 | x59 | x5a | x5b | x5c | x5d | x5e | x5f | x60 | x61 | x62 | x63 | x64 | x65 | x66 | x67 | x68 | x69 | x6a | x6b | x6c | x6d | x6e | x6f | x70 | x71 | x72 | x73 | x74 | x75 | x76 | x77 | x78 | x79 | x7a | x7b | x7c | x7d | x7e | x7f | x80 | x81 | x82 | x83 | x84 | x85 | x86 | x87 | x88 | x89 | x8a | x8b | x8c | x8d | x8e => Gt
+  | x8f => Eq
+  | _ => Lt
+  end.
+Definition compare_byte_x90 (b : byte) :=
+  match b with
+  | x00 | x01 | x02 | x03 | x04 | x05 | x06 | x07 | x08 | x09 | x0a | x0b | x0c | x0d | x0e | x0f | x10 | x11 | x12 | x13 | x14 | x15 | x16 | x17 | x18 | x19 | x1a | x1b | x1c | x1d | x1e | x1f | x20 | x21 | x22 | x23 | x24 | x25 | x26 | x27 | x28 | x29 | x2a | x2b | x2c | x2d | x2e | x2f | x30 | x31 | x32 | x33 | x34 | x35 | x36 | x37 | x38 | x39 | x3a | x3b | x3c | x3d | x3e | x3f | x40 | x41 | x42 | x43 | x44 | x45 | x46 | x47 | x48 | x49 | x4a | x4b | x4c | x4d | x4e | x4f | x50 | x51 | x52 | x53 | x54 | x55 | x56 | x57 | x58 | x59 | x5a | x5b | x5c | x5d | x5e | x5f | x60 | x61 | x62 | x63 | x64 | x65 | x66 | x67 | x68 | x69 | x6a | x6b | x6c | x6d | x6e | x6f | x70 | x71 | x72 | x73 | x74 | x75 | x76 | x77 | x78 | x79 | x7a | x7b | x7c | x7d | x7e | x7f | x80 | x81 | x82 | x83 | x84 | x85 | x86 | x87 | x88 | x89 | x8a | x8b | x8c | x8d | x8e | x8f => Gt
+  | x90 => Eq
+  | _ => Lt
+  end.
+Definition compare_byte_x91 (b : byte) :=
+  match b with
+  | x00 | x01 | x02 | x03 | x04 | x05 | x06 | x07 | x08 | x09 | x0a | x0b | x0c | x0d | x0e | x0f | x10 | x11 | x12 | x13 | x14 | x15 | x16 | x17 | x18 | x19 | x1a | x1b | x1c | x1d | x1e | x1f | x20 | x21 | x22 | x23 | x24 | x25 | x26 | x27 | x28 | x29 | x2a | x2b | x2c | x2d | x2e | x2f | x30 | x31 | x32 | x33 | x34 | x35 | x36 | x37 | x38 | x39 | x3a | x3b | x3c | x3d | x3e | x3f | x40 | x41 | x42 | x43 | x44 | x45 | x46 | x47 | x48 | x49 | x4a | x4b | x4c | x4d | x4e | x4f | x50 | x51 | x52 | x53 | x54 | x55 | x56 | x57 | x58 | x59 | x5a | x5b | x5c | x5d | x5e | x5f | x60 | x61 | x62 | x63 | x64 | x65 | x66 | x67 | x68 | x69 | x6a | x6b | x6c | x6d | x6e | x6f | x70 | x71 | x72 | x73 | x74 | x75 | x76 | x77 | x78 | x79 | x7a | x7b | x7c | x7d | x7e | x7f | x80 | x81 | x82 | x83 | x84 | x85 | x86 | x87 | x88 | x89 | x8a | x8b | x8c | x8d | x8e | x8f | x90 => Gt
+  | x91 => Eq
+  | _ => Lt
+  end.
+Definition compare_byte_x92 (b : byte) :=
+  match b with
+  | x00 | x01 | x02 | x03 | x04 | x05 | x06 | x07 | x08 | x09 | x0a | x0b | x0c | x0d | x0e | x0f | x10 | x11 | x12 | x13 | x14 | x15 | x16 | x17 | x18 | x19 | x1a | x1b | x1c | x1d | x1e | x1f | x20 | x21 | x22 | x23 | x24 | x25 | x26 | x27 | x28 | x29 | x2a | x2b | x2c | x2d | x2e | x2f | x30 | x31 | x32 | x33 | x34 | x35 | x36 | x37 | x38 | x39 | x3a | x3b | x3c | x3d | x3e | x3f | x40 | x41 | x42 | x43 | x44 | x45 | x46 | x47 | x48 | x49 | x4a | x4b | x4c | x4d | x4e | x4f | x50 | x51 | x52 | x53 | x54 | x55 | x56 | x57 | x58 | x59 | x5a | x5b | x5c | x5d | x5e | x5f | x60 | x61 | x62 | x63 | x64 | x65 | x66 | x67 | x68 | x69 | x6a | x6b | x6c | x6d | x6e | x6f | x70 | x71 | x72 | x73 | x74 | x75 | x76 | x77 | x78 | x79 | x7a | x7b | x7c | x7d | x7e | x7f | x80 | x81 | x82 | x83 | x84 | x85 | x86 | x87 | x88 | x89 | x8a | x8b | x8c | x8d | x8e | x8f | x90 | x91 => Gt
+  | x92 => Eq
+  | _ => Lt
+  end.
+Definition compare_byte_x93 (b : byte) :=
+  match b with
+  | x00 | x01 | x02 | x03 | x04 | x05 | x06 | x07 | x08 | x09 | x0a | x0b | x0c | x0d | x0e | x0f | x10 | x11 | x12 | x13 | x14 | x15 | x16 | x17 | x18 | x19 | x1a | x1b | x1c | x1d | x1e | x1f | x20 | x21 | x22 | x23 | x24 | x25 | x26 | x27 | x28 | x29 | x2a | x2b | x2c | x2d | x2e | x2f | x30 | x31 | x32 | x33 | x34 | x35 | x36 | x37 | x38 | x39 | x3a | x3b | x3c | x3d | x3e | x3f | x40 | x41 | x42 | x43 | x44 | x45 | x46 | x47 | x48 | x49 | x4a | x4b | x4c | x4d | x4e | x4f | x50 | x51 | x52 | x53 | x54 | x55 | x56 | x57 | x58 | x59 | x5a | x5b | x5c | x5d | x5e | x5f | x60 | x61 | x62 | x63 | x64 | x65 | x66 | x67 | x68 | x69 | x6a | x6b | x6c | x6d | x6e | x6f | x70 | x71 | x72 | x73 | x74 | x75 | x76 | x77 | x78 | x79 | x7a | x7b | x7c | x7d | x7e | x7f | x80 | x81 | x82 | x83 | x84 | x85 | x86 | x87 | x88 | x89 | x8a | x8b | x8c | x8d | x8e | x8f | x90 | x91 | x92 => Gt
+  | x93 => Eq
+  | _ => Lt
+  end.
+Definition compare_byte_x94 (b : byte) :=
+  match b with
+  | x00 | x01 | x02 | x03 | x04 | x05 | x06 | x07 | x08 | x09 | x0a | x0b | x0c | x0d | x0e | x0f | x10 | x11 | x12 | x13 | x14 | x15 | x16 | x17 | x18 | x19 | x1a | x1b | x1c | x1d | x1e | x1f | x20 | x21 | x22 | x23 | x24 | x25 | x26 | x27 | x28 | x29 | x2a | x2b | x2c | x2d | x2e | x2f | x30 | x31 | x32 | x33 | x34 | x35 | x36 | x37 | x38 | x39 | x3a | x3b | x3c | x3d | x3e | x3f | x40 | x41 | x42 | x43 | x44 | x45 | x46 | x47 | x48 | x49 | x4a | x4b | x4c | x4d | x4e | x4f | x50 | x51 | x52 | x53 | x54 | x55 | x56 | x57 | x58 | x59 | x5a | x5b | x5c | x5d | x5e | x5f | x60 | x61 | x62 | x63 | x64 | x65 | x66 | x67 | x68 | x69 | x6a | x6b | x6c | x6d | x6e | x6f | x70 | x71 | x72 | x73 | x74 | x75 | x76 | x77 | x78 | x79 | x7a | x7b | x7c | x7d | x7e | x7f | x80 | x81 | x82 | x83 | x84 | x85 | x86 | x87 | x88 | x89 | x8a | x8b | x8c | x8d | x8e | x8f | x90 | x91 | x92 | x93 => Gt
+  | x94 => Eq
+  | _ => Lt
+  end.
+Definition compare_byte_x95 (b : byte) :=
+  match b with
+  | x00 | x01 | x02 | x03 | x04 | x05 | x06 | x07 | x08 | x09 | x0a | x0b | x0c | x0d | x0e | x0f | x10 | x11 | x12 | x13 | x14 | x15 | x16 | x17 | x18 | x19 | x1a | x1b | x1c | x1d | x1e | x1f | x20 | x21 | x22 | x23 | x24 | x25 | x26 | x27 | x28 | x29 | x2a | x2b | x2c | x2d | x2e | x2f | x30 | x31 | x32 | x33 | x34 | x35 | x36 | x37 | x38 | x39 | x3a | x3b | x3c | x3d | x3e | x3f | x40 | x41 | x42 | x43 | x44 | x45 | x46 | x47 | x48 | x49 | x4a | x4b | x4c | x4d | x4e | x4f | x50 | x51 | x52 | x53 | x54 | x55 | x56 | x57 | x58 | x59 | x5a | x5b | x5c | x5d | x5e | x5f | x60 | x61 | x62 | x63 | x64 | x65 | x66 | x67 | x68 | x69 | x6a | x6b | x6c | x6d | x6e | x6f | x70 | x71 | x72 | x73 | x74 | x75 | x76 | x77 | x78 | x79 | x7a | x7b | x7c | x7d | x7e | x7f | x80 | x81 | x82 | x83 | x84 | x85 | x86 | x87 | x88 | x89 | x8a | x8b | x8c | x8d | x8e | x8f | x90 | x91 | x92 | x93 | x94 => Gt
+  | x95 => Eq
+  | _ => Lt
+  end.
+Definition compare_byte_x96 (b : byte) :=
+  match b with
+  | x00 | x01 | x02 | x03 | x04 | x05 | x06 | x07 | x08 | x09 | x0a | x0b | x0c | x0d | x0e | x0f | x10 | x11 | x12 | x13 | x14 | x15 | x16 | x17 | x18 | x19 | x1a | x1b | x1c | x1d | x1e | x1f | x20 | x21 | x22 | x23 | x24 | x25 | x26 | x27 | x28 | x29 | x2a | x2b | x2c | x2d | x2e | x2f | x30 | x31 | x32 | x33 | x34 | x35 | x36 | x37 | x38 | x39 | x3a | x3b | x3c | x3d | x3e | x3f | x40 | x41 | x42 | x43 | x44 | x45 | x46 | x47 | x48 | x49 | x4a | x4b | x4c | x4d | x4e | x4f | x50 | x51 | x52 | x53 | x54 | x55 | x56 | x57 | x58 | x59 | x5a | x5b | x5c | x5d | x5e | x5f | x60 | x61 | x62 | x63 | x64 | x65 | x66 | x67 | x68 | x69 | x6a | x6b | x6c | x6d | x6e | x6f | x70 | x71 | x72 | x73 | x74 | x75 | x76 | x77 | x78 | x79 | x7a | x7b | x7c | x7d | x7e | x7f | x80 | x81 | x82 | x83 | x84 | x85 | x86 | x87 | x88 | x89 | x8a | x8b | x8c | x8d | x8e | x8f | x90 | x91 | x92 | x93 | x94 | x95 => Gt
+  | x96 => Eq
+  | _ => Lt
+  end.
+Definition compare_byte_x97 (b : byte) :=
+  match b with
+  | x00 | x01 | x02 | x03 | x04 | x05 | x06 | x07 | x08 | x09 | x0a | x0b | x0c | x0d | x0e | x0f | x10 | x11 | x12 | x13 | x14 | x15 | x16 | x17 | x18 | x19 | x1a | x1b | x1c | x1d | x1e | x1f | x20 | x21 | x22 | x23 | x24 | x25 | x26 | x27 | x28 | x29 | x2a | x2b | x2c | x2d | x2e | x2f | x30 | x31 | x32 | x33 | x34 | x35 | x36 | x37 | x38 | x39 | x3a | x3b | x3c | x3d | x3e | x3f | x40 | x41 | x42 | x43 | x44 | x45 | x46 | x47 | x48 | x49 | x4a | x4b | x4c | x4d | x4e | x4f | x50 | x51 | x52 | x53 | x54 | x55 | x56 | x57 | x58 | x59 | x5a | x5b | x5c | x5d | x5e | x5f | x60 | x61 | x62 | x63 | x64 | x65 | x66 | x67 | x68 | x69 | x6a | x6b | x6c | x6d | x6e | x6f | x70 | x71 | x72 | x73 | x74 | x75 | x76 | x77 | x78 | x79 | x7a | x7b | x7c | x7d | x7e | x7f | x80 | x81 | x82 | x83 | x84 | x85 | x86 | x87 | x88 | x89 | x8a | x8b | x8c | x8d | x8e | x8f | x90 | x91 | x92 | x93 | x94 | x95 | x96 => Gt
+  | x97 => Eq
+  | _ => Lt
+  end.
+Definition compare_byte_x98 (b : byte) :=
+  match b with
+  | x00 | x01 | x02 | x03 | x04 | x05 | x06 | x07 | x08 | x09 | x0a | x0b | x0c | x0d | x0e | x0f | x10 | x11 | x12 | x13 | x14 | x15 | x16 | x17 | x18 | x19 | x1a | x1b | x1c | x1d | x1e | x1f | x20 | x21 | x22 | x23 | x24 | x25 | x26 | x27 | x28 | x29 | x2a | x2b | x2c | x2d | x2e | x2f | x30 | x31 | x32 | x33 | x34 | x35 | x36 | x37 | x38 | x39 | x3a | x3b | x3c | x3d | x3e | x3f | x40 | x41 | x42 | x43 | x44 | x45 | x46 | x47 | x48 | x49 | x4a | x4b | x4c | x4d | x4e | x4f | x50 | x51 | x52 | x53 | x54 | x55 | x56 | x57 | x58 | x59 | x5a | x5b | x5c | x5d | x5e | x5f | x60 | x61 | x62 | x63 | x64 | x65 | x66 | x67 | x68 | x69 | x6a | x6b | x6c | x6d | x6e | x6f | x70 | x71 | x72 | x73 | x74 | x75 | x76 | x77 | x78 | x79 | x7a | x7b | x7c | x7d | x7e | x7f | x80 | x81 | x82 | x83 | x84 | x85 | x86 | x87 | x88 | x89 | x8a | x8b | x8c | x8d | x8e | x8f | x90 | x91 | x92 | x93 | x94 | x95 | x96 | x97 => Gt
+  | x98 => Eq
+  | _ => Lt
+  end.
+Definition compare_byte_x99 (b : byte) :=
+  match b with
+  | x00 | x01 | x02 | x03 | x04 | x05 | x06 | x07 | x08 | x09 | x0a | x0b | x0c | x0d | x0e | x0f | x10 | x11 | x12 | x13 | x14 | x15 | x16 | x17 | x18 | x19 | x1a | x1b | x1c | x1d | x1e | x1f | x20 | x21 | x22 | x23 | x24 | x25 | x26 | x27 | x28 | x29 | x2a | x2b | x2c | x2d | x2e | x2f | x30 | x31 | x32 | x33 | x34 | x35 | x36 | x37 | x38 | x39 | x3a | x3b | x3c | x3d | x3e | x3f | x40 | x41 | x42 | x43 | x44 | x45 | x46 | x47 | x48 | x49 | x4a | x4b | x4c | x4d | x4e | x4f | x50 | x51 | x52 | x53 | x54 | x55 | x56 | x57 | x58 | x59 | x5a | x5b | x5c | x5d | x5e | x5f | x60 | x61 | x62 | x63 | x64 | x65 | x66 | x67 | x68 | x69 | x6a | x6b | x6c | x6d | x6e | x6f | x70 | x71 | x72 | x73 | x74 | x75 | x76 | x77 | x78 | x79 | x7a | x7b | x7c | x7d | x7e | x7f | x80 | x81 | x82 | x83 | x84 | x85 | x86 | x87 | x88 | x89 | x8a | x8b | x8c | x8d | x8e | x8f | x90 | x91 | x92 | x93 | x94 | x95 | x96 | x97 | x98 => Gt
+  | x99 => Eq
+  | _ => Lt
+  end.
+Definition compare_byte_x9a (b : byte) :=
+  match b with
+  | x00 | x01 | x02 | x03 | x04 | x05 | x06 | x07 | x08 | x09 | x0a | x0b | x0c | x0d | x0e | x0f | x10 | x11 | x12 | x13 | x14 | x15 | x16 | x17 | x18 | x19 | x1a | x1b | x1c | x1d | x1e | x1f | x20 | x21 | x22 | x23 | x24 | x25 | x26 | x27 | x28 | x29 | x2a | x2b | x2c | x2d | x2e | x2f | x30 | x31 | x32 | x33 | x34 | x35 | x36 | x37 | x38 | x39 | x3a | x3b | x3c | x3d | x3e | x3f | x40 | x41 | x42 | x43 | x44 | x45 | x46 | x47 | x48 | x49 | x4a | x4b | x4c | x4d | x4e | x4f | x50 | x51 | x52 | x53 | x54 | x55 | x56 | x57 | x58 | x59 | x5a | x5b | x5c | x5d | x5e | x5f | x60 | x61 | x62 | x63 | x64 | x65 | x66 | x67 | x68 | x69 | x6a | x6b | x6c | x6d | x6e | x6f | x70 | x71 | x72 | x73 | x74 | x75 | x76 | x77 | x78 | x79 | x7a | x7b | x7c | x7d | x7e | x7f | x80 | x81 | x82 | x83 | x84 | x85 | x86 | x87 | x88 | x89 | x8a | x8b | x8c | x8d | x8e | x8f | x90 | x91 | x92 | x93 | x94 | x95 | x96 | x97 | x98 | x99 => Gt
+  | x9a => Eq
+  | _ => Lt
+  end.
+Definition compare_byte_x9b (b : byte) :=
+  match b with
+  | x00 | x01 | x02 | x03 | x04 | x05 | x06 | x07 | x08 | x09 | x0a | x0b | x0c | x0d | x0e | x0f | x10 | x11 | x12 | x13 | x14 | x15 | x16 | x17 | x18 | x19 | x1a | x1b | x1c | x1d | x1e | x1f | x20 | x21 | x22 | x23 | x24 | x25 | x26 | x27 | x28 | x29 | x2a | x2b | x2c | x2d | x2e | x2f | x30 | x31 | x32 | x33 | x34 | x35 | x36 | x37 | x38 | x39 | x3a | x3b | x3c | x3d | x3e | x3f | x40 | x41 | x42 | x43 | x44 | x45 | x46 | x47 | x48 | x49 | x4a | x4b | x4c | x4d | x4e | x4f | x50 | x51 | x52 | x53 | x54 | x55 | x56 | x57 | x58 | x59 | x5a | x5b | x5c | x5d | x5e | x5f | x60 | x61 | x62 | x63 | x64 | x65 | x66 | x67 | x68 | x69 | x6a | x6b | x6c | x6d | x6e | x6f | x70 | x71 | x72 | x73 | x74 | x75 | x76 | x77 | x78 | x79 | x7a | x7b | x7c | x7d | x7e | x7f | x80 | x81 | x82 | x83 | x84 | x85 | x86 | x87 | x88 | x89 | x8a | x8b | x8c | x8d | x8e | x8f | x90 | x91 | x92 | x93 | x94 | x95 | x96 | x97 | x98 | x99 | x9a => Gt
+  | x9b => Eq
+  | _ => Lt
+  end.
+Definition compare_byte_x9c (b : byte) :=
+  match b with
+  | x00 | x01 | x02 | x03 | x04 | x05 | x06 | x07 | x08 | x09 | x0a | x0b | x0c | x0d | x0e | x0f | x10 | x11 | x12 | x13 | x14 | x15 | x16 | x17 | x18 | x19 | x1a | x1b | x1c | x1d | x1e | x1f | x20 | x21 | x22 | x23 | x24 | x25 | x26 | x27 | x28 | x29 | x2a | x2b | x2c | x2d | x2e | x2f | x30 | x31 | x32 | x33 | x34 | x35 | x36 | x37 | x38 | x39 | x3a | x3b | x3c | x3d | x3e | x3f | x40 | x41 | x42 | x43 | x44 | x45 | x46 | x47 | x48 | x49 | x4a | x4b | x4c | x4d | x4e | x4f | x50 | x51 | x52 | x53 | x54 | x55 | x56 | x57 | x58 | x59 | x5a | x5b | x5c | x5d | x5e | x5f | x60 | x61 | x62 | x63 | x64 | x65 | x66 | x67 | x68 | x69 | x6a | x6b | x6c | x6d | x6e | x6f | x70 | x71 | x72 | x73 | x74 | x75 | x76 | x77 | x78 | x79 | x7a | x7b | x7c | x7d | x7e | x7f | x80 | x81 | x82 | x83 | x84 | x85 | x86 | x87 | x88 | x89 | x8a | x8b | x8c | x8d | x8e | x8f | x90 | x91 | x92 | x93 | x94 | x95 | x96 | x97 | x98 | x99 | x9a | x9b => Gt
+  | x9c => Eq
+  | _ => Lt
+  end.
+Definition compare_byte_x9d (b : byte) :=
+  match b with
+  | x00 | x01 | x02 | x03 | x04 | x05 | x06 | x07 | x08 | x09 | x0a | x0b | x0c | x0d | x0e | x0f | x10 | x11 | x12 | x13 | x14 | x15 | x16 | x17 | x18 | x19 | x1a | x1b | x1c | x1d | x1e | x1f | x20 | x21 | x22 | x23 | x24 | x25 | x26 | x27 | x28 | x29 | x2a | x2b | x2c | x2d | x2e | x2f | x30 | x31 | x32 | x33 | x34 | x35 | x36 | x37 | x38 | x39 | x3a | x3b | x3c | x3d | x3e | x3f | x40 | x41 | x42 | x43 | x44 | x45 | x46 | x47 | x48 | x49 | x4a | x4b | x4c | x4d | x4e | x4f | x50 | x51 | x52 | x53 | x54 | x55 | x56 | x57 | x58 | x59 | x5a | x5b | x5c | x5d | x5e | x5f | x60 | x61 | x62 | x63 | x64 | x65 | x66 | x67 | x68 | x69 | x6a | x6b | x6c | x6d | x6e | x6f | x70 | x71 | x72 | x73 | x74 | x75 | x76 | x77 | x78 | x79 | x7a | x7b | x7c | x7d | x7e | x7f | x80 | x81 | x82 | x83 | x84 | x85 | x86 | x87 | x88 | x89 | x8a | x8b | x8c | x8d | x8e | x8f | x90 | x91 | x92 | x93 | x94 | x95 | x96 | x97 | x98 | x99 | x9a | x9b | x9c => Gt
+  | x9d => Eq
+  | _ => Lt
+  end.
+Definition compare_byte_x9e (b : byte) :=
+  match b with
+  | x00 | x01 | x02 | x03 | x04 | x05 | x06 | x07 | x08 | x09 | x0a | x0b | x0c | x0d | x0e | x0f | x10 | x11 | x12 | x13 | x14 | x15 | x16 | x17 | x18 | x19 | x1a | x1b | x1c | x1d | x1e | x1f | x20 | x21 | x22 | x23 | x24 | x25 | x26 | x27 | x28 | x29 | x2a | x2b | x2c | x2d | x2e | x2f | x30 | x31 | x32 | x33 | x34 | x35 | x36 | x37 | x38 | x39 | x3a | x3b | x3c | x3d | x3e | x3f | x40 | x41 | x42 | x43 | x44 | x45 | x46 | x47 | x48 | x49 | x4a | x4b | x4c | x4d | x4e | x4f | x50 | x51 | x52 | x53 | x54 | x55 | x56 | x57 | x58 | x59 | x5a | x5b | x5c | x5d | x5e | x5f | x60 | x61 | x62 | x63 | x64 | x65 | x66 | x67 | x68 | x69 | x6a | x6b | x6c | x6d | x6e | x6f | x70 | x71 | x72 | x73 | x74 | x75 | x76 | x77 | x78 | x79 | x7a | x7b | x7c | x7d | x7e | x7f | x80 | x81 | x82 | x83 | x84 | x85 | x86 | x87 | x88 | x89 | x8a | x8b | x8c | x8d | x8e | x8f | x90 | x91 | x92 | x93 | x94 | x95 | x96 | x97 | x98 | x99 | x9a | x9b | x9c | x9d => Gt
+  | x9e => Eq
+  | _ => Lt
+  end.
+Definition compare_byte_x9f (b : byte) :=
+  match b with
+  | x00 | x01 | x02 | x03 | x04 | x05 | x06 | x07 | x08 | x09 | x0a | x0b | x0c | x0d | x0e | x0f | x10 | x11 | x12 | x13 | x14 | x15 | x16 | x17 | x18 | x19 | x1a | x1b | x1c | x1d | x1e | x1f | x20 | x21 | x22 | x23 | x24 | x25 | x26 | x27 | x28 | x29 | x2a | x2b | x2c | x2d | x2e | x2f | x30 | x31 | x32 | x33 | x34 | x35 | x36 | x37 | x38 | x39 | x3a | x3b | x3c | x3d | x3e | x3f | x40 | x41 | x42 | x43 | x44 | x45 | x46 | x47 | x48 | x49 | x4a | x4b | x4c | x4d | x4e | x4f | x50 | x51 | x52 | x53 | x54 | x55 | x56 | x57 | x58 | x59 | x5a | x5b | x5c | x5d | x5e | x5f | x60 | x61 | x62 | x63 | x64 | x65 | x66 | x67 | x68 | x69 | x6a | x6b | x6c | x6d | x6e | x6f | x70 | x71 | x72 | x73 | x74 | x75 | x76 | x77 | x78 | x79 | x7a | x7b | x7c | x7d | x7e | x7f | x80 | x81 | x82 | x83 | x84 | x85 | x86 | x87 | x88 | x89 | x8a | x8b | x8c | x8d | x8e | x8f | x90 | x91 | x92 | x93 | x94 | x95 | x96 | x97 | x98 | x99 | x9a | x9b | x9c | x9d | x9e => Gt
+  | x9f => Eq
+  | _ => Lt
+  end.
+Definition compare_byte_xa0 (b : byte) :=
+  match b with
+  | x00 | x01 | x02 | x03 | x04 | x05 | x06 | x07 | x08 | x09 | x0a | x0b | x0c | x0d | x0e | x0f | x10 | x11 | x12 | x13 | x14 | x15 | x16 | x17 | x18 | x19 | x1a | x1b | x1c | x1d | x1e | x1f | x20 | x21 | x22 | x23 | x24 | x25 | x26 | x27 | x28 | x29 | x2a | x2b | x2c | x2d | x2e | x2f | x30 | x31 | x32 | x33 | x34 | x35 | x36 | x37 | x38 | x39 | x3a | x3b | x3c | x3d | x3e | x3f | x40 | x41 | x42 | x43 | x44 | x45 | x46 | x47 | x48 | x49 | x4a | x4b | x4c | x4d | x4e | x4f | x50 | x51 | x52 | x53 | x54 | x55 | x56 | x57 | x58 | x59 | x5a | x5b | x5c | x5d | x5e | x5f | x60 | x61 | x62 | x63 | x64 | x65 | x66 | x67 | x68 | x69 | x6a | x6b | x6c | x6d | x6e | x6f | x70 | x71 | x72 | x73 | x74 | x75 | x76 | x77 | x78 | x79 | x7a | x7b | x7c | x7d | x7e | x7f | x80 | x81 | x82 | x83 | x84 | x85 | x86 | x87 | x88 | x89 | x8a | x8b | x8c | x8d | x8e | x8f | x90 | x91 | x92 | x93 | x94 | x95 | x96 | x97 | x98 | x99 | x9a | x9b | x9c | x9d | x9e | x9f => Gt
+  | xa0 => Eq
+  | _ => Lt
+  end.
+Definition compare_byte_xa1 (b : byte) :=
+  match b with
+  | x00 | x01 | x02 | x03 | x04 | x05 | x06 | x07 | x08 | x09 | x0a | x0b | x0c | x0d | x0e | x0f | x10 | x11 | x12 | x13 | x14 | x15 | x16 | x17 | x18 | x19 | x1a | x1b | x1c | x1d | x1e | x1f | x20 | x21 | x22 | x23 | x24 | x25 | x26 | x27 | x28 | x29 | x2a | x2b | x2c | x2d | x2e | x2f | x30 | x31 | x32 | x33 | x34 | x35 | x36 | x37 | x38 | x39 | x3a | x3b | x3c | x3d | x3e | x3f | x40 | x41 | x42 | x43 | x44 | x45 | x46 | x47 | x48 | x49 | x4a | x4b | x4c | x4d | x4e | x4f | x50 | x51 | x52 | x53 | x54 | x55 | x56 | x57 | x58 | x59 | x5a | x5b | x5c | x5d | x5e | x5f | x60 | x61 | x62 | x63 | x64 | x65 | x66 | x67 | x68 | x69 | x6a | x6b | x6c | x6d | x6e | x6f | x70 | x71 | x72 | x73 | x74 | x75 | x76 | x77 | x78 | x79 | x7a | x7b | x7c | x7d | x7e | x7f | x80 | x81 | x82 | x83 | x84 | x85 | x86 | x87 | x88 | x89 | x8a | x8b | x8c | x8d | x8e | x8f | x90 | x91 | x92 | x93 | x94 | x95 | x96 | x97 | x98 | x99 | x9a | x9b | x9c | x9d | x9e | x9f | xa0 => Gt
+  | xa1 => Eq
+  | _ => Lt
+  end.
+Definition compare_byte_xa2 (b : byte) :=
+  match b with
+  | x00 | x01 | x02 | x03 | x04 | x05 | x06 | x07 | x08 | x09 | x0a | x0b | x0c | x0d | x0e | x0f | x10 | x11 | x12 | x13 | x14 | x15 | x16 | x17 | x18 | x19 | x1a | x1b | x1c | x1d | x1e | x1f | x20 | x21 | x22 | x23 | x24 | x25 | x26 | x27 | x28 | x29 | x2a | x2b | x2c | x2d | x2e | x2f | x30 | x31 | x32 | x33 | x34 | x35 | x36 | x37 | x38 | x39 | x3a | x3b | x3c | x3d | x3e | x3f | x40 | x41 | x42 | x43 | x44 | x45 | x46 | x47 | x48 | x49 | x4a | x4b | x4c | x4d | x4e | x4f | x50 | x51 | x52 | x53 | x54 | x55 | x56 | x57 | x58 | x59 | x5a | x5b | x5c | x5d | x5e | x5f | x60 | x61 | x62 | x63 | x64 | x65 | x66 | x67 | x68 | x69 | x6a | x6b | x6c | x6d | x6e | x6f | x70 | x71 | x72 | x73 | x74 | x75 | x76 | x77 | x78 | x79 | x7a | x7b | x7c | x7d | x7e | x7f | x80 | x81 | x82 | x83 | x84 | x85 | x86 | x87 | x88 | x89 | x8a | x8b | x8c | x8d | x8e | x8f | x90 | x91 | x92 | x93 | x94 | x95 | x96 | x97 | x98 | x99 | x9a | x9b | x9c | x9d | x9e | x9f | xa0 | xa1 => Gt
+  | xa2 => Eq
+  | _ => Lt
+  end.
+Definition compare_byte_xa3 (b : byte) :=
+  match b with
+  | x00 | x01 | x02 | x03 | x04 | x05 | x06 | x07 | x08 | x09 | x0a | x0b | x0c | x0d | x0e | x0f | x10 | x11 | x12 | x13 | x14 | x15 | x16 | x17 | x18 | x19 | x1a | x1b | x1c | x1d | x1e | x1f | x20 | x21 | x22 | x23 | x24 | x25 | x26 | x27 | x28 | x29 | x2a | x2b | x2c | x2d | x2e | x2f | x30 | x31 | x32 | x33 | x34 | x35 | x36 | x37 | x38 | x39 | x3a | x3b | x3c | x3d | x3e | x3f | x40 | x41 | x42 | x43 | x44 | x45 | x46 | x47 | x48 | x49 | x4a | x4b | x4c | x4d | x4e | x4f | x50 | x51 | x52 | x53 | x54 | x55 | x56 | x57 | x58 | x59 | x5a | x5b | x5c | x5d | x5e | x5f | x60 | x61 | x62 | x63 | x64 | x65 | x66 | x67 | x68 | x69 | x6a | x6b | x6c | x6d | x6e | x6f | x70 | x71 | x72 | x73 | x74 | x75 | x76 | x77 | x78 | x79 | x7a | x7b | x7c | x7d | x7e | x7f | x80 | x81 | x82 | x83 | x84 | x85 | x86 | x87 | x88 | x89 | x8a | x8b | x8c | x8d | x8e | x8f | x90 | x91 | x92 | x93 | x94 | x95 | x96 | x97 | x98 | x99 | x9a | x9b | x9c | x9d | x9e | x9f | xa0 | xa1 | xa2 => Gt
+  | xa3 => Eq
+  | _ => Lt
+  end.
+Definition compare_byte_xa4 (b : byte) :=
+  match b with
+  | x00 | x01 | x02 | x03 | x04 | x05 | x06 | x07 | x08 | x09 | x0a | x0b | x0c | x0d | x0e | x0f | x10 | x11 | x12 | x13 | x14 | x15 | x16 | x17 | x18 | x19 | x1a | x1b | x1c | x1d | x1e | x1f | x20 | x21 | x22 | x23 | x24 | x25 | x26 | x27 | x28 | x29 | x2a | x2b | x2c | x2d | x2e | x2f | x30 | x31 | x32 | x33 | x34 | x35 | x36 | x37 | x38 | x39 | x3a | x3b | x3c | x3d | x3e | x3f | x40 | x41 | x42 | x43 | x44 | x45 | x46 | x47 | x48 | x49 | x4a | x4b | x4c | x4d | x4e | x4f | x50 | x51 | x52 | x53 | x54 | x55 | x56 | x57 | x58 | x59 | x5a | x5b | x5c | x5d | x5e | x5f | x60 | x61 | x62 | x63 | x64 | x65 | x66 | x67 | x68 | x69 | x6a | x6b | x6c | x6d | x6e | x6f | x70 | x71 | x72 | x73 | x74 | x75 | x76 | x77 | x78 | x79 | x7a | x7b | x7c | x7d | x7e | x7f | x80 | x81 | x82 | x83 | x84 | x85 | x86 | x87 | x88 | x89 | x8a | x8b | x8c | x8d | x8e | x8f | x90 | x91 | x92 | x93 | x94 | x95 | x96 | x97 | x98 | x99 | x9a | x9b | x9c | x9d | x9e | x9f | xa0 | xa1 | xa2 | xa3 => Gt
+  | xa4 => Eq
+  | _ => Lt
+  end.
+Definition compare_byte_xa5 (b : byte) :=
+  match b with
+  | x00 | x01 | x02 | x03 | x04 | x05 | x06 | x07 | x08 | x09 | x0a | x0b | x0c | x0d | x0e | x0f | x10 | x11 | x12 | x13 | x14 | x15 | x16 | x17 | x18 | x19 | x1a | x1b | x1c | x1d | x1e | x1f | x20 | x21 | x22 | x23 | x24 | x25 | x26 | x27 | x28 | x29 | x2a | x2b | x2c | x2d | x2e | x2f | x30 | x31 | x32 | x33 | x34 | x35 | x36 | x37 | x38 | x39 | x3a | x3b | x3c | x3d | x3e | x3f | x40 | x41 | x42 | x43 | x44 | x45 | x46 | x47 | x48 | x49 | x4a | x4b | x4c | x4d | x4e | x4f | x50 | x51 | x52 | x53 | x54 | x55 | x56 | x57 | x58 | x59 | x5a | x5b | x5c | x5d | x5e | x5f | x60 | x61 | x62 | x63 | x64 | x65 | x66 | x67 | x68 | x69 | x6a | x6b | x6c | x6d | x6e | x6f | x70 | x71 | x72 | x73 | x74 | x75 | x76 | x77 | x78 | x79 | x7a | x7b | x7c | x7d | x7e | x7f | x80 | x81 | x82 | x83 | x84 | x85 | x86 | x87 | x88 | x89 | x8a | x8b | x8c | x8d | x8e | x8f | x90 | x91 | x92 | x93 | x94 | x95 | x96 | x97 | x98 | x99 | x9a | x9b | x9c | x9d | x9e | x9f | xa0 | xa1 | xa2 | xa3 | xa4 => Gt
+  | xa5 => Eq
+  | _ => Lt
+  end.
+Definition compare_byte_xa6 (b : byte) :=
+  match b with
+  | x00 | x01 | x02 | x03 | x04 | x05 | x06 | x07 | x08 | x09 | x0a | x0b | x0c | x0d | x0e | x0f | x10 | x11 | x12 | x13 | x14 | x15 | x16 | x17 | x18 | x19 | x1a | x1b | x1c | x1d | x1e | x1f | x20 | x21 | x22 | x23 | x24 | x25 | x26 | x27 | x28 | x29 | x2a | x2b | x2c | x2d | x2e | x2f | x30 | x31 | x32 | x33 | x34 | x35 | x36 | x37 | x38 | x39 | x3a | x3b | x3c | x3d | x3e | x3f | x40 | x41 | x42 | x43 | x44 | x45 | x46 | x47 | x48 | x49 | x4a | x4b | x4c | x4d | x4e | x4f | x50 | x51 | x52 | x53 | x54 | x55 | x56 | x57 | x58 | x59 | x5a | x5b | x5c | x5d | x5e | x5f | x60 | x61 | x62 | x63 | x64 | x65 | x66 | x67 | x68 | x69 | x6a | x6b | x6c | x6d | x6e | x6f | x70 | x71 | x72 | x73 | x74 | x75 | x76 | x77 | x78 | x79 | x7a | x7b | x7c | x7d | x7e | x7f | x80 | x81 | x82 | x83 | x84 | x85 | x86 | x87 | x88 | x89 | x8a | x8b | x8c | x8d | x8e | x8f | x90 | x91 | x92 | x93 | x94 | x95 | x96 | x97 | x98 | x99 | x9a | x9b | x9c | x9d | x9e | x9f | xa0 | xa1 | xa2 | xa3 | xa4 | xa5 => Gt
+  | xa6 => Eq
+  | _ => Lt
+  end.
+Definition compare_byte_xa7 (b : byte) :=
+  match b with
+  | x00 | x01 | x02 | x03 | x04 | x05 | x06 | x07 | x08 | x09 | x0a | x0b | x0c | x0d | x0e | x0f | x10 | x11 | x12 | x13 | x14 | x15 | x16 | x17 | x18 | x19 | x1a | x1b | x1c | x1d | x1e | x1f | x20 | x21 | x22 | x23 | x24 | x25 | x26 | x27 | x28 | x29 | x2a | x2b | x2c | x2d | x2e | x2f | x30 | x31 | x32 | x33 | x34 | x35 | x36 | x37 | x38 | x39 | x3a | x3b | x3c | x3d | x3e | x3f | x40 | x41 | x42 | x43 | x44 | x45 | x46 | x47 | x48 | x49 | x4a | x4b | x4c | x4d | x4e | x4f | x50 | x51 | x52 | x53 | x54 | x55 | x56 | x57 | x58 | x59 | x5a | x5b | x5c | x5d | x5e | x5f | x60 | x61 | x62 | x63 | x64 | x65 | x66 | x67 | x68 | x69 | x6a | x6b | x6c | x6d | x6e | x6f | x70 | x71 | x72 | x73 | x74 | x75 | x76 | x77 | x78 | x79 | x7a | x7b | x7c | x7d | x7e | x7f | x80 | x81 | x82 | x83 | x84 | x85 | x86 | x87 | x88 | x89 | x8a | x8b | x8c | x8d | x8e | x8f | x90 | x91 | x92 | x93 | x94 | x95 | x96 | x97 | x98 | x99 | x9a | x9b | x9c | x9d | x9e | x9f | xa0 | xa1 | xa2 | xa3 | xa4 | xa5 | xa6 => Gt
+  | xa7 => Eq
+  | _ => Lt
+  end.
+Definition compare_byte_xa8 (b : byte) :=
+  match b with
+  | x00 | x01 | x02 | x03 | x04 | x05 | x06 | x07 | x08 | x09 | x0a | x0b | x0c | x0d | x0e | x0f | x10 | x11 | x12 | x13 | x14 | x15 | x16 | x17 | x18 | x19 | x1a | x1b | x1c | x1d | x1e | x1f | x20 | x21 | x22 | x23 | x24 | x25 | x26 | x27 | x28 | x29 | x2a | x2b | x2c | x2d | x2e | x2f | x30 | x31 | x32 | x33 | x34 | x35 | x36 | x37 | x38 | x39 | x3a | x3b | x3c | x3d | x3e | x3f | x40 | x41 | x42 | x43 | x44 | x45 | x46 | x47 | x48 | x49 | x4a | x4b | x4c | x4d | x4e | x4f | x50 | x51 | x52 | x53 | x54 | x55 | x56 | x57 | x58 | x59 | x5a | x5b | x5c | x5d | x5e | x5f | x60 | x61 | x62 | x63 | x64 | x65 | x66 | x67 | x68 | x69 | x6a | x6b | x6c | x6d | x6e | x6f | x70 | x71 | x72 | x73 | x74 | x75 | x76 | x77 | x78 | x79 | x7a | x7b | x7c | x7d | x7e | x7f | x80 | x81 | x82 | x83 | x84 | x85 | x86 | x87 | x88 | x89 | x8a | x8b | x8c | x8d | x8e | x8f | x90 | x91 | x92 | x93 | x94 | x95 | x96 | x97 | x98 | x99 | x9a | x9b | x9c | x9d | x9e | x9f | xa0 | xa1 | xa2 | xa3 | xa4 | xa5 | xa6 | xa7 => Gt
+  | xa8 => Eq
+  | _ => Lt
+  end.
+Definition compare_byte_xa9 (b : byte) :=
+  match b with
+  | x00 | x01 | x02 | x03 | x04 | x05 | x06 | x07 | x08 | x09 | x0a | x0b | x0c | x0d | x0e | x0f | x10 | x11 | x12 | x13 | x14 | x15 | x16 | x17 | x18 | x19 | x1a | x1b | x1c | x1d | x1e | x1f | x20 | x21 | x22 | x23 | x24 | x25 | x26 | x27 | x28 | x29 | x2a | x2b | x2c | x2d | x2e | x2f | x30 | x31 | x32 | x33 | x34 | x35 | x36 | x37 | x38 | x39 | x3a | x3b | x3c | x3d | x3e | x3f | x40 | x41 | x42 | x43 | x44 | x45 | x46 | x47 | x48 | x49 | x4a | x4b | x4c | x4d | x4e | x4f | x50 | x51 | x52 | x53 | x54 | x55 | x56 | x57 | x58 | x59 | x5a | x5b | x5c | x5d | x5e | x5f | x60 | x61 | x62 | x63 | x64 | x65 | x66 | x67 | x68 | x69 | x6a | x6b | x6c | x6d | x6e | x6f | x70 | x71 | x72 | x73 | x74 | x75 | x76 | x77 | x78 | x79 | x7a | x7b | x7c | x7d | x7e | x7f | x80 | x81 | x82 | x83 | x84 | x85 | x86 | x87 | x88 | x89 | x8a | x8b | x8c | x8d | x8e | x8f | x90 | x91 | x92 | x93 | x94 | x95 | x96 | x97 | x98 | x99 | x9a | x9b | x9c | x9d | x9e | x9f | xa0 | xa1 | xa2 | xa3 | xa4 | xa5 | xa6 | xa7 | xa8 => Gt
+  | xa9 => Eq
+  | _ => Lt
+  end.
+Definition compare_byte_xaa (b : byte) :=
+  match b with
+  | x00 | x01 | x02 | x03 | x04 | x05 | x06 | x07 | x08 | x09 | x0a | x0b | x0c | x0d | x0e | x0f | x10 | x11 | x12 | x13 | x14 | x15 | x16 | x17 | x18 | x19 | x1a | x1b | x1c | x1d | x1e | x1f | x20 | x21 | x22 | x23 | x24 | x25 | x26 | x27 | x28 | x29 | x2a | x2b | x2c | x2d | x2e | x2f | x30 | x31 | x32 | x33 | x34 | x35 | x36 | x37 | x38 | x39 | x3a | x3b | x3c | x3d | x3e | x3f | x40 | x41 | x42 | x43 | x44 | x45 | x46 | x47 | x48 | x49 | x4a | x4b | x4c | x4d | x4e | x4f | x50 | x51 | x52 | x53 | x54 | x55 | x56 | x57 | x58 | x59 | x5a | x5b | x5c | x5d | x5e | x5f | x60 | x61 | x62 | x63 | x64 | x65 | x66 | x67 | x68 | x69 | x6a | x6b | x6c | x6d | x6e | x6f | x70 | x71 | x72 | x73 | x74 | x75 | x76 | x77 | x78 | x79 | x7a | x7b | x7c | x7d | x7e | x7f | x80 | x81 | x82 | x83 | x84 | x85 | x86 | x87 | x88 | x89 | x8a | x8b | x8c | x8d | x8e | x8f | x90 | x91 | x92 | x93 | x94 | x95 | x96 | x97 | x98 | x99 | x9a | x9b | x9c | x9d | x9e | x9f | xa0 | xa1 | xa2 | xa3 | xa4 | xa5 | xa6 | xa7 | xa8 | xa9 => Gt
+  | xaa => Eq
+  | _ => Lt
+  end.
+Definition compare_byte_xab (b : byte) :=
+  match b with
+  | x00 | x01 | x02 | x03 | x04 | x05 | x06 | x07 | x08 | x09 | x0a | x0b | x0c | x0d | x0e | x0f | x10 | x11 | x12 | x13 | x14 | x15 | x16 | x17 | x18 | x19 | x1a | x1b | x1c | x1d | x1e | x1f | x20 | x21 | x22 | x23 | x24 | x25 | x26 | x27 | x28 | x29 | x2a | x2b | x2c | x2d | x2e | x2f | x30 | x31 | x32 | x33 | x34 | x35 | x36 | x37 | x38 | x39 | x3a | x3b | x3c | x3d | x3e | x3f | x40 | x41 | x42 | x43 | x44 | x45 | x46 | x47 | x48 | x49 | x4a | x4b | x4c | x4d | x4e | x4f | x50 | x51 | x52 | x53 | x54 | x55 | x56 | x57 | x58 | x59 | x5a | x5b | x5c | x5d | x5e | x5f | x60 | x61 | x62 | x63 | x64 | x65 | x66 | x67 | x68 | x69 | x6a | x6b | x6c | x6d | x6e | x6f | x70 | x71 | x72 | x73 | x74 | x75 | x76 | x77 | x78 | x79 | x7a | x7b | x7c | x7d | x7e | x7f | x80 | x81 | x82 | x83 | x84 | x85 | x86 | x87 | x88 | x89 | x8a | x8b | x8c | x8d | x8e | x8f | x90 | x91 | x92 | x93 | x94 | x95 | x96 | x97 | x98 | x99 | x9a | x9b | x9c | x9d | x9e | x9f | xa0 | xa1 | xa2 | xa3 | xa4 | xa5 | xa6 | xa7 | xa8 | xa9 | xaa => Gt
+  | xab => Eq
+  | _ => Lt
+  end.
+Definition compare_byte_xac (b : byte) :=
+  match b with
+  | x00 | x01 | x02 | x03 | x04 | x05 | x06 | x07 | x08 | x09 | x0a | x0b | x0c | x0d | x0e | x0f | x10 | x11 | x12 | x13 | x14 | x15 | x16 | x17 | x18 | x19 | x1a | x1b | x1c | x1d | x1e | x1f | x20 | x21 | x22 | x23 | x24 | x25 | x26 | x27 | x28 | x29 | x2a | x2b | x2c | x2d | x2e | x2f | x30 | x31 | x32 | x33 | x34 | x35 | x36 | x37 | x38 | x39 | x3a | x3b | x3c | x3d | x3e | x3f | x40 | x41 | x42 | x43 | x44 | x45 | x46 | x47 | x48 | x49 | x4a | x4b | x4c | x4d | x4e | x4f | x50 | x51 | x52 | x53 | x54 | x55 | x56 | x57 | x58 | x59 | x5a | x5b | x5c | x5d | x5e | x5f | x60 | x61 | x62 | x63 | x64 | x65 | x66 | x67 | x68 | x69 | x6a | x6b | x6c | x6d | x6e | x6f | x70 | x71 | x72 | x73 | x74 | x75 | x76 | x77 | x78 | x79 | x7a | x7b | x7c | x7d | x7e | x7f | x80 | x81 | x82 | x83 | x84 | x85 | x86 | x87 | x88 | x89 | x8a | x8b | x8c | x8d | x8e | x8f | x90 | x91 | x92 | x93 | x94 | x95 | x96 | x97 | x98 | x99 | x9a | x9b | x9c | x9d | x9e | x9f | xa0 | xa1 | xa2 | xa3 | xa4 | xa5 | xa6 | xa7 | xa8 | xa9 | xaa | xab => Gt
+  | xac => Eq
+  | _ => Lt
+  end.
+Definition compare_byte_xad (b : byte) :=
+  match b with
+  | x00 | x01 | x02 | x03 | x04 | x05 | x06 | x07 | x08 | x09 | x0a | x0b | x0c | x0d | x0e | x0f | x10 | x11 | x12 | x13 | x14 | x15 | x16 | x17 | x18 | x19 | x1a | x1b | x1c | x1d | x1e | x1f | x20 | x21 | x22 | x23 | x24 | x25 | x26 | x27 | x28 | x29 | x2a | x2b | x2c | x2d | x2e | x2f | x30 | x31 | x32 | x33 | x34 | x35 | x36 | x37 | x38 | x39 | x3a | x3b | x3c | x3d | x3e | x3f | x40 | x41 | x42 | x43 | x44 | x45 | x46 | x47 | x48 | x49 | x4a | x4b | x4c | x4d | x4e | x4f | x50 | x51 | x52 | x53 | x54 | x55 | x56 | x57 | x58 | x59 | x5a | x5b | x5c | x5d | x5e | x5f | x60 | x61 | x62 | x63 | x64 | x65 | x66 | x67 | x68 | x69 | x6a | x6b | x6c | x6d | x6e | x6f | x70 | x71 | x72 | x73 | x74 | x75 | x76 | x77 | x78 | x79 | x7a | x7b | x7c | x7d | x7e | x7f | x80 | x81 | x82 | x83 | x84 | x85 | x86 | x87 | x88 | x89 | x8a | x8b | x8c | x8d | x8e | x8f | x90 | x91 | x92 | x93 | x94 | x95 | x96 | x97 | x98 | x99 | x9a | x9b | x9c | x9d | x9e | x9f | xa0 | xa1 | xa2 | xa3 | xa4 | xa5 | xa6 | xa7 | xa8 | xa9 | xaa | xab | xac => Gt
+  | xad => Eq
+  | _ => Lt
+  end.
+Definition compare_byte_xae (b : byte) :=
+  match b with
+  | x00 | x01 | x02 | x03 | x04 | x05 | x06 | x07 | x08 | x09 | x0a | x0b | x0c | x0d | x0e | x0f | x10 | x11 | x12 | x13 | x14 | x15 | x16 | x17 | x18 | x19 | x1a | x1b | x1c | x1d | x1e | x1f | x20 | x21 | x22 | x23 | x24 | x25 | x26 | x27 | x28 | x29 | x2a | x2b | x2c | x2d | x2e | x2f | x30 | x31 | x32 | x33 | x34 | x35 | x36 | x37 | x38 | x39 | x3a | x3b | x3c | x3d | x3e | x3f | x40 | x41 | x42 | x43 | x44 | x45 | x46 | x47 | x48 | x49 | x4a | x4b | x4c | x4d | x4e | x4f | x50 | x51 | x52 | x53 | x54 | x55 | x56 | x57 | x58 | x59 | x5a | x5b | x5c | x5d | x5e | x5f | x60 | x61 | x62 | x63 | x64 | x65 | x66 | x67 | x68 | x69 | x6a | x6b | x6c | x6d | x6e | x6f | x70 | x71 | x72 | x73 | x74 | x75 | x76 | x77 | x78 | x79 | x7a | x7b | x7c | x7d | x7e | x7f | x80 | x81 | x82 | x83 | x84 | x85 | x86 | x87 | x88 | x89 | x8a | x8b | x8c | x8d | x8e | x8f | x90 | x91 | x92 | x93 | x94 | x95 | x96 | x97 | x98 | x99 | x9a | x9b | x9c | x9d | x9e | x9f | xa0 | xa1 | xa2 | xa3 | xa4 | xa5 | xa6 | xa7 | xa8 | xa9 | xaa | xab | xac | xad => Gt
+  | xae => Eq
+  | _ => Lt
+  end.
+Definition compare_byte_xaf (b : byte) :=
+  match b with
+  | x00 | x01 | x02 | x03 | x04 | x05 | x06 | x07 | x08 | x09 | x0a | x0b | x0c | x0d | x0e | x0f | x10 | x11 | x12 | x13 | x14 | x15 | x16 | x17 | x18 | x19 | x1a | x1b | x1c | x1d | x1e | x1f | x20 | x21 | x22 | x23 | x24 | x25 | x26 | x27 | x28 | x29 | x2a | x2b | x2c | x2d | x2e | x2f | x30 | x31 | x32 | x33 | x34 | x35 | x36 | x37 | x38 | x39 | x3a | x3b | x3c | x3d | x3e | x3f | x40 | x41 | x42 | x43 | x44 | x45 | x46 | x47 | x48 | x49 | x4a | x4b | x4c | x4d | x4e | x4f | x50 | x51 | x52 | x53 | x54 | x55 | x56 | x57 | x58 | x59 | x5a | x5b | x5c | x5d | x5e | x5f | x60 | x61 | x62 | x63 | x64 | x65 | x66 | x67 | x68 | x69 | x6a | x6b | x6c | x6d | x6e | x6f | x70 | x71 | x72 | x73 | x74 | x75 | x76 | x77 | x78 | x79 | x7a | x7b | x7c | x7d | x7e | x7f | x80 | x81 | x82 | x83 | x84 | x85 | x86 | x87 | x88 | x89 | x8a | x8b | x8c | x8d | x8e | x8f | x90 | x91 | x92 | x93 | x94 | x95 | x96 | x97 | x98 | x99 | x9a | x9b | x9c | x9d | x9e | x9f | xa0 | xa1 | xa2 | xa3 | xa4 | xa5 | xa6 | xa7 | xa8 | xa9 | xaa | xab | xac | xad | xae => Gt
+  | xaf => Eq
+  | _ => Lt
+  end.
+Definition compare_byte_xb0 (b : byte) :=
+  match b with
+  | x00 | x01 | x02 | x03 | x04 | x05 | x06 | x07 | x08 | x09 | x0a | x0b | x0c | x0d | x0e | x0f | x10 | x11 | x12 | x13 | x14 | x15 | x16 | x17 | x18 | x19 | x1a | x1b | x1c | x1d | x1e | x1f | x20 | x21 | x22 | x23 | x24 | x25 | x26 | x27 | x28 | x29 | x2a | x2b | x2c | x2d | x2e | x2f | x30 | x31 | x32 | x33 | x34 | x35 | x36 | x37 | x38 | x39 | x3a | x3b | x3c | x3d | x3e | x3f | x40 | x41 | x42 | x43 | x44 | x45 | x46 | x47 | x48 | x49 | x4a | x4b | x4c | x4d | x4e | x4f | x50 | x51 | x52 | x53 | x54 | x55 | x56 | x57 | x58 | x59 | x5a | x5b | x5c | x5d | x5e | x5f | x60 | x61 | x62 | x63 | x64 | x65 | x66 | x67 | x68 | x69 | x6a | x6b | x6c | x6d | x6e | x6f | x70 | x71 | x72 | x73 | x74 | x75 | x76 | x77 | x78 | x79 | x7a | x7b | x7c | x7d | x7e | x7f | x80 | x81 | x82 | x83 | x84 | x85 | x86 | x87 | x88 | x89 | x8a | x8b | x8c | x8d | x8e | x8f | x90 | x91 | x92 | x93 | x94 | x95 | x96 | x97 | x98 | x99 | x9a | x9b | x9c | x9d | x9e | x9f | xa0 | xa1 | xa2 | xa3 | xa4 | xa5 | xa6 | xa7 | xa8 | xa9 | xaa | xab | xac | xad | xae | xaf => Gt
+  | xb0 => Eq
+  | _ => Lt
+  end.
+Definition compare_byte_xb1 (b : byte) :=
+  match b with
+  | x00 | x01 | x02 | x03 | x04 | x05 | x06 | x07 | x08 | x09 | x0a | x0b | x0c | x0d | x0e | x0f | x10 | x11 | x12 | x13 | x14 | x15 | x16 | x17 | x18 | x19 | x1a | x1b | x1c | x1d | x1e | x1f | x20 | x21 | x22 | x23 | x24 | x25 | x26 | x27 | x28 | x29 | x2a | x2b | x2c | x2d | x2e | x2f | x30 | x31 | x32 | x33 | x34 | x35 | x36 | x37 | x38 | x39 | x3a | x3b | x3c | x3d | x3e | x3f | x40 | x41 | x42 | x43 | x44 | x45 | x46 | x47 | x48 | x49 | x4a | x4b | x4c | x4d | x4e | x4f | x50 | x51 | x52 | x53 | x54 | x55 | x56 | x57 | x58 | x59 | x5a | x5b | x5c | x5d | x5e | x5f | x60 | x61 | x62 | x63 | x64 | x65 | x66 | x67 | x68 | x69 | x6a | x6b | x6c | x6d | x6e | x6f | x70 | x71 | x72 | x73 | x74 | x75 | x76 | x77 | x78 | x79 | x7a | x7b | x7c | x7d | x7e | x7f | x80 | x81 | x82 | x83 | x84 | x85 | x86 | x87 | x88 | x89 | x8a | x8b | x8c | x8d | x8e | x8f | x90 | x91 | x92 | x93 | x94 | x95 | x96 | x97 | x98 | x99 | x9a | x9b | x9c | x9d | x9e | x9f | xa0 | xa1 | xa2 | xa3 | xa4 | xa5 | xa6 | xa7 | xa8 | xa9 | xaa | xab | xac | xad | xae | xaf | xb0 => Gt
+  | xb1 => Eq
+  | _ => Lt
+  end.
+Definition compare_byte_xb2 (b : byte) :=
+  match b with
+  | x00 | x01 | x02 | x03 | x04 | x05 | x06 | x07 | x08 | x09 | x0a | x0b | x0c | x0d | x0e | x0f | x10 | x11 | x12 | x13 | x14 | x15 | x16 | x17 | x18 | x19 | x1a | x1b | x1c | x1d | x1e | x1f | x20 | x21 | x22 | x23 | x24 | x25 | x26 | x27 | x28 | x29 | x2a | x2b | x2c | x2d | x2e | x2f | x30 | x31 | x32 | x33 | x34 | x35 | x36 | x37 | x38 | x39 | x3a | x3b | x3c | x3d | x3e | x3f | x40 | x41 | x42 | x43 | x44 | x45 | x46 | x47 | x48 | x49 | x4a | x4b | x4c | x4d | x4e | x4f | x50 | x51 | x52 | x53 | x54 | x55 | x56 | x57 | x58 | x59 | x5a | x5b | x5c | x5d | x5e | x5f | x60 | x61 | x62 | x63 | x64 | x65 | x66 | x67 | x68 | x69 | x6a | x6b | x6c | x6d | x6e | x6f | x70 | x71 | x72 | x73 | x74 | x75 | x76 | x77 | x78 | x79 | x7a | x7b | x7c | x7d | x7e | x7f | x80 | x81 | x82 | x83 | x84 | x85 | x86 | x87 | x88 | x89 | x8a | x8b | x8c | x8d | x8e | x8f | x90 | x91 | x92 | x93 | x94 | x95 | x96 | x97 | x98 | x99 | x9a | x9b | x9c | x9d | x9e | x9f | xa0 | xa1 | xa2 | xa3 | xa4 | xa5 | xa6 | xa7 | xa8 | xa9 | xaa | xab | xac | xad | xae | xaf | xb0 | xb1 => Gt
+  | xb2 => Eq
+  | _ => Lt
+  end.
+Definition compare_byte_xb3 (b : byte) :=
+  match b with
+  | x00 | x01 | x02 | x03 | x04 | x05 | x06 | x07 | x08 | x09 | x0a | x0b | x0c | x0d | x0e | x0f | x10 | x11 | x12 | x13 | x14 | x15 | x16 | x17 | x18 | x19 | x1a | x1b | x1c | x1d | x1e | x1f | x20 | x21 | x22 | x23 | x24 | x25 | x26 | x27 | x28 | x29 | x2a | x2b | x2c | x2d | x2e | x2f | x30 | x31 | x32 | x33 | x34 | x35 | x36 | x37 | x38 | x39 | x3a | x3b | x3c | x3d | x3e | x3f | x40 | x41 | x42 | x43 | x44 | x45 | x46 | x47 | x48 | x49 | x4a | x4b | x4c | x4d | x4e | x4f | x50 | x51 | x52 | x53 | x54 | x55 | x56 | x57 | x58 | x59 | x5a | x5b | x5c | x5d | x5e | x5f | x60 | x61 | x62 | x63 | x64 | x65 | x66 | x67 | x68 | x69 | x6a | x6b | x6c | x6d | x6e | x6f | x70 | x71 | x72 | x73 | x74 | x75 | x76 | x77 | x78 | x79 | x7a | x7b | x7c | x7d | x7e | x7f | x80 | x81 | x82 | x83 | x84 | x85 | x86 | x87 | x88 | x89 | x8a | x8b | x8c | x8d | x8e | x8f | x90 | x91 | x92 | x93 | x94 | x95 | x96 | x97 | x98 | x99 | x9a | x9b | x9c | x9d | x9e | x9f | xa0 | xa1 | xa2 | xa3 | xa4 | xa5 | xa6 | xa7 | xa8 | xa9 | xaa | xab | xac | xad | xae | xaf | xb0 | xb1 | xb2 => Gt
+  | xb3 => Eq
+  | _ => Lt
+  end.
+Definition compare_byte_xb4 (b : byte) :=
+  match b with
+  | x00 | x01 | x02 | x03 | x04 | x05 | x06 | x07 | x08 | x09 | x0a | x0b | x0c | x0d | x0e | x0f | x10 | x11 | x12 | x13 | x14 | x15 | x16 | x17 | x18 | x19 | x1a | x1b | x1c | x1d | x1e | x1f | x20 | x21 | x22 | x23 | x24 | x25 | x26 | x27 | x28 | x29 | x2a | x2b | x2c | x2d | x2e | x2f | x30 | x31 | x32 | x33 | x34 | x35 | x36 | x37 | x38 | x39 | x3a | x3b | x3c | x3d | x3e | x3f | x40 | x41 | x42 | x43 | x44 | x45 | x46 | x47 | x48 | x49 | x4a | x4b | x4c | x4d | x4e | x4f | x50 | x51 | x52 | x53 | x54 | x55 | x56 | x57 | x58 | x59 | x5a | x5b | x5c | x5d | x5e | x5f | x60 | x61 | x62 | x63 | x64 | x65 | x66 | x67 | x68 | x69 | x6a | x6b | x6c | x6d | x6e | x6f | x70 | x71 | x72 | x73 | x74 | x75 | x76 | x77 | x78 | x79 | x7a | x7b | x7c | x7d | x7e | x7f | x80 | x81 | x82 | x83 | x84 | x85 | x86 | x87 | x88 | x89 | x8a | x8b | x8c | x8d | x8e | x8f | x90 | x91 | x92 | x93 | x94 | x95 | x96 | x97 | x98 | x99 | x9a | x9b | x9c | x9d | x9e | x9f | xa0 | xa1 | xa2 | xa3 | xa4 | xa5 | xa6 | xa7 | xa8 | xa9 | xaa | xab | xac | xad | xae | xaf | xb0 | xb1 | xb2 | xb3 => Gt
+  | xb4 => Eq
+  | _ => Lt
+  end.
+Definition compare_byte_xb5 (b : byte) :=
+  match b with
+  | x00 | x01 | x02 | x03 | x04 | x05 | x06 | x07 | x08 | x09 | x0a | x0b | x0c | x0d | x0e | x0f | x10 | x11 | x12 | x13 | x14 | x15 | x16 | x17 | x18 | x19 | x1a | x1b | x1c | x1d | x1e | x1f | x20 | x21 | x22 | x23 | x24 | x25 | x26 | x27 | x28 | x29 | x2a | x2b | x2c | x2d | x2e | x2f | x30 | x31 | x32 | x33 | x34 | x35 | x36 | x37 | x38 | x39 | x3a | x3b | x3c | x3d | x3e | x3f | x40 | x41 | x42 | x43 | x44 | x45 | x46 | x47 | x48 | x49 | x4a | x4b | x4c | x4d | x4e | x4f | x50 | x51 | x52 | x53 | x54 | x55 | x56 | x57 | x58 | x59 | x5a | x5b | x5c | x5d | x5e | x5f | x60 | x61 | x62 | x63 | x64 | x65 | x66 | x67 | x68 | x69 | x6a | x6b | x6c | x6d | x6e | x6f | x70 | x71 | x72 | x73 | x74 | x75 | x76 | x77 | x78 | x79 | x7a | x7b | x7c | x7d | x7e | x7f | x80 | x81 | x82 | x83 | x84 | x85 | x86 | x87 | x88 | x89 | x8a | x8b | x8c | x8d | x8e | x8f | x90 | x91 | x92 | x93 | x94 | x95 | x96 | x97 | x98 | x99 | x9a | x9b | x9c | x9d | x9e | x9f | xa0 | xa1 | xa2 | xa3 | xa4 | xa5 | xa6 | xa7 | xa8 | xa9 | xaa | xab | xac | xad | xae | xaf | xb0 | xb1 | xb2 | xb3 | xb4 => Gt
+  | xb5 => Eq
+  | _ => Lt
+  end.
+Definition compare_byte_xb6 (b : byte) :=
+  match b with
+  | x00 | x01 | x02 | x03 | x04 | x05 | x06 | x07 | x08 | x09 | x0a | x0b | x0c | x0d | x0e | x0f | x10 | x11 | x12 | x13 | x14 | x15 | x16 | x17 | x18 | x19 | x1a | x1b | x1c | x1d | x1e | x1f | x20 | x21 | x22 | x23 | x24 | x25 | x26 | x27 | x28 | x29 | x2a | x2b | x2c | x2d | x2e | x2f | x30 | x31 | x32 | x33 | x34 | x35 | x36 | x37 | x38 | x39 | x3a | x3b | x3c | x3d | x3e | x3f | x40 | x41 | x42 | x43 | x44 | x45 | x46 | x47 | x48 | x49 | x4a | x4b | x4c | x4d | x4e | x4f | x50 | x51 | x52 | x53 | x54 | x55 | x56 | x57 | x58 | x59 | x5a | x5b | x5c | x5d | x5e | x5f | x60 | x61 | x62 | x63 | x64 | x65 | x66 | x67 | x68 | x69 | x6a | x6b | x6c | x6d | x6e | x6f | x70 | x71 | x72 | x73 | x74 | x75 | x76 | x77 | x78 | x79 | x7a | x7b | x7c | x7d | x7e | x7f | x80 | x81 | x82 | x83 | x84 | x85 | x86 | x87 | x88 | x89 | x8a | x8b | x8c | x8d | x8e | x8f | x90 | x91 | x92 | x93 | x94 | x95 | x96 | x97 | x98 | x99 | x9a | x9b | x9c | x9d | x9e | x9f | xa0 | xa1 | xa2 | xa3 | xa4 | xa5 | xa6 | xa7 | xa8 | xa9 | xaa | xab | xac | xad | xae | xaf | xb0 | xb1 | xb2 | xb3 | xb4 | xb5 => Gt
+  | xb6 => Eq
+  | _ => Lt
+  end.
+Definition compare_byte_xb7 (b : byte) :=
+  match b with
+  | x00 | x01 | x02 | x03 | x04 | x05 | x06 | x07 | x08 | x09 | x0a | x0b | x0c | x0d | x0e | x0f | x10 | x11 | x12 | x13 | x14 | x15 | x16 | x17 | x18 | x19 | x1a | x1b | x1c | x1d | x1e | x1f | x20 | x21 | x22 | x23 | x24 | x25 | x26 | x27 | x28 | x29 | x2a | x2b | x2c | x2d | x2e | x2f | x30 | x31 | x32 | x33 | x34 | x35 | x36 | x37 | x38 | x39 | x3a | x3b | x3c | x3d | x3e | x3f | x40 | x41 | x42 | x43 | x44 | x45 | x46 | x47 | x48 | x49 | x4a | x4b | x4c | x4d | x4e | x4f | x50 | x51 | x52 | x53 | x54 | x55 | x56 | x57 | x58 | x59 | x5a | x5b | x5c | x5d | x5e | x5f | x60 | x61 | x62 | x63 | x64 | x65 | x66 | x67 | x68 | x69 | x6a | x6b | x6c | x6d | x6e | x6f | x70 | x71 | x72 | x73 | x74 | x75 | x76 | x77 | x78 | x79 | x7a | x7b | x7c | x7d | x7e | x7f | x80 | x81 | x82 | x83 | x84 | x85 | x86 | x87 | x88 | x89 | x8a | x8b | x8c | x8d | x8e | x8f | x90 | x91 | x92 | x93 | x94 | x95 | x96 | x97 | x98 | x99 | x9a | x9b | x9c | x9d | x9e | x9f | xa0 | xa1 | xa2 | xa3 | xa4 | xa5 | xa6 | xa7 | xa8 | xa9 | xaa | xab | xac | xad | xae | xaf | xb0 | xb1 | xb2 | xb3 | xb4 | xb5 | xb6 => Gt
+  | xb7 => Eq
+  | _ => Lt
+  end.
+Definition compare_byte_xb8 (b : byte) :=
+  match b with
+  | x00 | x01 | x02 | x03 | x04 | x05 | x06 | x07 | x08 | x09 | x0a | x0b | x0c | x0d | x0e | x0f | x10 | x11 | x12 | x13 | x14 | x15 | x16 | x17 | x18 | x19 | x1a | x1b | x1c | x1d | x1e | x1f | x20 | x21 | x22 | x23 | x24 | x25 | x26 | x27 | x28 | x29 | x2a | x2b | x2c | x2d | x2e | x2f | x30 | x31 | x32 | x33 | x34 | x35 | x36 | x37 | x38 | x39 | x3a | x3b | x3c | x3d | x3e | x3f | x40 | x41 | x42 | x43 | x44 | x45 | x46 | x47 | x48 | x49 | x4a | x4b | x4c | x4d | x4e | x4f | x50 | x51 | x52 | x53 | x54 | x55 | x56 | x57 | x58 | x59 | x5a | x5b | x5c | x5d | x5e | x5f | x60 | x61 | x62 | x63 | x64 | x65 | x66 | x67 | x68 | x69 | x6a | x6b | x6c | x6d | x6e | x6f | x70 | x71 | x72 | x73 | x74 | x75 | x76 | x77 | x78 | x79 | x7a | x7b | x7c | x7d | x7e | x7f | x80 | x81 | x82 | x83 | x84 | x85 | x86 | x87 | x88 | x89 | x8a | x8b | x8c | x8d | x8e | x8f | x90 | x91 | x92 | x93 | x94 | x95 | x96 | x97 | x98 | x99 | x9a | x9b | x9c | x9d | x9e | x9f | xa0 | xa1 | xa2 | xa3 | xa4 | xa5 | xa6 | xa7 | xa8 | xa9 | xaa | xab | xac | xad | xae | xaf | xb0 | xb1 | xb2 | xb3 | xb4 | xb5 | xb6 | xb7 => Gt
+  | xb8 => Eq
+  | _ => Lt
+  end.
+Definition compare_byte_xb9 (b : byte) :=
+  match b with
+  | x00 | x01 | x02 | x03 | x04 | x05 | x06 | x07 | x08 | x09 | x0a | x0b | x0c | x0d | x0e | x0f | x10 | x11 | x12 | x13 | x14 | x15 | x16 | x17 | x18 | x19 | x1a | x1b | x1c | x1d | x1e | x1f | x20 | x21 | x22 | x23 | x24 | x25 | x26 | x27 | x28 | x29 | x2a | x2b | x2c | x2d | x2e | x2f | x30 | x31 | x32 | x33 | x34 | x35 | x36 | x37 | x38 | x39 | x3a | x3b | x3c | x3d | x3e | x3f | x40 | x41 | x42 | x43 | x44 | x45 | x46 | x47 | x48 | x49 | x4a | x4b | x4c | x4d | x4e | x4f | x50 | x51 | x52 | x53 | x54 | x55 | x56 | x57 | x58 | x59 | x5a | x5b | x5c | x5d | x5e | x5f | x60 | x61 | x62 | x63 | x64 | x65 | x66 | x67 | x68 | x69 | x6a | x6b | x6c | x6d | x6e | x6f | x70 | x71 | x72 | x73 | x74 | x75 | x76 | x77 | x78 | x79 | x7a | x7b | x7c | x7d | x7e | x7f | x80 | x81 | x82 | x83 | x84 | x85 | x86 | x87 | x88 | x89 | x8a | x8b | x8c | x8d | x8e | x8f | x90 | x91 | x92 | x93 | x94 | x95 | x96 | x97 | x98 | x99 | x9a | x9b | x9c | x9d | x9e | x9f | xa0 | xa1 | xa2 | xa3 | xa4 | xa5 | xa6 | xa7 | xa8 | xa9 | xaa | xab | xac | xad | xae | xaf | xb0 | xb1 | xb2 | xb3 | xb4 | xb5 | xb6 | xb7 | xb8 => Gt
+  | xb9 => Eq
+  | _ => Lt
+  end.
+Definition compare_byte_xba (b : byte) :=
+  match b with
+  | x00 | x01 | x02 | x03 | x04 | x05 | x06 | x07 | x08 | x09 | x0a | x0b | x0c | x0d | x0e | x0f | x10 | x11 | x12 | x13 | x14 | x15 | x16 | x17 | x18 | x19 | x1a | x1b | x1c | x1d | x1e | x1f | x20 | x21 | x22 | x23 | x24 | x25 | x26 | x27 | x28 | x29 | x2a | x2b | x2c | x2d | x2e | x2f | x30 | x31 | x32 | x33 | x34 | x35 | x36 | x37 | x38 | x39 | x3a | x3b | x3c | x3d | x3e | x3f | x40 | x41 | x42 | x43 | x44 | x45 | x46 | x47 | x48 | x49 | x4a | x4b | x4c | x4d | x4e | x4f | x50 | x51 | x52 | x53 | x54 | x55 | x56 | x57 | x58 | x59 | x5a | x5b | x5c | x5d | x5e | x5f | x60 | x61 | x62 | x63 | x64 | x65 | x66 | x67 | x68 | x69 | x6a | x6b | x6c | x6d | x6e | x6f | x70 | x71 | x72 | x73 | x74 | x75 | x76 | x77 | x78 | x79 | x7a | x7b | x7c | x7d | x7e | x7f | x80 | x81 | x82 | x83 | x84 | x85 | x86 | x87 | x88 | x89 | x8a | x8b | x8c | x8d | x8e | x8f | x90 | x91 | x92 | x93 | x94 | x95 | x96 | x97 | x98 | x99 | x9a | x9b | x9c | x9d | x9e | x9f | xa0 | xa1 | xa2 | xa3 | xa4 | xa5 | xa6 | xa7 | xa8 | xa9 | xaa | xab | xac | xad | xae | xaf | xb0 | xb1 | xb2 | xb3 | xb4 | xb5 | xb6 | xb7 | xb8 | xb9 => Gt
+  | xba => Eq
+  | _ => Lt
+  end.
+Definition compare_byte_xbb (b : byte) :=
+  match b with
+  | x00 | x01 | x02 | x03 | x04 | x05 | x06 | x07 | x08 | x09 | x0a | x0b | x0c | x0d | x0e | x0f | x10 | x11 | x12 | x13 | x14 | x15 | x16 | x17 | x18 | x19 | x1a | x1b | x1c | x1d | x1e | x1f | x20 | x21 | x22 | x23 | x24 | x25 | x26 | x27 | x28 | x29 | x2a | x2b | x2c | x2d | x2e | x2f | x30 | x31 | x32 | x33 | x34 | x35 | x36 | x37 | x38 | x39 | x3a | x3b | x3c | x3d | x3e | x3f | x40 | x41 | x42 | x43 | x44 | x45 | x46 | x47 | x48 | x49 | x4a | x4b | x4c | x4d | x4e | x4f | x50 | x51 | x52 | x53 | x54 | x55 | x56 | x57 | x58 | x59 | x5a | x5b | x5c | x5d | x5e | x5f | x60 | x61 | x62 | x63 | x64 | x65 | x66 | x67 | x68 | x69 | x6a | x6b | x6c | x6d | x6e | x6f | x70 | x71 | x72 | x73 | x74 | x75 | x76 | x77 | x78 | x79 | x7a | x7b | x7c | x7d | x7e | x7f | x80 | x81 | x82 | x83 | x84 | x85 | x86 | x87 | x88 | x89 | x8a | x8b | x8c | x8d | x8e | x8f | x90 | x91 | x92 | x93 | x94 | x95 | x96 | x97 | x98 | x99 | x9a | x9b | x9c | x9d | x9e | x9f | xa0 | xa1 | xa2 | xa3 | xa4 | xa5 | xa6 | xa7 | xa8 | xa9 | xaa | xab | xac | xad | xae | xaf | xb0 | xb1 | xb2 | xb3 | xb4 | xb5 | xb6 | xb7 | xb8 | xb9 | xba => Gt
+  | xbb => Eq
+  | _ => Lt
+  end.
+Definition compare_byte_xbc (b : byte) :=
+  match b with
+  | x00 | x01 | x02 | x03 | x04 | x05 | x06 | x07 | x08 | x09 | x0a | x0b | x0c | x0d | x0e | x0f | x10 | x11 | x12 | x13 | x14 | x15 | x16 | x17 | x18 | x19 | x1a | x1b | x1c | x1d | x1e | x1f | x20 | x21 | x22 | x23 | x24 | x25 | x26 | x27 | x28 | x29 | x2a | x2b | x2c | x2d | x2e | x2f | x30 | x31 | x32 | x33 | x34 | x35 | x36 | x37 | x38 | x39 | x3a | x3b | x3c | x3d | x3e | x3f | x40 | x41 | x42 | x43 | x44 | x45 | x46 | x47 | x48 | x49 | x4a | x4b | x4c | x4d | x4e | x4f | x50 | x51 | x52 | x53 | x54 | x55 | x56 | x57 | x58 | x59 | x5a | x5b | x5c | x5d | x5e | x5f | x60 | x61 | x62 | x63 | x64 | x65 | x66 | x67 | x68 | x69 | x6a | x6b | x6c | x6d | x6e | x6f | x70 | x71 | x72 | x73 | x74 | x75 | x76 | x77 | x78 | x79 | x7a | x7b | x7c | x7d | x7e | x7f | x80 | x81 | x82 | x83 | x84 | x85 | x86 | x87 | x88 | x89 | x8a | x8b | x8c | x8d | x8e | x8f | x90 | x91 | x92 | x93 | x94 | x95 | x96 | x97 | x98 | x99 | x9a | x9b | x9c | x9d | x9e | x9f | xa0 | xa1 | xa2 | xa3 | xa4 | xa5 | xa6 | xa7 | xa8 | xa9 | xaa | xab | xac | xad | xae | xaf | xb0 | xb1 | xb2 | xb3 | xb4 | xb5 | xb6 | xb7 | xb8 | xb9 | xba | xbb => Gt
+  | xbc => Eq
+  | _ => Lt
+  end.
+Definition compare_byte_xbd (b : byte) :=
+  match b with
+  | x00 | x01 | x02 | x03 | x04 | x05 | x06 | x07 | x08 | x09 | x0a | x0b | x0c | x0d | x0e | x0f | x10 | x11 | x12 | x13 | x14 | x15 | x16 | x17 | x18 | x19 | x1a | x1b | x1c | x1d | x1e | x1f | x20 | x21 | x22 | x23 | x24 | x25 | x26 | x27 | x28 | x29 | x2a | x2b | x2c | x2d | x2e | x2f | x30 | x31 | x32 | x33 | x34 | x35 | x36 | x37 | x38 | x39 | x3a | x3b | x3c | x3d | x3e | x3f | x40 | x41 | x42 | x43 | x44 | x45 | x46 | x47 | x48 | x49 | x4a | x4b | x4c | x4d | x4e | x4f | x50 | x51 | x52 | x53 | x54 | x55 | x56 | x57 | x58 | x59 | x5a | x5b | x5c | x5d | x5e | x5f | x60 | x61 | x62 | x63 | x64 | x65 | x66 | x67 | x68 | x69 | x6a | x6b | x6c | x6d | x6e | x6f | x70 | x71 | x72 | x73 | x74 | x75 | x76 | x77 | x78 | x79 | x7a | x7b | x7c | x7d | x7e | x7f | x80 | x81 | x82 | x83 | x84 | x85 | x86 | x87 | x88 | x89 | x8a | x8b | x8c | x8d | x8e | x8f | x90 | x91 | x92 | x93 | x94 | x95 | x96 | x97 | x98 | x99 | x9a | x9b | x9c | x9d | x9e | x9f | xa0 | xa1 | xa2 | xa3 | xa4 | xa5 | xa6 | xa7 | xa8 | xa9 | xaa | xab | xac | xad | xae | xaf | xb0 | xb1 | xb2 | xb3 | xb4 | xb5 | xb6 | xb7 | xb8 | xb9 | xba | xbb | xbc => Gt
+  | xbd => Eq
+  | _ => Lt
+  end.
+Definition compare_byte_xbe (b : byte) :=
+  match b with
+  | x00 | x01 | x02 | x03 | x04 | x05 | x06 | x07 | x08 | x09 | x0a | x0b | x0c | x0d | x0e | x0f | x10 | x11 | x12 | x13 | x14 | x15 | x16 | x17 | x18 | x19 | x1a | x1b | x1c | x1d | x1e | x1f | x20 | x21 | x22 | x23 | x24 | x25 | x26 | x27 | x28 | x29 | x2a | x2b | x2c | x2d | x2e | x2f | x30 | x31 | x32 | x33 | x34 | x35 | x36 | x37 | x38 | x39 | x3a | x3b | x3c | x3d | x3e | x3f | x40 | x41 | x42 | x43 | x44 | x45 | x46 | x47 | x48 | x49 | x4a | x4b | x4c | x4d | x4e | x4f | x50 | x51 | x52 | x53 | x54 | x55 | x56 | x57 | x58 | x59 | x5a | x5b | x5c | x5d | x5e | x5f | x60 | x61 | x62 | x63 | x64 | x65 | x66 | x67 | x68 | x69 | x6a | x6b | x6c | x6d | x6e | x6f | x70 | x71 | x72 | x73 | x74 | x75 | x76 | x77 | x78 | x79 | x7a | x7b | x7c | x7d | x7e | x7f | x80 | x81 | x82 | x83 | x84 | x85 | x86 | x87 | x88 | x89 | x8a | x8b | x8c | x8d | x8e | x8f | x90 | x91 | x92 | x93 | x94 | x95 | x96 | x97 | x98 | x99 | x9a | x9b | x9c | x9d | x9e | x9f | xa0 | xa1 | xa2 | xa3 | xa4 | xa5 | xa6 | xa7 | xa8 | xa9 | xaa | xab | xac | xad | xae | xaf | xb0 | xb1 | xb2 | xb3 | xb4 | xb5 | xb6 | xb7 | xb8 | xb9 | xba | xbb | xbc | xbd => Gt
+  | xbe => Eq
+  | _ => Lt
+  end.
+Definition compare_byte_xbf (b : byte) :=
+  match b with
+  | x00 | x01 | x02 | x03 | x04 | x05 | x06 | x07 | x08 | x09 | x0a | x0b | x0c | x0d | x0e | x0f | x10 | x11 | x12 | x13 | x14 | x15 | x16 | x17 | x18 | x19 | x1a | x1b | x1c | x1d | x1e | x1f | x20 | x21 | x22 | x23 | x24 | x25 | x26 | x27 | x28 | x29 | x2a | x2b | x2c | x2d | x2e | x2f | x30 | x31 | x32 | x33 | x34 | x35 | x36 | x37 | x38 | x39 | x3a | x3b | x3c | x3d | x3e | x3f | x40 | x41 | x42 | x43 | x44 | x45 | x46 | x47 | x48 | x49 | x4a | x4b | x4c | x4d | x4e | x4f | x50 | x51 | x52 | x53 | x54 | x55 | x56 | x57 | x58 | x59 | x5a | x5b | x5c | x5d | x5e | x5f | x60 | x61 | x62 | x63 | x64 | x65 | x66 | x67 | x68 | x69 | x6a | x6b | x6c | x6d | x6e | x6f | x70 | x71 | x72 | x73 | x74 | x75 | x76 | x77 | x78 | x79 | x7a | x7b | x7c | x7d | x7e | x7f | x80 | x81 | x82 | x83 | x84 | x85 | x86 | x87 | x88 | x89 | x8a | x8b | x8c | x8d | x8e | x8f | x90 | x91 | x92 | x93 | x94 | x95 | x96 | x97 | x98 | x99 | x9a | x9b | x9c | x9d | x9e | x9f | xa0 | xa1 | xa2 | xa3 | xa4 | xa5 | xa6 | xa7 | xa8 | xa9 | xaa | xab | xac | xad | xae | xaf | xb0 | xb1 | xb2 | xb3 | xb4 | xb5 | xb6 | xb7 | xb8 | xb9 | xba | xbb | xbc | xbd | xbe => Gt
+  | xbf => Eq
+  | _ => Lt
+  end.
+Definition compare_byte_xc0 (b : byte) :=
+  match b with
+  | x00 | x01 | x02 | x03 | x04 | x05 | x06 | x07 | x08 | x09 | x0a | x0b | x0c | x0d | x0e | x0f | x10 | x11 | x12 | x13 | x14 | x15 | x16 | x17 | x18 | x19 | x1a | x1b | x1c | x1d | x1e | x1f | x20 | x21 | x22 | x23 | x24 | x25 | x26 | x27 | x28 | x29 | x2a | x2b | x2c | x2d | x2e | x2f | x30 | x31 | x32 | x33 | x34 | x35 | x36 | x37 | x38 | x39 | x3a | x3b | x3c | x3d | x3e | x3f | x40 | x41 | x42 | x43 | x44 | x45 | x46 | x47 | x48 | x49 | x4a | x4b | x4c | x4d | x4e | x4f | x50 | x51 | x52 | x53 | x54 | x55 | x56 | x57 | x58 | x59 | x5a | x5b | x5c | x5d | x5e | x5f | x60 | x61 | x62 | x63 | x64 | x65 | x66 | x67 | x68 | x69 | x6a | x6b | x6c | x6d | x6e | x6f | x70 | x71 | x72 | x73 | x74 | x75 | x76 | x77 | x78 | x79 | x7a | x7b | x7c | x7d | x7e | x7f | x80 | x81 | x82 | x83 | x84 | x85 | x86 | x87 | x88 | x89 | x8a | x8b | x8c | x8d | x8e | x8f | x90 | x91 | x92 | x93 | x94 | x95 | x96 | x97 | x98 | x99 | x9a | x9b | x9c | x9d | x9e | x9f | xa0 | xa1 | xa2 | xa3 | xa4 | xa5 | xa6 | xa7 | xa8 | xa9 | xaa | xab | xac | xad | xae | xaf | xb0 | xb1 | xb2 | xb3 | xb4 | xb5 | xb6 | xb7 | xb8 | xb9 | xba | xbb | xbc | xbd | xbe | xbf => Gt
+  | xc0 => Eq
+  | _ => Lt
+  end.
+Definition compare_byte_xc1 (b : byte) :=
+  match b with
+  | x00 | x01 | x02 | x03 | x04 | x05 | x06 | x07 | x08 | x09 | x0a | x0b | x0c | x0d | x0e | x0f | x10 | x11 | x12 | x13 | x14 | x15 | x16 | x17 | x18 | x19 | x1a | x1b | x1c | x1d | x1e | x1f | x20 | x21 | x22 | x23 | x24 | x25 | x26 | x27 | x28 | x29 | x2a | x2b | x2c | x2d | x2e | x2f | x30 | x31 | x32 | x33 | x34 | x35 | x36 | x37 | x38 | x39 | x3a | x3b | x3c | x3d | x3e | x3f | x40 | x41 | x42 | x43 | x44 | x45 | x46 | x47 | x48 | x49 | x4a | x4b | x4c | x4d | x4e | x4f | x50 | x51 | x52 | x53 | x54 | x55 | x56 | x57 | x58 | x59 | x5a | x5b | x5c | x5d | x5e | x5f | x60 | x61 | x62 | x63 | x64 | x65 | x66 | x67 | x68 | x69 | x6a | x6b | x6c | x6d | x6e | x6f | x70 | x71 | x72 | x73 | x74 | x75 | x76 | x77 | x78 | x79 | x7a | x7b | x7c | x7d | x7e | x7f | x80 | x81 | x82 | x83 | x84 | x85 | x86 | x87 | x88 | x89 | x8a | x8b | x8c | x8d | x8e | x8f | x90 | x91 | x92 | x93 | x94 | x95 | x96 | x97 | x98 | x99 | x9a | x9b | x9c | x9d | x9e | x9f | xa0 | xa1 | xa2 | xa3 | xa4 | xa5 | xa6 | xa7 | xa8 | xa9 | xaa | xab | xac | xad | xae | xaf | xb0 | xb1 | xb2 | xb3 | xb4 | xb5 | xb6 | xb7 | xb8 | xb9 | xba | xbb | xbc | xbd | xbe | xbf | xc0 => Gt
+  | xc1 => Eq
+  | _ => Lt
+  end.
+Definition compare_byte_xc2 (b : byte) :=
+  match b with
+  | x00 | x01 | x02 | x03 | x04 | x05 | x06 | x07 | x08 | x09 | x0a | x0b | x0c | x0d | x0e | x0f | x10 | x11 | x12 | x13 | x14 | x15 | x16 | x17 | x18 | x19 | x1a | x1b | x1c | x1d | x1e | x1f | x20 | x21 | x22 | x23 | x24 | x25 | x26 | x27 | x28 | x29 | x2a | x2b | x2c | x2d | x2e | x2f | x30 | x31 | x32 | x33 | x34 | x35 | x36 | x37 | x38 | x39 | x3a | x3b | x3c | x3d | x3e | x3f | x40 | x41 | x42 | x43 | x44 | x45 | x46 | x47 | x48 | x49 | x4a | x4b | x4c | x4d | x4e | x4f | x50 | x51 | x52 | x53 | x54 | x55 | x56 | x57 | x58 | x59 | x5a | x5b | x5c | x5d | x5e | x5f | x60 | x61 | x62 | x63 | x64 | x65 | x66 | x67 | x68 | x69 | x6a | x6b | x6c | x6d | x6e | x6f | x70 | x71 | x72 | x73 | x74 | x75 | x76 | x77 | x78 | x79 | x7a | x7b | x7c | x7d | x7e | x7f | x80 | x81 | x82 | x83 | x84 | x85 | x86 | x87 | x88 | x89 | x8a | x8b | x8c | x8d | x8e | x8f | x90 | x91 | x92 | x93 | x94 | x95 | x96 | x97 | x98 | x99 | x9a | x9b | x9c | x9d | x9e | x9f | xa0 | xa1 | xa2 | xa3 | xa4 | xa5 | xa6 | xa7 | xa8 | xa9 | xaa | xab | xac | xad | xae | xaf | xb0 | xb1 | xb2 | xb3 | xb4 | xb5 | xb6 | xb7 | xb8 | xb9 | xba | xbb | xbc | xbd | xbe | xbf | xc0 | xc1 => Gt
+  | xc2 => Eq
+  | _ => Lt
+  end.
+Definition compare_byte_xc3 (b : byte) :=
+  match b with
+  | x00 | x01 | x02 | x03 | x04 | x05 | x06 | x07 | x08 | x09 | x0a | x0b | x0c | x0d | x0e | x0f | x10 | x11 | x12 | x13 | x14 | x15 | x16 | x17 | x18 | x19 | x1a | x1b | x1c | x1d | x1e | x1f | x20 | x21 | x22 | x23 | x24 | x25 | x26 | x27 | x28 | x29 | x2a | x2b | x2c | x2d | x2e | x2f | x30 | x31 | x32 | x33 | x34 | x35 | x36 | x37 | x38 | x39 | x3a | x3b | x3c | x3d | x3e | x3f | x40 | x41 | x42 | x43 | x44 | x45 | x46 | x47 | x48 | x49 | x4a | x4b | x4c | x4d | x4e | x4f | x50 | x51 | x52 | x53 | x54 | x55 | x56 | x57 | x58 | x59 | x5a | x5b | x5c | x5d | x5e | x5f | x60 | x61 | x62 | x63 | x64 | x65 | x66 | x67 | x68 | x69 | x6a | x6b | x6c | x6d | x6e | x6f | x70 | x71 | x72 | x73 | x74 | x75 | x76 | x77 | x78 | x79 | x7a | x7b | x7c | x7d | x7e | x7f | x80 | x81 | x82 | x83 | x84 | x85 | x86 | x87 | x88 | x89 | x8a | x8b | x8c | x8d | x8e | x8f | x90 | x91 | x92 | x93 | x94 | x95 | x96 | x97 | x98 | x99 | x9a | x9b | x9c | x9d | x9e | x9f | xa0 | xa1 | xa2 | xa3 | xa4 | xa5 | xa6 | xa7 | xa8 | xa9 | xaa | xab | xac | xad | xae | xaf | xb0 | xb1 | xb2 | xb3 | xb4 | xb5 | xb6 | xb7 | xb8 | xb9 | xba | xbb | xbc | xbd | xbe | xbf | xc0 | xc1 | xc2 => Gt
+  | xc3 => Eq
+  | _ => Lt
+  end.
+Definition compare_byte_xc4 (b : byte) :=
+  match b with
+  | x00 | x01 | x02 | x03 | x04 | x05 | x06 | x07 | x08 | x09 | x0a | x0b | x0c | x0d | x0e | x0f | x10 | x11 | x12 | x13 | x14 | x15 | x16 | x17 | x18 | x19 | x1a | x1b | x1c | x1d | x1e | x1f | x20 | x21 | x22 | x23 | x24 | x25 | x26 | x27 | x28 | x29 | x2a | x2b | x2c | x2d | x2e | x2f | x30 | x31 | x32 | x33 | x34 | x35 | x36 | x37 | x38 | x39 | x3a | x3b | x3c | x3d | x3e | x3f | x40 | x41 | x42 | x43 | x44 | x45 | x46 | x47 | x48 | x49 | x4a | x4b | x4c | x4d | x4e | x4f | x50 | x51 | x52 | x53 | x54 | x55 | x56 | x57 | x58 | x59 | x5a | x5b | x5c | x5d | x5e | x5f | x60 | x61 | x62 | x63 | x64 | x65 | x66 | x67 | x68 | x69 | x6a | x6b | x6c | x6d | x6e | x6f | x70 | x71 | x72 | x73 | x74 | x75 | x76 | x77 | x78 | x79 | x7a | x7b | x7c | x7d | x7e | x7f | x80 | x81 | x82 | x83 | x84 | x85 | x86 | x87 | x88 | x89 | x8a | x8b | x8c | x8d | x8e | x8f | x90 | x91 | x92 | x93 | x94 | x95 | x96 | x97 | x98 | x99 | x9a | x9b | x9c | x9d | x9e | x9f | xa0 | xa1 | xa2 | xa3 | xa4 | xa5 | xa6 | xa7 | xa8 | xa9 | xaa | xab | xac | xad | xae | xaf | xb0 | xb1 | xb2 | xb3 | xb4 | xb5 | xb6 | xb7 | xb8 | xb9 | xba | xbb | xbc | xbd | xbe | xbf | xc0 | xc1 | xc2 | xc3 => Gt
+  | xc4 => Eq
+  | _ => Lt
+  end.
+Definition compare_byte_xc5 (b : byte) :=
+  match b with
+  | x00 | x01 | x02 | x03 | x04 | x05 | x06 | x07 | x08 | x09 | x0a | x0b | x0c | x0d | x0e | x0f | x10 | x11 | x12 | x13 | x14 | x15 | x16 | x17 | x18 | x19 | x1a | x1b | x1c | x1d | x1e | x1f | x20 | x21 | x22 | x23 | x24 | x25 | x26 | x27 | x28 | x29 | x2a | x2b | x2c | x2d | x2e | x2f | x30 | x31 | x32 | x33 | x34 | x35 | x36 | x37 | x38 | x39 | x3a | x3b | x3c | x3d | x3e | x3f | x40 | x41 | x42 | x43 | x44 | x45 | x46 | x47 | x48 | x49 | x4a | x4b | x4c | x4d | x4e | x4f | x50 | x51 | x52 | x53 | x54 | x55 | x56 | x57 | x58 | x59 | x5a | x5b | x5c | x5d | x5e | x5f | x60 | x61 | x62 | x63 | x64 | x65 | x66 | x67 | x68 | x69 | x6a | x6b | x6c | x6d | x6e | x6f | x70 | x71 | x72 | x73 | x74 | x75 | x76 | x77 | x78 | x79 | x7a | x7b | x7c | x7d | x7e | x7f | x80 | x81 | x82 | x83 | x84 | x85 | x86 | x87 | x88 | x89 | x8a | x8b | x8c | x8d | x8e | x8f | x90 | x91 | x92 | x93 | x94 | x95 | x96 | x97 | x98 | x99 | x9a | x9b | x9c | x9d | x9e | x9f | xa0 | xa1 | xa2 | xa3 | xa4 | xa5 | xa6 | xa7 | xa8 | xa9 | xaa | xab | xac | xad | xae | xaf | xb0 | xb1 | xb2 | xb3 | xb4 | xb5 | xb6 | xb7 | xb8 | xb9 | xba | xbb | xbc | xbd | xbe | xbf | xc0 | xc1 | xc2 | xc3 | xc4 => Gt
+  | xc5 => Eq
+  | _ => Lt
+  end.
+Definition compare_byte_xc6 (b : byte) :=
+  match b with
+  | x00 | x01 | x02 | x03 | x04 | x05 | x06 | x07 | x08 | x09 | x0a | x0b | x0c | x0d | x0e | x0f | x10 | x11 | x12 | x13 | x14 | x15 | x16 | x17 | x18 | x19 | x1a | x1b | x1c | x1d | x1e | x1f | x20 | x21 | x22 | x23 | x24 | x25 | x26 | x27 | x28 | x29 | x2a | x2b | x2c | x2d | x2e | x2f | x30 | x31 | x32 | x33 | x34 | x35 | x36 | x37 | x38 | x39 | x3a | x3b | x3c | x3d | x3e | x3f | x40 | x41 | x42 | x43 | x44 | x45 | x46 | x47 | x48 | x49 | x4a | x4b | x4c | x4d | x4e | x4f | x50 | x51 | x52 | x53 | x54 | x55 | x56 | x57 | x58 | x59 | x5a | x5b | x5c | x5d | x5e | x5f | x60 | x61 | x62 | x63 | x64 | x65 | x66 | x67 | x68 | x69 | x6a | x6b | x6c | x6d | x6e | x6f | x70 | x71 | x72 | x73 | x74 | x75 | x76 | x77 | x78 | x79 | x7a | x7b | x7c | x7d | x7e | x7f | x80 | x81 | x82 | x83 | x84 | x85 | x86 | x87 | x88 | x89 | x8a | x8b | x8c | x8d | x8e | x8f | x90 | x91 | x92 | x93 | x94 | x95 | x96 | x97 | x98 | x99 | x9a | x9b | x9c | x9d | x9e | x9f | xa0 | xa1 | xa2 | xa3 | xa4 | xa5 | xa6 | xa7 | xa8 | xa9 | xaa | xab | xac | xad | xae | xaf | xb0 | xb1 | xb2 | xb3 | xb4 | xb5 | xb6 | xb7 | xb8 | xb9 | xba | xbb | xbc | xbd | xbe | xbf | xc0 | xc1 | xc2 | xc3 | xc4 | xc5 => Gt
+  | xc6 => Eq
+  | _ => Lt
+  end.
+Definition compare_byte_xc7 (b : byte) :=
+  match b with
+  | x00 | x01 | x02 | x03 | x04 | x05 | x06 | x07 | x08 | x09 | x0a | x0b | x0c | x0d | x0e | x0f | x10 | x11 | x12 | x13 | x14 | x15 | x16 | x17 | x18 | x19 | x1a | x1b | x1c | x1d | x1e | x1f | x20 | x21 | x22 | x23 | x24 | x25 | x26 | x27 | x28 | x29 | x2a | x2b | x2c | x2d | x2e | x2f | x30 | x31 | x32 | x33 | x34 | x35 | x36 | x37 | x38 | x39 | x3a | x3b | x3c | x3d | x3e | x3f | x40 | x41 | x42 | x43 | x44 | x45 | x46 | x47 | x48 | x49 | x4a | x4b | x4c | x4d | x4e | x4f | x50 | x51 | x52 | x53 | x54 | x55 | x56 | x57 | x58 | x59 | x5a | x5b | x5c | x5d | x5e | x5f | x60 | x61 | x62 | x63 | x64 | x65 | x66 | x67 | x68 | x69 | x6a | x6b | x6c | x6d | x6e | x6f | x70 | x71 | x72 | x73 | x74 | x75 | x76 | x77 | x78 | x79 | x7a | x7b | x7c | x7d | x7e | x7f | x80 | x81 | x82 | x83 | x84 | x85 | x86 | x87 | x88 | x89 | x8a | x8b | x8c | x8d | x8e | x8f | x90 | x91 | x92 | x93 | x94 | x95 | x96 | x97 | x98 | x99 | x9a | x9b | x9c | x9d | x9e | x9f | xa0 | xa1 | xa2 | xa3 | xa4 | xa5 | xa6 | xa7 | xa8 | xa9 | xaa | xab | xac | xad | xae | xaf | xb0 | xb1 | xb2 | xb3 | xb4 | xb5 | xb6 | xb7 | xb8 | xb9 | xba | xbb | xbc | xbd | xbe | xbf | xc0 | xc1 | xc2 | xc3 | xc4 | xc5 | xc6 => Gt
+  | xc7 => Eq
+  | _ => Lt
+  end.
+Definition compare_byte_xc8 (b : byte) :=
+  match b with
+  | x00 | x01 | x02 | x03 | x04 | x05 | x06 | x07 | x08 | x09 | x0a | x0b | x0c | x0d | x0e | x0f | x10 | x11 | x12 | x13 | x14 | x15 | x16 | x17 | x18 | x19 | x1a | x1b | x1c | x1d | x1e | x1f | x20 | x21 | x22 | x23 | x24 | x25 | x26 | x27 | x28 | x29 | x2a | x2b | x2c | x2d | x2e | x2f | x30 | x31 | x32 | x33 | x34 | x35 | x36 | x37 | x38 | x39 | x3a | x3b | x3c | x3d | x3e | x3f | x40 | x41 | x42 | x43 | x44 | x45 | x46 | x47 | x48 | x49 | x4a | x4b | x4c | x4d | x4e | x4f | x50 | x51 | x52 | x53 | x54 | x55 | x56 | x57 | x58 | x59 | x5a | x5b | x5c | x5d | x5e | x5f | x60 | x61 | x62 | x63 | x64 | x65 | x66 | x67 | x68 | x69 | x6a | x6b | x6c | x6d | x6e | x6f | x70 | x71 | x72 | x73 | x74 | x75 | x76 | x77 | x78 | x79 | x7a | x7b | x7c | x7d | x7e | x7f | x80 | x81 | x82 | x83 | x84 | x85 | x86 | x87 | x88 | x89 | x8a | x8b | x8c | x8d | x8e | x8f | x90 | x91 | x92 | x93 | x94 | x95 | x96 | x97 | x98 | x99 | x9a | x9b | x9c | x9d | x9e | x9f | xa0 | xa1 | xa2 | xa3 | xa4 | xa5 | xa6 | xa7 | xa8 | xa9 | xaa | xab | xac | xad | xae | xaf | xb0 | xb1 | xb2 | xb3 | xb4 | xb5 | xb6 | xb7 | xb8 | xb9 | xba | xbb | xbc | xbd | xbe | xbf | xc0 | xc1 | xc2 | xc3 | xc4 | xc5 | xc6 | xc7 => Gt
+  | xc8 => Eq
+  | _ => Lt
+  end.
+Definition compare_byte_xc9 (b : byte) :=
+  match b with
+  | x00 | x01 | x02 | x03 | x04 | x05 | x06 | x07 | x08 | x09 | x0a | x0b | x0c | x0d | x0e | x0f | x10 | x11 | x12 | x13 | x14 | x15 | x16 | x17 | x18 | x19 | x1a | x1b | x1c | x1d | x1e | x1f | x20 | x21 | x22 | x23 | x24 | x25 | x26 | x27 | x28 | x29 | x2a | x2b | x2c | x2d | x2e | x2f | x30 | x31 | x32 | x33 | x34 | x35 | x36 | x37 | x38 | x39 | x3a | x3b | x3c | x3d | x3e | x3f | x40 | x41 | x42 | x43 | x44 | x45 | x46 | x47 | x48 | x49 | x4a | x4b | x4c | x4d | x4e | x4f | x50 | x51 | x52 | x53 | x54 | x55 | x56 | x57 | x58 | x59 | x5a | x5b | x5c | x5d | x5e | x5f | x60 | x61 | x62 | x63 | x64 | x65 | x66 | x67 | x68 | x69 | x6a | x6b | x6c | x6d | x6e | x6f | x70 | x71 | x72 | x73 | x74 | x75 | x76 | x77 | x78 | x79 | x7a | x7b | x7c | x7d | x7e | x7f | x80 | x81 | x82 | x83 | x84 | x85 | x86 | x87 | x88 | x89 | x8a | x8b | x8c | x8d | x8e | x8f | x90 | x91 | x92 | x93 | x94 | x95 | x96 | x97 | x98 | x99 | x9a | x9b | x9c | x9d | x9e | x9f | xa0 | xa1 | xa2 | xa3 | xa4 | xa5 | xa6 | xa7 | xa8 | xa9 | xaa | xab | xac | xad | xae | xaf | xb0 | xb1 | xb2 | xb3 | xb4 | xb5 | xb6 | xb7 | xb8 | xb9 | xba | xbb | xbc | xbd | xbe | xbf | xc0 | xc1 | xc2 | xc3 | xc4 | xc5 | xc6 | xc7 | xc8 => Gt
+  | xc9 => Eq
+  | _ => Lt
+  end.
+Definition compare_byte_xca (b : byte) :=
+  match b with
+  | x00 | x01 | x02 | x03 | x04 | x05 | x06 | x07 | x08 | x09 | x0a | x0b | x0c | x0d | x0e | x0f | x10 | x11 | x12 | x13 | x14 | x15 | x16 | x17 | x18 | x19 | x1a | x1b | x1c | x1d | x1e | x1f | x20 | x21 | x22 | x23 | x24 | x25 | x26 | x27 | x28 | x29 | x2a | x2b | x2c | x2d | x2e | x2f | x30 | x31 | x32 | x33 | x34 | x35 | x36 | x37 | x38 | x39 | x3a | x3b | x3c | x3d | x3e | x3f | x40 | x41 | x42 | x43 | x44 | x45 | x46 | x47 | x48 | x49 | x4a | x4b | x4c | x4d | x4e | x4f | x50 | x51 | x52 | x53 | x54 | x55 | x56 | x57 | x58 | x59 | x5a | x5b | x5c | x5d | x5e | x5f | x60 | x61 | x62 | x63 | x64 | x65 | x66 | x67 | x68 | x69 | x6a | x6b | x6c | x6d | x6e | x6f | x70 | x71 | x72 | x73 | x74 | x75 | x76 | x77 | x78 | x79 | x7a | x7b | x7c | x7d | x7e | x7f | x80 | x81 | x82 | x83 | x84 | x85 | x86 | x87 | x88 | x89 | x8a | x8b | x8c | x8d | x8e | x8f | x90 | x91 | x92 | x93 | x94 | x95 | x96 | x97 | x98 | x99 | x9a | x9b | x9c | x9d | x9e | x9f | xa0 | xa1 | xa2 | xa3 | xa4 | xa5 | xa6 | xa7 | xa8 | xa9 | xaa | xab | xac | xad | xae | xaf | xb0 | xb1 | xb2 | xb3 | xb4 | xb5 | xb6 | xb7 | xb8 | xb9 | xba | xbb | xbc | xbd | xbe | xbf | xc0 | xc1 | xc2 | xc3 | xc4 | xc5 | xc6 | xc7 | xc8 | xc9 => Gt
+  | xca => Eq
+  | _ => Lt
+  end.
+Definition compare_byte_xcb (b : byte) :=
+  match b with
+  | x00 | x01 | x02 | x03 | x04 | x05 | x06 | x07 | x08 | x09 | x0a | x0b | x0c | x0d | x0e | x0f | x10 | x11 | x12 | x13 | x14 | x15 | x16 | x17 | x18 | x19 | x1a | x1b | x1c | x1d | x1e | x1f | x20 | x21 | x22 | x23 | x24 | x25 | x26 | x27 | x28 | x29 | x2a | x2b | x2c | x2d | x2e | x2f | x30 | x31 | x32 | x33 | x34 | x35 | x36 | x37 | x38 | x39 | x3a | x3b | x3c | x3d | x3e | x3f | x40 | x41 | x42 | x43 | x44 | x45 | x46 | x47 | x48 | x49 | x4a | x4b | x4c | x4d | x4e | x4f | x50 | x51 | x52 | x53 | x54 | x55 | x56 | x57 | x58 | x59 | x5a | x5b | x5c | x5d | x5e | x5f | x60 | x61 | x62 | x63 | x64 | x65 | x66 | x67 | x68 | x69 | x6a | x6b | x6c | x6d | x6e | x6f | x70 | x71 | x72 | x73 | x74 | x75 | x76 | x77 | x78 | x79 | x7a | x7b | x7c | x7d | x7e | x7f | x80 | x81 | x82 | x83 | x84 | x85 | x86 | x87 | x88 | x89 | x8a | x8b | x8c | x8d | x8e | x8f | x90 | x91 | x92 | x93 | x94 | x95 | x96 | x97 | x98 | x99 | x9a | x9b | x9c | x9d | x9e | x9f | xa0 | xa1 | xa2 | xa3 | xa4 | xa5 | xa6 | xa7 | xa8 | xa9 | xaa | xab | xac | xad | xae | xaf | xb0 | xb1 | xb2 | xb3 | xb4 | xb5 | xb6 | xb7 | xb8 | xb9 | xba | xbb | xbc | xbd | xbe | xbf | xc0 | xc1 | xc2 | xc3 | xc4 | xc5 | xc6 | xc7 | xc8 | xc9 | xca => Gt
+  | xcb => Eq
+  | _ => Lt
+  end.
+Definition compare_byte_xcc (b : byte) :=
+  match b with
+  | x00 | x01 | x02 | x03 | x04 | x05 | x06 | x07 | x08 | x09 | x0a | x0b | x0c | x0d | x0e | x0f | x10 | x11 | x12 | x13 | x14 | x15 | x16 | x17 | x18 | x19 | x1a | x1b | x1c | x1d | x1e | x1f | x20 | x21 | x22 | x23 | x24 | x25 | x26 | x27 | x28 | x29 | x2a | x2b | x2c | x2d | x2e | x2f | x30 | x31 | x32 | x33 | x34 | x35 | x36 | x37 | x38 | x39 | x3a | x3b | x3c | x3d | x3e | x3f | x40 | x41 | x42 | x43 | x44 | x45 | x46 | x47 | x48 | x49 | x4a | x4b | x4c | x4d | x4e | x4f | x50 | x51 | x52 | x53 | x54 | x55 | x56 | x57 | x58 | x59 | x5a | x5b | x5c | x5d | x5e | x5f | x60 | x61 | x62 | x63 | x64 | x65 | x66 | x67 | x68 | x69 | x6a | x6b | x6c | x6d | x6e | x6f | x70 | x71 | x72 | x73 | x74 | x75 | x76 | x77 | x78 | x79 | x7a | x7b | x7c | x7d | x7e | x7f | x80 | x81 | x82 | x83 | x84 | x85 | x86 | x87 | x88 | x89 | x8a | x8b | x8c | x8d | x8e | x8f | x90 | x91 | x92 | x93 | x94 | x95 | x96 | x97 | x98 | x99 | x9a | x9b | x9c | x9d | x9e | x9f | xa0 | xa1 | xa2 | xa3 | xa4 | xa5 | xa6 | xa7 | xa8 | xa9 | xaa | xab | xac | xad | xae | xaf | xb0 | xb1 | xb2 | xb3 | xb4 | xb5 | xb6 | xb7 | xb8 | xb9 | xba | xbb | xbc | xbd | xbe | xbf | xc0 | xc1 | xc2 | xc3 | xc4 | xc5 | xc6 | xc7 | xc8 | xc9 | xca | xcb => Gt
+  | xcc => Eq
+  | _ => Lt
+  end.
+Definition compare_byte_xcd (b : byte) :=
+  match b with
+  | x00 | x01 | x02 | x03 | x04 | x05 | x06 | x07 | x08 | x09 | x0a | x0b | x0c | x0d | x0e | x0f | x10 | x11 | x12 | x13 | x14 | x15 | x16 | x17 | x18 | x19 | x1a | x1b | x1c | x1d | x1e | x1f | x20 | x21 | x22 | x23 | x24 | x25 | x26 | x27 | x28 | x29 | x2a | x2b | x2c | x2d | x2e | x2f | x30 | x31 | x32 | x33 | x34 | x35 | x36 | x37 | x38 | x39 | x3a | x3b | x3c | x3d | x3e | x3f | x40 | x41 | x42 | x43 | x44 | x45 | x46 | x47 | x48 | x49 | x4a | x4b | x4c | x4d | x4e | x4f | x50 | x51 | x52 | x53 | x54 | x55 | x56 | x57 | x58 | x59 | x5a | x5b | x5c | x5d | x5e | x5f | x60 | x61 | x62 | x63 | x64 | x65 | x66 | x67 | x68 | x69 | x6a | x6b | x6c | x6d | x6e | x6f | x70 | x71 | x72 | x73 | x74 | x75 | x76 | x77 | x78 | x79 | x7a | x7b | x7c | x7d | x7e | x7f | x80 | x81 | x82 | x83 | x84 | x85 | x86 | x87 | x88 | x89 | x8a | x8b | x8c | x8d | x8e | x8f | x90 | x91 | x92 | x93 | x94 | x95 | x96 | x97 | x98 | x99 | x9a | x9b | x9c | x9d | x9e | x9f | xa0 | xa1 | xa2 | xa3 | xa4 | xa5 | xa6 | xa7 | xa8 | xa9 | xaa | xab | xac | xad | xae | xaf | xb0 | xb1 | xb2 | xb3 | xb4 | xb5 | xb6 | xb7 | xb8 | xb9 | xba | xbb | xbc | xbd | xbe | xbf | xc0 | xc1 | xc2 | xc3 | xc4 | xc5 | xc6 | xc7 | xc8 | xc9 | xca | xcb | xcc => Gt
+  | xcd => Eq
+  | _ => Lt
+  end.
+Definition compare_byte_xce (b : byte) :=
+  match b with
+  | x00 | x01 | x02 | x03 | x04 | x05 | x06 | x07 | x08 | x09 | x0a | x0b | x0c | x0d | x0e | x0f | x10 | x11 | x12 | x13 | x14 | x15 | x16 | x17 | x18 | x19 | x1a | x1b | x1c | x1d | x1e | x1f | x20 | x21 | x22 | x23 | x24 | x25 | x26 | x27 | x28 | x29 | x2a | x2b | x2c | x2d | x2e | x2f | x30 | x31 | x32 | x33 | x34 | x35 | x36 | x37 | x38 | x39 | x3a | x3b | x3c | x3d | x3e | x3f | x40 | x41 | x42 | x43 | x44 | x45 | x46 | x47 | x48 | x49 | x4a | x4b | x4c | x4d | x4e | x4f | x50 | x51 | x52 | x53 | x54 | x55 | x56 | x57 | x58 | x59 | x5a | x5b | x5c | x5d | x5e | x5f | x60 | x61 | x62 | x63 | x64 | x65 | x66 | x67 | x68 | x69 | x6a | x6b | x6c | x6d | x6e | x6f | x70 | x71 | x72 | x73 | x74 | x75 | x76 | x77 | x78 | x79 | x7a | x7b | x7c | x7d | x7e | x7f | x80 | x81 | x82 | x83 | x84 | x85 | x86 | x87 | x88 | x89 | x8a | x8b | x8c | x8d | x8e | x8f | x90 | x91 | x92 | x93 | x94 | x95 | x96 | x97 | x98 | x99 | x9a | x9b | x9c | x9d | x9e | x9f | xa0 | xa1 | xa2 | xa3 | xa4 | xa5 | xa6 | xa7 | xa8 | xa9 | xaa | xab | xac | xad | xae | xaf | xb0 | xb1 | xb2 | xb3 | xb4 | xb5 | xb6 | xb7 | xb8 | xb9 | xba | xbb | xbc | xbd | xbe | xbf | xc0 | xc1 | xc2 | xc3 | xc4 | xc5 | xc6 | xc7 | xc8 | xc9 | xca | xcb | xcc | xcd => Gt
+  | xce => Eq
+  | _ => Lt
+  end.
+Definition compare_byte_xcf (b : byte) :=
+  match b with
+  | x00 | x01 | x02 | x03 | x04 | x05 | x06 | x07 | x08 | x09 | x0a | x0b | x0c | x0d | x0e | x0f | x10 | x11 | x12 | x13 | x14 | x15 | x16 | x17 | x18 | x19 | x1a | x1b | x1c | x1d | x1e | x1f | x20 | x21 | x22 | x23 | x24 | x25 | x26 | x27 | x28 | x29 | x2a | x2b | x2c | x2d | x2e | x2f | x30 | x31 | x32 | x33 | x34 | x35 | x36 | x37 | x38 | x39 | x3a | x3b | x3c | x3d | x3e | x3f | x40 | x41 | x42 | x43 | x44 | x45 | x46 | x47 | x48 | x49 | x4a | x4b | x4c | x4d | x4e | x4f | x50 | x51 | x52 | x53 | x54 | x55 | x56 | x57 | x58 | x59 | x5a | x5b | x5c | x5d | x5e | x5f | x60 | x61 | x62 | x63 | x64 | x65 | x66 | x67 | x68 | x69 | x6a | x6b | x6c | x6d | x6e | x6f | x70 | x71 | x72 | x73 | x74 | x75 | x76 | x77 | x78 | x79 | x7a | x7b | x7c | x7d | x7e | x7f | x80 | x81 | x82 | x83 | x84 | x85 | x86 | x87 | x88 | x89 | x8a | x8b | x8c | x8d | x8e | x8f | x90 | x91 | x92 | x93 | x94 | x95 | x96 | x97 | x98 | x99 | x9a | x9b | x9c | x9d | x9e | x9f | xa0 | xa1 | xa2 | xa3 | xa4 | xa5 | xa6 | xa7 | xa8 | xa9 | xaa | xab | xac | xad | xae | xaf | xb0 | xb1 | xb2 | xb3 | xb4 | xb5 | xb6 | xb7 | xb8 | xb9 | xba | xbb | xbc | xbd | xbe | xbf | xc0 | xc1 | xc2 | xc3 | xc4 | xc5 | xc6 | xc7 | xc8 | xc9 | xca | xcb | xcc | xcd | xce => Gt
+  | xcf => Eq
+  | _ => Lt
+  end.
+Definition compare_byte_xd0 (b : byte) :=
+  match b with
+  | x00 | x01 | x02 | x03 | x04 | x05 | x06 | x07 | x08 | x09 | x0a | x0b | x0c | x0d | x0e | x0f | x10 | x11 | x12 | x13 | x14 | x15 | x16 | x17 | x18 | x19 | x1a | x1b | x1c | x1d | x1e | x1f | x20 | x21 | x22 | x23 | x24 | x25 | x26 | x27 | x28 | x29 | x2a | x2b | x2c | x2d | x2e | x2f | x30 | x31 | x32 | x33 | x34 | x35 | x36 | x37 | x38 | x39 | x3a | x3b | x3c | x3d | x3e | x3f | x40 | x41 | x42 | x43 | x44 | x45 | x46 | x47 | x48 | x49 | x4a | x4b | x4c | x4d | x4e | x4f | x50 | x51 | x52 | x53 | x54 | x55 | x56 | x57 | x58 | x59 | x5a | x5b | x5c | x5d | x5e | x5f | x60 | x61 | x62 | x63 | x64 | x65 | x66 | x67 | x68 | x69 | x6a | x6b | x6c | x6d | x6e | x6f | x70 | x71 | x72 | x73 | x74 | x75 | x76 | x77 | x78 | x79 | x7a | x7b | x7c | x7d | x7e | x7f | x80 | x81 | x82 | x83 | x84 | x85 | x86 | x87 | x88 | x89 | x8a | x8b | x8c | x8d | x8e | x8f | x90 | x91 | x92 | x93 | x94 | x95 | x96 | x97 | x98 | x99 | x9a | x9b | x9c | x9d | x9e | x9f | xa0 | xa1 | xa2 | xa3 | xa4 | xa5 | xa6 | xa7 | xa8 | xa9 | xaa | xab | xac | xad | xae | xaf | xb0 | xb1 | xb2 | xb3 | xb4 | xb5 | xb6 | xb7 | xb8 | xb9 | xba | xbb | xbc | xbd | xbe | xbf | xc0 | xc1 | xc2 | xc3 | xc4 | xc5 | xc6 | xc7 | xc8 | xc9 | xca | xcb | xcc | xcd | xce | xcf => Gt
+  | xd0 => Eq
+  | _ => Lt
+  end.
+Definition compare_byte_xd1 (b : byte) :=
+  match b with
+  | x00 | x01 | x02 | x03 | x04 | x05 | x06 | x07 | x08 | x09 | x0a | x0b | x0c | x0d | x0e | x0f | x10 | x11 | x12 | x13 | x14 | x15 | x16 | x17 | x18 | x19 | x1a | x1b | x1c | x1d | x1e | x1f | x20 | x21 | x22 | x23 | x24 | x25 | x26 | x27 | x28 | x29 | x2a | x2b | x2c | x2d | x2e | x2f | x30 | x31 | x32 | x33 | x34 | x35 | x36 | x37 | x38 | x39 | x3a | x3b | x3c | x3d | x3e | x3f | x40 | x41 | x42 | x43 | x44 | x45 | x46 | x47 | x48 | x49 | x4a | x4b | x4c | x4d | x4e | x4f | x50 | x51 | x52 | x53 | x54 | x55 | x56 | x57 | x58 | x59 | x5a | x5b | x5c | x5d | x5e | x5f | x60 | x61 | x62 | x63 | x64 | x65 | x66 | x67 | x68 | x69 | x6a | x6b | x6c | x6d | x6e | x6f | x70 | x71 | x72 | x73 | x74 | x75 | x76 | x77 | x78 | x79 | x7a | x7b | x7c | x7d | x7e | x7f | x80 | x81 | x82 | x83 | x84 | x85 | x86 | x87 | x88 | x89 | x8a | x8b | x8c | x8d | x8e | x8f | x90 | x91 | x92 | x93 | x94 | x95 | x96 | x97 | x98 | x99 | x9a | x9b | x9c | x9d | x9e | x9f | xa0 | xa1 | xa2 | xa3 | xa4 | xa5 | xa6 | xa7 | xa8 | xa9 | xaa | xab | xac | xad | xae | xaf | xb0 | xb1 | xb2 | xb3 | xb4 | xb5 | xb6 | xb7 | xb8 | xb9 | xba | xbb | xbc | xbd | xbe | xbf | xc0 | xc1 | xc2 | xc3 | xc4 | xc5 | xc6 | xc7 | xc8 | xc9 | xca | xcb | xcc | xcd | xce | xcf | xd0 => Gt
+  | xd1 => Eq
+  | _ => Lt
+  end.
+Definition compare_byte_xd2 (b : byte) :=
+  match b with
+  | x00 | x01 | x02 | x03 | x04 | x05 | x06 | x07 | x08 | x09 | x0a | x0b | x0c | x0d | x0e | x0f | x10 | x11 | x12 | x13 | x14 | x15 | x16 | x17 | x18 | x19 | x1a | x1b | x1c | x1d | x1e | x1f | x20 | x21 | x22 | x23 | x24 | x25 | x26 | x27 | x28 | x29 | x2a | x2b | x2c | x2d | x2e | x2f | x30 | x31 | x32 | x33 | x34 | x35 | x36 | x37 | x38 | x39 | x3a | x3b | x3c | x3d | x3e | x3f | x40 | x41 | x42 | x43 | x44 | x45 | x46 | x47 | x48 | x49 | x4a | x4b | x4c | x4d | x4e | x4f | x50 | x51 | x52 | x53 | x54 | x55 | x56 | x57 | x58 | x59 | x5a | x5b | x5c | x5d | x5e | x5f | x60 | x61 | x62 | x63 | x64 | x65 | x66 | x67 | x68 | x69 | x6a | x6b | x6c | x6d | x6e | x6f | x70 | x71 | x72 | x73 | x74 | x75 | x76 | x77 | x78 | x79 | x7a | x7b | x7c | x7d | x7e | x7f | x80 | x81 | x82 | x83 | x84 | x85 | x86 | x87 | x88 | x89 | x8a | x8b | x8c | x8d | x8e | x8f | x90 | x91 | x92 | x93 | x94 | x95 | x96 | x97 | x98 | x99 | x9a | x9b | x9c | x9d | x9e | x9f | xa0 | xa1 | xa2 | xa3 | xa4 | xa5 | xa6 | xa7 | xa8 | xa9 | xaa | xab | xac | xad | xae | xaf | xb0 | xb1 | xb2 | xb3 | xb4 | xb5 | xb6 | xb7 | xb8 | xb9 | xba | xbb | xbc | xbd | xbe | xbf | xc0 | xc1 | xc2 | xc3 | xc4 | xc5 | xc6 | xc7 | xc8 | xc9 | xca | xcb | xcc | xcd | xce | xcf | xd0 | xd1 => Gt
+  | xd2 => Eq
+  | _ => Lt
+  end.
+Definition compare_byte_xd3 (b : byte) :=
+  match b with
+  | x00 | x01 | x02 | x03 | x04 | x05 | x06 | x07 | x08 | x09 | x0a | x0b | x0c | x0d | x0e | x0f | x10 | x11 | x12 | x13 | x14 | x15 | x16 | x17 | x18 | x19 | x1a | x1b | x1c | x1d | x1e | x1f | x20 | x21 | x22 | x23 | x24 | x25 | x26 | x27 | x28 | x29 | x2a | x2b | x2c | x2d | x2e | x2f | x30 | x31 | x32 | x33 | x34 | x35 | x36 | x37 | x38 | x39 | x3a | x3b | x3c | x3d | x3e | x3f | x40 | x41 | x42 | x43 | x44 | x45 | x46 | x47 | x48 | x49 | x4a | x4b | x4c | x4d | x4e | x4f | x50 | x51 | x52 | x53 | x54 | x55 | x56 | x57 | x58 | x59 | x5a | x5b | x5c | x5d | x5e | x5f | x60 | x61 | x62 | x63 | x64 | x65 | x66 | x67 | x68 | x69 | x6a | x6b | x6c | x6d | x6e | x6f | x70 | x71 | x72 | x73 | x74 | x75 | x76 | x77 | x78 | x79 | x7a | x7b | x7c | x7d | x7e | x7f | x80 | x81 | x82 | x83 | x84 | x85 | x86 | x87 | x88 | x89 | x8a | x8b | x8c | x8d | x8e | x8f | x90 | x91 | x92 | x93 | x94 | x95 | x96 | x97 | x98 | x99 | x9a | x9b | x9c | x9d | x9e | x9f | xa0 | xa1 | xa2 | xa3 | xa4 | xa5 | xa6 | xa7 | xa8 | xa9 | xaa | xab | xac | xad | xae | xaf | xb0 | xb1 | xb2 | xb3 | xb4 | xb5 | xb6 | xb7 | xb8 | xb9 | xba | xbb | xbc | xbd | xbe | xbf | xc0 | xc1 | xc2 | xc3 | xc4 | xc5 | xc6 | xc7 | xc8 | xc9 | xca | xcb | xcc | xcd | xce | xcf | xd0 | xd1 | xd2 => Gt
+  | xd3 => Eq
+  | _ => Lt
+  end.
+Definition compare_byte_xd4 (b : byte) :=
+  match b with
+  | x00 | x01 | x02 | x03 | x04 | x05 | x06 | x07 | x08 | x09 | x0a | x0b | x0c | x0d | x0e | x0f | x10 | x11 | x12 | x13 | x14 | x15 | x16 | x17 | x18 | x19 | x1a | x1b | x1c | x1d | x1e | x1f | x20 | x21 | x22 | x23 | x24 | x25 | x26 | x27 | x28 | x29 | x2a | x2b | x2c | x2d | x2e | x2f | x30 | x31 | x32 | x33 | x34 | x35 | x36 | x37 | x38 | x39 | x3a | x3b | x3c | x3d | x3e | x3f | x40 | x41 | x42 | x43 | x44 | x45 | x46 | x47 | x48 | x49 | x4a | x4b | x4c | x4d | x4e | x4f | x50 | x51 | x52 | x53 | x54 | x55 | x56 | x57 | x58 | x59 | x5a | x5b | x5c | x5d | x5e | x5f | x60 | x61 | x62 | x63 | x64 | x65 | x66 | x67 | x68 | x69 | x6a | x6b | x6c | x6d | x6e | x6f | x70 | x71 | x72 | x73 | x74 | x75 | x76 | x77 | x78 | x79 | x7a | x7b | x7c | x7d | x7e | x7f | x80 | x81 | x82 | x83 | x84 | x85 | x86 | x87 | x88 | x89 | x8a | x8b | x8c | x8d | x8e | x8f | x90 | x91 | x92 | x93 | x94 | x95 | x96 | x97 | x98 | x99 | x9a | x9b | x9c | x9d | x9e | x9f | xa0 | xa1 | xa2 | xa3 | xa4 | xa5 | xa6 | xa7 | xa8 | xa9 | xaa | xab | xac | xad | xae | xaf | xb0 | xb1 | xb2 | xb3 | xb4 | xb5 | xb6 | xb7 | xb8 | xb9 | xba | xbb | xbc | xbd | xbe | xbf | xc0 | xc1 | xc2 | xc3 | xc4 | xc5 | xc6 | xc7 | xc8 | xc9 | xca | xcb | xcc | xcd | xce | xcf | xd0 | xd1 | xd2 | xd3 => Gt
+  | xd4 => Eq
+  | _ => Lt
+  end.
+Definition compare_byte_xd5 (b : byte) :=
+  match b with
+  | x00 | x01 | x02 | x03 | x04 | x05 | x06 | x07 | x08 | x09 | x0a | x0b | x0c | x0d | x0e | x0f | x10 | x11 | x12 | x13 | x14 | x15 | x16 | x17 | x18 | x19 | x1a | x1b | x1c | x1d | x1e | x1f | x20 | x21 | x22 | x23 | x24 | x25 | x26 | x27 | x28 | x29 | x2a | x2b | x2c | x2d | x2e | x2f | x30 | x31 | x32 | x33 | x34 | x35 | x36 | x37 | x38 | x39 | x3a | x3b | x3c | x3d | x3e | x3f | x40 | x41 | x42 | x43 | x44 | x45 | x46 | x47 | x48 | x49 | x4a | x4b | x4c | x4d | x4e | x4f | x50 | x51 | x52 | x53 | x54 | x55 | x56 | x57 | x58 | x59 | x5a | x5b | x5c | x5d | x5e | x5f | x60 | x61 | x62 | x63 | x64 | x65 | x66 | x67 | x68 | x69 | x6a | x6b | x6c | x6d | x6e | x6f | x70 | x71 | x72 | x73 | x74 | x75 | x76 | x77 | x78 | x79 | x7a | x7b | x7c | x7d | x7e | x7f | x80 | x81 | x82 | x83 | x84 | x85 | x86 | x87 | x88 | x89 | x8a | x8b | x8c | x8d | x8e | x8f | x90 | x91 | x92 | x93 | x94 | x95 | x96 | x97 | x98 | x99 | x9a | x9b | x9c | x9d | x9e | x9f | xa0 | xa1 | xa2 | xa3 | xa4 | xa5 | xa6 | xa7 | xa8 | xa9 | xaa | xab | xac | xad | xae | xaf | xb0 | xb1 | xb2 | xb3 | xb4 | xb5 | xb6 | xb7 | xb8 | xb9 | xba | xbb | xbc | xbd | xbe | xbf | xc0 | xc1 | xc2 | xc3 | xc4 | xc5 | xc6 | xc7 | xc8 | xc9 | xca | xcb | xcc | xcd | xce | xcf | xd0 | xd1 | xd2 | xd3 | xd4 => Gt
+  | xd5 => Eq
+  | _ => Lt
+  end.
+Definition compare_byte_xd6 (b : byte) :=
+  match b with
+  | x00 | x01 | x02 | x03 | x04 | x05 | x06 | x07 | x08 | x09 | x0a | x0b | x0c | x0d | x0e | x0f | x10 | x11 | x12 | x13 | x14 | x15 | x16 | x17 | x18 | x19 | x1a | x1b | x1c | x1d | x1e | x1f | x20 | x21 | x22 | x23 | x24 | x25 | x26 | x27 | x28 | x29 | x2a | x2b | x2c | x2d | x2e | x2f | x30 | x31 | x32 | x33 | x34 | x35 | x36 | x37 | x38 | x39 | x3a | x3b | x3c | x3d | x3e | x3f | x40 | x41 | x42 | x43 | x44 | x45 | x46 | x47 | x48 | x49 | x4a | x4b | x4c | x4d | x4e | x4f | x50 | x51 | x52 | x53 | x54 | x55 | x56 | x57 | x58 | x59 | x5a | x5b | x5c | x5d | x5e | x5f | x60 | x61 | x62 | x63 | x64 | x65 | x66 | x67 | x68 | x69 | x6a | x6b | x6c | x6d | x6e | x6f | x70 | x71 | x72 | x73 | x74 | x75 | x76 | x77 | x78 | x79 | x7a | x7b | x7c | x7d | x7e | x7f | x80 | x81 | x82 | x83 | x84 | x85 | x86 | x87 | x88 | x89 | x8a | x8b | x8c | x8d | x8e | x8f | x90 | x91 | x92 | x93 | x94 | x95 | x96 | x97 | x98 | x99 | x9a | x9b | x9c | x9d | x9e | x9f | xa0 | xa1 | xa2 | xa3 | xa4 | xa5 | xa6 | xa7 | xa8 | xa9 | xaa | xab | xac | xad | xae | xaf | xb0 | xb1 | xb2 | xb3 | xb4 | xb5 | xb6 | xb7 | xb8 | xb9 | xba | xbb | xbc | xbd | xbe | xbf | xc0 | xc1 | xc2 | xc3 | xc4 | xc5 | xc6 | xc7 | xc8 | xc9 | xca | xcb | xcc | xcd | xce | xcf | xd0 | xd1 | xd2 | xd3 | xd4 | xd5 => Gt
+  | xd6 => Eq
+  | _ => Lt
+  end.
+Definition compare_byte_xd7 (b : byte) :=
+  match b with
+  | x00 | x01 | x02 | x03 | x04 | x05 | x06 | x07 | x08 | x09 | x0a | x0b | x0c | x0d | x0e | x0f | x10 | x11 | x12 | x13 | x14 | x15 | x16 | x17 | x18 | x19 | x1a | x1b | x1c | x1d | x1e | x1f | x20 | x21 | x22 | x23 | x24 | x25 | x26 | x27 | x28 | x29 | x2a | x2b | x2c | x2d | x2e | x2f | x30 | x31 | x32 | x33 | x34 | x35 | x36 | x37 | x38 | x39 | x3a | x3b | x3c | x3d | x3e | x3f | x40 | x41 | x42 | x43 | x44 | x45 | x46 | x47 | x48 | x49 | x4a | x4b | x4c | x4d | x4e | x4f | x50 | x51 | x52 | x53 | x54 | x55 | x56 | x57 | x58 | x59 | x5a | x5b | x5c | x5d | x5e | x5f | x60 | x61 | x62 | x63 | x64 | x65 | x66 | x67 | x68 | x69 | x6a | x6b | x6c | x6d | x6e | x6f | x70 | x71 | x72 | x73 | x74 | x75 | x76 | x77 | x78 | x79 | x7a | x7b | x7c | x7d | x7e | x7f | x80 | x81 | x82 | x83 | x84 | x85 | x86 | x87 | x88 | x89 | x8a | x8b | x8c | x8d | x8e | x8f | x90 | x91 | x92 | x93 | x94 | x95 | x96 | x97 | x98 | x99 | x9a | x9b | x9c | x9d | x9e | x9f | xa0 | xa1 | xa2 | xa3 | xa4 | xa5 | xa6 | xa7 | xa8 | xa9 | xaa | xab | xac | xad | xae | xaf | xb0 | xb1 | xb2 | xb3 | xb4 | xb5 | xb6 | xb7 | xb8 | xb9 | xba | xbb | xbc | xbd | xbe | xbf | xc0 | xc1 | xc2 | xc3 | xc4 | xc5 | xc6 | xc7 | xc8 | xc9 | xca | xcb | xcc | xcd | xce | xcf | xd0 | xd1 | xd2 | xd3 | xd4 | xd5 | xd6 => Gt
+  | xd7 => Eq
+  | _ => Lt
+  end.
+Definition compare_byte_xd8 (b : byte) :=
+  match b with
+  | x00 | x01 | x02 | x03 | x04 | x05 | x06 | x07 | x08 | x09 | x0a | x0b | x0c | x0d | x0e | x0f | x10 | x11 | x12 | x13 | x14 | x15 | x16 | x17 | x18 | x19 | x1a | x1b | x1c | x1d | x1e | x1f | x20 | x21 | x22 | x23 | x24 | x25 | x26 | x27 | x28 | x29 | x2a | x2b | x2c | x2d | x2e | x2f | x30 | x31 | x32 | x33 | x34 | x35 | x36 | x37 | x38 | x39 | x3a | x3b | x3c | x3d | x3e | x3f | x40 | x41 | x42 | x43 | x44 | x45 | x46 | x47 | x48 | x49 | x4a | x4b | x4c | x4d | x4e | x4f | x50 | x51 | x52 | x53 | x54 | x55 | x56 | x57 | x58 | x59 | x5a | x5b | x5c | x5d | x5e | x5f | x60 | x61 | x62 | x63 | x64 | x65 | x66 | x67 | x68 | x69 | x6a | x6b | x6c | x6d | x6e | x6f | x70 | x71 | x72 | x73 | x74 | x75 | x76 | x77 | x78 | x79 | x7a | x7b | x7c | x7d | x7e | x7f | x80 | x81 | x82 | x83 | x84 | x85 | x86 | x87 | x88 | x89 | x8a | x8b | x8c | x8d | x8e | x8f | x90 | x91 | x92 | x93 | x94 | x95 | x96 | x97 | x98 | x99 | x9a | x9b | x9c | x9d | x9e | x9f | xa0 | xa1 | xa2 | xa3 | xa4 | xa5 | xa6 | xa7 | xa8 | xa9 | xaa | xab | xac | xad | xae | xaf | xb0 | xb1 | xb2 | xb3 | xb4 | xb5 | xb6 | xb7 | xb8 | xb9 | xba | xbb | xbc | xbd | xbe | xbf | xc0 | xc1 | xc2 | xc3 | xc4 | xc5 | xc6 | xc7 | xc8 | xc9 | xca | xcb | xcc | xcd | xce | xcf | xd0 | xd1 | xd2 | xd3 | xd4 | xd5 | xd6 | xd7 => Gt
+  | xd8 => Eq
+  | _ => Lt
+  end.
+Definition compare_byte_xd9 (b : byte) :=
+  match b with
+  | x00 | x01 | x02 | x03 | x04 | x05 | x06 | x07 | x08 | x09 | x0a | x0b | x0c | x0d | x0e | x0f | x10 | x11 | x12 | x13 | x14 | x15 | x16 | x17 | x18 | x19 | x1a | x1b | x1c | x1d | x1e | x1f | x20 | x21 | x22 | x23 | x24 | x25 | x26 | x27 | x28 | x29 | x2a | x2b | x2c | x2d | x2e | x2f | x30 | x31 | x32 | x33 | x34 | x35 | x36 | x37 | x38 | x39 | x3a | x3b | x3c | x3d | x3e | x3f | x40 | x41 | x42 | x43 | x44 | x45 | x46 | x47 | x48 | x49 | x4a | x4b | x4c | x4d | x4e | x4f | x50 | x51 | x52 | x53 | x54 | x55 | x56 | x57 | x58 | x59 | x5a | x5b | x5c | x5d | x5e | x5f | x60 | x61 | x62 | x63 | x64 | x65 | x66 | x67 | x68 | x69 | x6a | x6b | x6c | x6d | x6e | x6f | x70 | x71 | x72 | x73 | x74 | x75 | x76 | x77 | x78 | x79 | x7a | x7b | x7c | x7d | x7e | x7f | x80 | x81 | x82 | x83 | x84 | x85 | x86 | x87 | x88 | x89 | x8a | x8b | x8c | x8d | x8e | x8f | x90 | x91 | x92 | x93 | x94 | x95 | x96 | x97 | x98 | x99 | x9a | x9b | x9c | x9d | x9e | x9f | xa0 | xa1 | xa2 | xa3 | xa4 | xa5 | xa6 | xa7 | xa8 | xa9 | xaa | xab | xac | xad | xae | xaf | xb0 | xb1 | xb2 | xb3 | xb4 | xb5 | xb6 | xb7 | xb8 | xb9 | xba | xbb | xbc | xbd | xbe | xbf | xc0 | xc1 | xc2 | xc3 | xc4 | xc5 | xc6 | xc7 | xc8 | xc9 | xca | xcb | xcc | xcd | xce | xcf | xd0 | xd1 | xd2 | xd3 | xd4 | xd5 | xd6 | xd7 | xd8 => Gt
+  | xd9 => Eq
+  | _ => Lt
+  end.
+Definition compare_byte_xda (b : byte) :=
+  match b with
+  | x00 | x01 | x02 | x03 | x04 | x05 | x06 | x07 | x08 | x09 | x0a | x0b | x0c | x0d | x0e | x0f | x10 | x11 | x12 | x13 | x14 | x15 | x16 | x17 | x18 | x19 | x1a | x1b | x1c | x1d | x1e | x1f | x20 | x21 | x22 | x23 | x24 | x25 | x26 | x27 | x28 | x29 | x2a | x2b | x2c | x2d | x2e | x2f | x30 | x31 | x32 | x33 | x34 | x35 | x36 | x37 | x38 | x39 | x3a | x3b | x3c | x3d | x3e | x3f | x40 | x41 | x42 | x43 | x44 | x45 | x46 | x47 | x48 | x49 | x4a | x4b | x4c | x4d | x4e | x4f | x50 | x51 | x52 | x53 | x54 | x55 | x56 | x57 | x58 | x59 | x5a | x5b | x5c | x5d | x5e | x5f | x60 | x61 | x62 | x63 | x64 | x65 | x66 | x67 | x68 | x69 | x6a | x6b | x6c | x6d | x6e | x6f | x70 | x71 | x72 | x73 | x74 | x75 | x76 | x77 | x78 | x79 | x7a | x7b | x7c | x7d | x7e | x7f | x80 | x81 | x82 | x83 | x84 | x85 | x86 | x87 | x88 | x89 | x8a | x8b | x8c | x8d | x8e | x8f | x90 | x91 | x92 | x93 | x94 | x95 | x96 | x97 | x98 | x99 | x9a | x9b | x9c | x9d | x9e | x9f | xa0 | xa1 | xa2 | xa3 | xa4 | xa5 | xa6 | xa7 | xa8 | xa9 | xaa | xab | xac | xad | xae | xaf | xb0 | xb1 | xb2 | xb3 | xb4 | xb5 | xb6 | xb7 | xb8 | xb9 | xba | xbb | xbc | xbd | xbe | xbf | xc0 | xc1 | xc2 | xc3 | xc4 | xc5 | xc6 | xc7 | xc8 | xc9 | xca | xcb | xcc | xcd | xce | xcf | xd0 | xd1 | xd2 | xd3 | xd4 | xd5 | xd6 | xd7 | xd8 | xd9 => Gt
+  | xda => Eq
+  | _ => Lt
+  end.
+Definition compare_byte_xdb (b : byte) :=
+  match b with
+  | x00 | x01 | x02 | x03 | x04 | x05 | x06 | x07 | x08 | x09 | x0a | x0b | x0c | x0d | x0e | x0f | x10 | x11 | x12 | x13 | x14 | x15 | x16 | x17 | x18 | x19 | x1a | x1b | x1c | x1d | x1e | x1f | x20 | x21 | x22 | x23 | x24 | x25 | x26 | x27 | x28 | x29 | x2a | x2b | x2c | x2d | x2e | x2f | x30 | x31 | x32 | x33 | x34 | x35 | x36 | x37 | x38 | x39 | x3a | x3b | x3c | x3d | x3e | x3f | x40 | x41 | x42 | x43 | x44 | x45 | x46 | x47 | x48 | x49 | x4a | x4b | x4c | x4d | x4e | x4f | x50 | x51 | x52 | x53 | x54 | x55 | x56 | x57 | x58 | x59 | x5a | x5b | x5c | x5d | x5e | x5f | x60 | x61 | x62 | x63 | x64 | x65 | x66 | x67 | x68 | x69 | x6a | x6b | x6c | x6d | x6e | x6f | x70 | x71 | x72 | x73 | x74 | x75 | x76 | x77 | x78 | x79 | x7a | x7b | x7c | x7d | x7e | x7f | x80 | x81 | x82 | x83 | x84 | x85 | x86 | x87 | x88 | x89 | x8a | x8b | x8c | x8d | x8e | x8f | x90 | x91 | x92 | x93 | x94 | x95 | x96 | x97 | x98 | x99 | x9a | x9b | x9c | x9d | x9e | x9f | xa0 | xa1 | xa2 | xa3 | xa4 | xa5 | xa6 | xa7 | xa8 | xa9 | xaa | xab | xac | xad | xae | xaf | xb0 | xb1 | xb2 | xb3 | xb4 | xb5 | xb6 | xb7 | xb8 | xb9 | xba | xbb | xbc | xbd | xbe | xbf | xc0 | xc1 | xc2 | xc3 | xc4 | xc5 | xc6 | xc7 | xc8 | xc9 | xca | xcb | xcc | xcd | xce | xcf | xd0 | xd1 | xd2 | xd3 | xd4 | xd5 | xd6 | xd7 | xd8 | xd9 | xda => Gt
+  | xdb => Eq
+  | _ => Lt
+  end.
+Definition compare_byte_xdc (b : byte) :=
+  match b with
+  | x00 | x01 | x02 | x03 | x04 | x05 | x06 | x07 | x08 | x09 | x0a | x0b | x0c | x0d | x0e | x0f | x10 | x11 | x12 | x13 | x14 | x15 | x16 | x17 | x18 | x19 | x1a | x1b | x1c | x1d | x1e | x1f | x20 | x21 | x22 | x23 | x24 | x25 | x26 | x27 | x28 | x29 | x2a | x2b | x2c | x2d | x2e | x2f | x30 | x31 | x32 | x33 | x34 | x35 | x36 | x37 | x38 | x39 | x3a | x3b | x3c | x3d | x3e | x3f | x40 | x41 | x42 | x43 | x44 | x45 | x46 | x47 | x48 | x49 | x4a | x4b | x4c | x4d | x4e | x4f | x50 | x51 | x52 | x53 | x54 | x55 | x56 | x57 | x58 | x59 | x5a | x5b | x5c | x5d | x5e | x5f | x60 | x61 | x62 | x63 | x64 | x65 | x66 | x67 | x68 | x69 | x6a | x6b | x6c | x6d | x6e | x6f | x70 | x71 | x72 | x73 | x74 | x75 | x76 | x77 | x78 | x79 | x7a | x7b | x7c | x7d | x7e | x7f | x80 | x81 | x82 | x83 | x84 | x85 | x86 | x87 | x88 | x89 | x8a | x8b | x8c | x8d | x8e | x8f | x90 | x91 | x92 | x93 | x94 | x95 | x96 | x97 | x98 | x99 | x9a | x9b | x9c | x9d | x9e | x9f | xa0 | xa1 | xa2 | xa3 | xa4 | xa5 | xa6 | xa7 | xa8 | xa9 | xaa | xab | xac | xad | xae | xaf | xb0 | xb1 | xb2 | xb3 | xb4 | xb5 | xb6 | xb7 | xb8 | xb9 | xba | xbb | xbc | xbd | xbe | xbf | xc0 | xc1 | xc2 | xc3 | xc4 | xc5 | xc6 | xc7 | xc8 | xc9 | xca | xcb | xcc | xcd | xce | xcf | xd0 | xd1 | xd2 | xd3 | xd4 | xd5 | xd6 | xd7 | xd8 | xd9 | xda | xdb => Gt
+  | xdc => Eq
+  | _ => Lt
+  end.
+Definition compare_byte_xdd (b : byte) :=
+  match b with
+  | x00 | x01 | x02 | x03 | x04 | x05 | x06 | x07 | x08 | x09 | x0a | x0b | x0c | x0d | x0e | x0f | x10 | x11 | x12 | x13 | x14 | x15 | x16 | x17 | x18 | x19 | x1a | x1b | x1c | x1d | x1e | x1f | x20 | x21 | x22 | x23 | x24 | x25 | x26 | x27 | x28 | x29 | x2a | x2b | x2c | x2d | x2e | x2f | x30 | x31 | x32 | x33 | x34 | x35 | x36 | x37 | x38 | x39 | x3a | x3b | x3c | x3d | x3e | x3f | x40 | x41 | x42 | x43 | x44 | x45 | x46 | x47 | x48 | x49 | x4a | x4b | x4c | x4d | x4e | x4f | x50 | x51 | x52 | x53 | x54 | x55 | x56 | x57 | x58 | x59 | x5a | x5b | x5c | x5d | x5e | x5f | x60 | x61 | x62 | x63 | x64 | x65 | x66 | x67 | x68 | x69 | x6a | x6b | x6c | x6d | x6e | x6f | x70 | x71 | x72 | x73 | x74 | x75 | x76 | x77 | x78 | x79 | x7a | x7b | x7c | x7d | x7e | x7f | x80 | x81 | x82 | x83 | x84 | x85 | x86 | x87 | x88 | x89 | x8a | x8b | x8c | x8d | x8e | x8f | x90 | x91 | x92 | x93 | x94 | x95 | x96 | x97 | x98 | x99 | x9a | x9b | x9c | x9d | x9e | x9f | xa0 | xa1 | xa2 | xa3 | xa4 | xa5 | xa6 | xa7 | xa8 | xa9 | xaa | xab | xac | xad | xae | xaf | xb0 | xb1 | xb2 | xb3 | xb4 | xb5 | xb6 | xb7 | xb8 | xb9 | xba | xbb | xbc | xbd | xbe | xbf | xc0 | xc1 | xc2 | xc3 | xc4 | xc5 | xc6 | xc7 | xc8 | xc9 | xca | xcb | xcc | xcd | xce | xcf | xd0 | xd1 | xd2 | xd3 | xd4 | xd5 | xd6 | xd7 | xd8 | xd9 | xda | xdb | xdc => Gt
+  | xdd => Eq
+  | _ => Lt
+  end.
+Definition compare_byte_xde (b : byte) :=
+  match b with
+  | x00 | x01 | x02 | x03 | x04 | x05 | x06 | x07 | x08 | x09 | x0a | x0b | x0c | x0d | x0e | x0f | x10 | x11 | x12 | x13 | x14 | x15 | x16 | x17 | x18 | x19 | x1a | x1b | x1c | x1d | x1e | x1f | x20 | x21 | x22 | x23 | x24 | x25 | x26 | x27 | x28 | x29 | x2a | x2b | x2c | x2d | x2e | x2f | x30 | x31 | x32 | x33 | x34 | x35 | x36 | x37 | x38 | x39 | x3a | x3b | x3c | x3d | x3e | x3f | x40 | x41 | x42 | x43 | x44 | x45 | x46 | x47 | x48 | x49 | x4a | x4b | x4c | x4d | x4e | x4f | x50 | x51 | x52 | x53 | x54 | x55 | x56 | x57 | x58 | x59 | x5a | x5b | x5c | x5d | x5e | x5f | x60 | x61 | x62 | x63 | x64 | x65 | x66 | x67 | x68 | x69 | x6a | x6b | x6c | x6d | x6e | x6f | x70 | x71 | x72 | x73 | x74 | x75 | x76 | x77 | x78 | x79 | x7a | x7b | x7c | x7d | x7e | x7f | x80 | x81 | x82 | x83 | x84 | x85 | x86 | x87 | x88 | x89 | x8a | x8b | x8c | x8d | x8e | x8f | x90 | x91 | x92 | x93 | x94 | x95 | x96 | x97 | x98 | x99 | x9a | x9b | x9c | x9d | x9e | x9f | xa0 | xa1 | xa2 | xa3 | xa4 | xa5 | xa6 | xa7 | xa8 | xa9 | xaa | xab | xac | xad | xae | xaf | xb0 | xb1 | xb2 | xb3 | xb4 | xb5 | xb6 | xb7 | xb8 | xb9 | xba | xbb | xbc | xbd | xbe | xbf | xc0 | xc1 | xc2 | xc3 | xc4 | xc5 | xc6 | xc7 | xc8 | xc9 | xca | xcb | xcc | xcd | xce | xcf | xd0 | xd1 | xd2 | xd3 | xd4 | xd5 | xd6 | xd7 | xd8 | xd9 | xda | xdb | xdc | xdd => Gt
+  | xde => Eq
+  | _ => Lt
+  end.
+Definition compare_byte_xdf (b : byte) :=
+  match b with
+  | x00 | x01 | x02 | x03 | x04 | x05 | x06 | x07 | x08 | x09 | x0a | x0b | x0c | x0d | x0e | x0f | x10 | x11 | x12 | x13 | x14 | x15 | x16 | x17 | x18 | x19 | x1a | x1b | x1c | x1d | x1e | x1f | x20 | x21 | x22 | x23 | x24 | x25 | x26 | x27 | x28 | x29 | x2a | x2b | x2c | x2d | x2e | x2f | x30 | x31 | x32 | x33 | x34 | x35 | x36 | x37 | x38 | x39 | x3a | x3b | x3c | x3d | x3e | x3f | x40 | x41 | x42 | x43 | x44 | x45 | x46 | x47 | x48 | x49 | x4a | x4b | x4c | x4d | x4e | x4f | x50 | x51 | x52 | x53 | x54 | x55 | x56 | x57 | x58 | x59 | x5a | x5b | x5c | x5d | x5e | x5f | x60 | x61 | x62 | x63 | x64 | x65 | x66 | x67 | x68 | x69 | x6a | x6b | x6c | x6d | x6e | x6f | x70 | x71 | x72 | x73 | x74 | x75 | x76 | x77 | x78 | x79 | x7a | x7b | x7c | x7d | x7e | x7f | x80 | x81 | x82 | x83 | x84 | x85 | x86 | x87 | x88 | x89 | x8a | x8b | x8c | x8d | x8e | x8f | x90 | x91 | x92 | x93 | x94 | x95 | x96 | x97 | x98 | x99 | x9a | x9b | x9c | x9d | x9e | x9f | xa0 | xa1 | xa2 | xa3 | xa4 | xa5 | xa6 | xa7 | xa8 | xa9 | xaa | xab | xac | xad | xae | xaf | xb0 | xb1 | xb2 | xb3 | xb4 | xb5 | xb6 | xb7 | xb8 | xb9 | xba | xbb | xbc | xbd | xbe | xbf | xc0 | xc1 | xc2 | xc3 | xc4 | xc5 | xc6 | xc7 | xc8 | xc9 | xca | xcb | xcc | xcd | xce | xcf | xd0 | xd1 | xd2 | xd3 | xd4 | xd5 | xd6 | xd7 | xd8 | xd9 | xda | xdb | xdc | xdd | xde => Gt
+  | xdf => Eq
+  | _ => Lt
+  end.
+Definition compare_byte_xe0 (b : byte) :=
+  match b with
+  | x00 | x01 | x02 | x03 | x04 | x05 | x06 | x07 | x08 | x09 | x0a | x0b | x0c | x0d | x0e | x0f | x10 | x11 | x12 | x13 | x14 | x15 | x16 | x17 | x18 | x19 | x1a | x1b | x1c | x1d | x1e | x1f | x20 | x21 | x22 | x23 | x24 | x25 | x26 | x27 | x28 | x29 | x2a | x2b | x2c | x2d | x2e | x2f | x30 | x31 | x32 | x33 | x34 | x35 | x36 | x37 | x38 | x39 | x3a | x3b | x3c | x3d | x3e | x3f | x40 | x41 | x42 | x43 | x44 | x45 | x46 | x47 | x48 | x49 | x4a | x4b | x4c | x4d | x4e | x4f | x50 | x51 | x52 | x53 | x54 | x55 | x56 | x57 | x58 | x59 | x5a | x5b | x5c | x5d | x5e | x5f | x60 | x61 | x62 | x63 | x64 | x65 | x66 | x67 | x68 | x69 | x6a | x6b | x6c | x6d | x6e | x6f | x70 | x71 | x72 | x73 | x74 | x75 | x76 | x77 | x78 | x79 | x7a | x7b | x7c | x7d | x7e | x7f | x80 | x81 | x82 | x83 | x84 | x85 | x86 | x87 | x88 | x89 | x8a | x8b | x8c | x8d | x8e | x8f | x90 | x91 | x92 | x93 | x94 | x95 | x96 | x97 | x98 | x99 | x9a | x9b | x9c | x9d | x9e | x9f | xa0 | xa1 | xa2 | xa3 | xa4 | xa5 | xa6 | xa7 | xa8 | xa9 | xaa | xab | xac | xad | xae | xaf | xb0 | xb1 | xb2 | xb3 | xb4 | xb5 | xb6 | xb7 | xb8 | xb9 | xba | xbb | xbc | xbd | xbe | xbf | xc0 | xc1 | xc2 | xc3 | xc4 | xc5 | xc6 | xc7 | xc8 | xc9 | xca | xcb | xcc | xcd | xce | xcf | xd0 | xd1 | xd2 | xd3 | xd4 | xd5 | xd6 | xd7 | xd8 | xd9 | xda | xdb | xdc | xdd | xde | xdf => Gt
+  | xe0 => Eq
+  | _ => Lt
+  end.
+Definition compare_byte_xe1 (b : byte) :=
+  match b with
+  | x00 | x01 | x02 | x03 | x04 | x05 | x06 | x07 | x08 | x09 | x0a | x0b | x0c | x0d | x0e | x0f | x10 | x11 | x12 | x13 | x14 | x15 | x16 | x17 | x18 | x19 | x1a | x1b | x1c | x1d | x1e | x1f | x20 | x21 | x22 | x23 | x24 | x25 | x26 | x27 | x28 | x29 | x2a | x2b | x2c | x2d | x2e | x2f | x30 | x31 | x32 | x33 | x34 | x35 | x36 | x37 | x38 | x39 | x3a | x3b | x3c | x3d | x3e | x3f | x40 | x41 | x42 | x43 | x44 | x45 | x46 | x47 | x48 | x49 | x4a | x4b | x4c | x4d | x4e | x4f | x50 | x51 | x52 | x53 | x54 | x55 | x56 | x57 | x58 | x59 | x5a | x5b | x5c | x5d | x5e | x5f | x60 | x61 | x62 | x63 | x64 | x65 | x66 | x67 | x68 | x69 | x6a | x6b | x6c | x6d | x6e | x6f | x70 | x71 | x72 | x73 | x74 | x75 | x76 | x77 | x78 | x79 | x7a | x7b | x7c | x7d | x7e | x7f | x80 | x81 | x82 | x83 | x84 | x85 | x86 | x87 | x88 | x89 | x8a | x8b | x8c | x8d | x8e | x8f | x90 | x91 | x92 | x93 | x94 | x95 | x96 | x97 | x98 | x99 | x9a | x9b | x9c | x9d | x9e | x9f | xa0 | xa1 | xa2 | xa3 | xa4 | xa5 | xa6 | xa7 | xa8 | xa9 | xaa | xab | xac | xad | xae | xaf | xb0 | xb1 | xb2 | xb3 | xb4 | xb5 | xb6 | xb7 | xb8 | xb9 | xba | xbb | xbc | xbd | xbe | xbf | xc0 | xc1 | xc2 | xc3 | xc4 | xc5 | xc6 | xc7 | xc8 | xc9 | xca | xcb | xcc | xcd | xce | xcf | xd0 | xd1 | xd2 | xd3 | xd4 | xd5 | xd6 | xd7 | xd8 | xd9 | xda | xdb | xdc | xdd | xde | xdf | xe0 => Gt
+  | xe1 => Eq
+  | _ => Lt
+  end.
+Definition compare_byte_xe2 (b : byte) :=
+  match b with
+  | x00 | x01 | x02 | x03 | x04 | x05 | x06 | x07 | x08 | x09 | x0a | x0b | x0c | x0d | x0e | x0f | x10 | x11 | x12 | x13 | x14 | x15 | x16 | x17 | x18 | x19 | x1a | x1b | x1c | x1d | x1e | x1f | x20 | x21 | x22 | x23 | x24 | x25 | x26 | x27 | x28 | x29 | x2a | x2b | x2c | x2d | x2e | x2f | x30 | x31 | x32 | x33 | x34 | x35 | x36 | x37 | x38 | x39 | x3a | x3b | x3c | x3d | x3e | x3f | x40 | x41 | x42 | x43 | x44 | x45 | x46 | x47 | x48 | x49 | x4a | x4b | x4c | x4d | x4e | x4f | x50 | x51 | x52 | x53 | x54 | x55 | x56 | x57 | x58 | x59 | x5a | x5b | x5c | x5d | x5e | x5f | x60 | x61 | x62 | x63 | x64 | x65 | x66 | x67 | x68 | x69 | x6a | x6b | x6c | x6d | x6e | x6f | x70 | x71 | x72 | x73 | x74 | x75 | x76 | x77 | x78 | x79 | x7a | x7b | x7c | x7d | x7e | x7f | x80 | x81 | x82 | x83 | x84 | x85 | x86 | x87 | x88 | x89 | x8a | x8b | x8c | x8d | x8e | x8f | x90 | x91 | x92 | x93 | x94 | x95 | x96 | x97 | x98 | x99 | x9a | x9b | x9c | x9d | x9e | x9f | xa0 | xa1 | xa2 | xa3 | xa4 | xa5 | xa6 | xa7 | xa8 | xa9 | xaa | xab | xac | xad | xae | xaf | xb0 | xb1 | xb2 | xb3 | xb4 | xb5 | xb6 | xb7 | xb8 | xb9 | xba | xbb | xbc | xbd | xbe | xbf | xc0 | xc1 | xc2 | xc3 | xc4 | xc5 | xc6 | xc7 | xc8 | xc9 | xca | xcb | xcc | xcd | xce | xcf | xd0 | xd1 | xd2 | xd3 | xd4 | xd5 | xd6 | xd7 | xd8 | xd9 | xda | xdb | xdc | xdd | xde | xdf | xe0 | xe1 => Gt
+  | xe2 => Eq
+  | _ => Lt
+  end.
+Definition compare_byte_xe3 (b : byte) :=
+  match b with
+  | x00 | x01 | x02 | x03 | x04 | x05 | x06 | x07 | x08 | x09 | x0a | x0b | x0c | x0d | x0e | x0f | x10 | x11 | x12 | x13 | x14 | x15 | x16 | x17 | x18 | x19 | x1a | x1b | x1c | x1d | x1e | x1f | x20 | x21 | x22 | x23 | x24 | x25 | x26 | x27 | x28 | x29 | x2a | x2b | x2c | x2d | x2e | x2f | x30 | x31 | x32 | x33 | x34 | x35 | x36 | x37 | x38 | x39 | x3a | x3b | x3c | x3d | x3e | x3f | x40 | x41 | x42 | x43 | x44 | x45 | x46 | x47 | x48 | x49 | x4a | x4b | x4c | x4d | x4e | x4f | x50 | x51 | x52 | x53 | x54 | x55 | x56 | x57 | x58 | x59 | x5a | x5b | x5c | x5d | x5e | x5f | x60 | x61 | x62 | x63 | x64 | x65 | x66 | x67 | x68 | x69 | x6a | x6b | x6c | x6d | x6e | x6f | x70 | x71 | x72 | x73 | x74 | x75 | x76 | x77 | x78 | x79 | x7a | x7b | x7c | x7d | x7e | x7f | x80 | x81 | x82 | x83 | x84 | x85 | x86 | x87 | x88 | x89 | x8a | x8b | x8c | x8d | x8e | x8f | x90 | x91 | x92 | x93 | x94 | x95 | x96 | x97 | x98 | x99 | x9a | x9b | x9c | x9d | x9e | x9f | xa0 | xa1 | xa2 | xa3 | xa4 | xa5 | xa6 | xa7 | xa8 | xa9 | xaa | xab | xac | xad | xae | xaf | xb0 | xb1 | xb2 | xb3 | xb4 | xb5 | xb6 | xb7 | xb8 | xb9 | xba | xbb | xbc | xbd | xbe | xbf | xc0 | xc1 | xc2 | xc3 | xc4 | xc5 | xc6 | xc7 | xc8 | xc9 | xca | xcb | xcc | xcd | xce | xcf | xd0 | xd1 | xd2 | xd3 | xd4 | xd5 | xd6 | xd7 | xd8 | xd9 | xda | xdb | xdc | xdd | xde | xdf | xe0 | xe1 | xe2 => Gt
+  | xe3 => Eq
+  | _ => Lt
+  end.
+Definition compare_byte_xe4 (b : byte) :=
+  match b with
+  | x00 | x01 | x02 | x03 | x04 | x05 | x06 | x07 | x08 | x09 | x0a | x0b | x0c | x0d | x0e | x0f | x10 | x11 | x12 | x13 | x14 | x15 | x16 | x17 | x18 | x19 | x1a | x1b | x1c | x1d | x1e | x1f | x20 | x21 | x22 | x23 | x24 | x25 | x26 | x27 | x28 | x29 | x2a | x2b | x2c | x2d | x2e | x2f | x30 | x31 | x32 | x33 | x34 | x35 | x36 | x37 | x38 | x39 | x3a | x3b | x3c | x3d | x3e | x3f | x40 | x41 | x42 | x43 | x44 | x45 | x46 | x47 | x48 | x49 | x4a | x4b | x4c | x4d | x4e | x4f | x50 | x51 | x52 | x53 | x54 | x55 | x56 | x57 | x58 | x59 | x5a | x5b | x5c | x5d | x5e | x5f | x60 | x61 | x62 | x63 | x64 | x65 | x66 | x67 | x68 | x69 | x6a | x6b | x6c | x6d | x6e | x6f | x70 | x71 | x72 | x73 | x74 | x75 | x76 | x77 | x78 | x79 | x7a | x7b | x7c | x7d | x7e | x7f | x80 | x81 | x82 | x83 | x84 | x85 | x86 | x87 | x88 | x89 | x8a | x8b | x8c | x8d | x8e | x8f | x90 | x91 | x92 | x93 | x94 | x95 | x96 | x97 | x98 | x99 | x9a | x9b | x9c | x9d | x9e | x9f | xa0 | xa1 | xa2 | xa3 | xa4 | xa5 | xa6 | xa7 | xa8 | xa9 | xaa | xab | xac | xad | xae | xaf | xb0 | xb1 | xb2 | xb3 | xb4 | xb5 | xb6 | xb7 | xb8 | xb9 | xba | xbb | xbc | xbd | xbe | xbf | xc0 | xc1 | xc2 | xc3 | xc4 | xc5 | xc6 | xc7 | xc8 | xc9 | xca | xcb | xcc | xcd | xce | xcf | xd0 | xd1 | xd2 | xd3 | xd4 | xd5 | xd6 | xd7 | xd8 | xd9 | xda | xdb | xdc | xdd | xde | xdf | xe0 | xe1 | xe2 | xe3 => Gt
+  | xe4 => Eq
+  | _ => Lt
+  end.
+Definition compare_byte_xe5 (b : byte) :=
+  match b with
+  | x00 | x01 | x02 | x03 | x04 | x05 | x06 | x07 | x08 | x09 | x0a | x0b | x0c | x0d | x0e | x0f | x10 | x11 | x12 | x13 | x14 | x15 | x16 | x17 | x18 | x19 | x1a | x1b | x1c | x1d | x1e | x1f | x20 | x21 | x22 | x23 | x24 | x25 | x26 | x27 | x28 | x29 | x2a | x2b | x2c | x2d | x2e | x2f | x30 | x31 | x32 | x33 | x34 | x35 | x36 | x37 | x38 | x39 | x3a | x3b | x3c | x3d | x3e | x3f | x40 | x41 | x42 | x43 | x44 | x45 | x46 | x47 | x48 | x49 | x4a | x4b | x4c | x4d | x4e | x4f | x50 | x51 | x52 | x53 | x54 | x55 | x56 | x57 | x58 | x59 | x5a | x5b | x5c | x5d | x5e | x5f | x60 | x61 | x62 | x63 | x64 | x65 | x66 | x67 | x68 | x69 | x6a | x6b | x6c | x6d | x6e | x6f | x70 | x71 | x72 | x73 | x74 | x75 | x76 | x77 | x78 | x79 | x7a | x7b | x7c | x7d | x7e | x7f | x80 | x81 | x82 | x83 | x84 | x85 | x86 | x87 | x88 | x89 | x8a | x8b | x8c | x8d | x8e | x8f | x90 | x91 | x92 | x93 | x94 | x95 | x96 | x97 | x98 | x99 | x9a | x9b | x9c | x9d | x9e | x9f | xa0 | xa1 | xa2 | xa3 | xa4 | xa5 | xa6 | xa7 | xa8 | xa9 | xaa | xab | xac | xad | xae | xaf | xb0 | xb1 | xb2 | xb3 | xb4 | xb5 | xb6 | xb7 | xb8 | xb9 | xba | xbb | xbc | xbd | xbe | xbf | xc0 | xc1 | xc2 | xc3 | xc4 | xc5 | xc6 | xc7 | xc8 | xc9 | xca | xcb | xcc | xcd | xce | xcf | xd0 | xd1 | xd2 | xd3 | xd4 | xd5 | xd6 | xd7 | xd8 | xd9 | xda | xdb | xdc | xdd | xde | xdf | xe0 | xe1 | xe2 | xe3 | xe4 => Gt
+  | xe5 => Eq
+  | _ => Lt
+  end.
+Definition compare_byte_xe6 (b : byte) :=
+  match b with
+  | x00 | x01 | x02 | x03 | x04 | x05 | x06 | x07 | x08 | x09 | x0a | x0b | x0c | x0d | x0e | x0f | x10 | x11 | x12 | x13 | x14 | x15 | x16 | x17 | x18 | x19 | x1a | x1b | x1c | x1d | x1e | x1f | x20 | x21 | x22 | x23 | x24 | x25 | x26 | x27 | x28 | x29 | x2a | x2b | x2c | x2d | x2e | x2f | x30 | x31 | x32 | x33 | x34 | x35 | x36 | x37 | x38 | x39 | x3a | x3b | x3c | x3d | x3e | x3f | x40 | x41 | x42 | x43 | x44 | x45 | x46 | x47 | x48 | x49 | x4a | x4b | x4c | x4d | x4e | x4f | x50 | x51 | x52 | x53 | x54 | x55 | x56 | x57 | x58 | x59 | x5a | x5b | x5c | x5d | x5e | x5f | x60 | x61 | x62 | x63 | x64 | x65 | x66 | x67 | x68 | x69 | x6a | x6b | x6c | x6d | x6e | x6f | x70 | x71 | x72 | x73 | x74 | x75 | x76 | x77 | x78 | x79 | x7a | x7b | x7c | x7d | x7e | x7f | x80 | x81 | x82 | x83 | x84 | x85 | x86 | x87 | x88 | x89 | x8a | x8b | x8c | x8d | x8e | x8f | x90 | x91 | x92 | x93 | x94 | x95 | x96 | x97 | x98 | x99 | x9a | x9b | x9c | x9d | x9e | x9f | xa0 | xa1 | xa2 | xa3 | xa4 | xa5 | xa6 | xa7 | xa8 | xa9 | xaa | xab | xac | xad | xae | xaf | xb0 | xb1 | xb2 | xb3 | xb4 | xb5 | xb6 | xb7 | xb8 | xb9 | xba | xbb | xbc | xbd | xbe | xbf | xc0 | xc1 | xc2 | xc3 | xc4 | xc5 | xc6 | xc7 | xc8 | xc9 | xca | xcb | xcc | xcd | xce | xcf | xd0 | xd1 | xd2 | xd3 | xd4 | xd5 | xd6 | xd7 | xd8 | xd9 | xda | xdb | xdc | xdd | xde | xdf | xe0 | xe1 | xe2 | xe3 | xe4 | xe5 => Gt
+  | xe6 => Eq
+  | _ => Lt
+  end.
+Definition compare_byte_xe7 (b : byte) :=
+  match b with
+  | x00 | x01 | x02 | x03 | x04 | x05 | x06 | x07 | x08 | x09 | x0a | x0b | x0c | x0d | x0e | x0f | x10 | x11 | x12 | x13 | x14 | x15 | x16 | x17 | x18 | x19 | x1a | x1b | x1c | x1d | x1e | x1f | x20 | x21 | x22 | x23 | x24 | x25 | x26 | x27 | x28 | x29 | x2a | x2b | x2c | x2d | x2e | x2f | x30 | x31 | x32 | x33 | x34 | x35 | x36 | x37 | x38 | x39 | x3a | x3b | x3c | x3d | x3e | x3f | x40 | x41 | x42 | x43 | x44 | x45 | x46 | x47 | x48 | x49 | x4a | x4b | x4c | x4d | x4e | x4f | x50 | x51 | x52 | x53 | x54 | x55 | x56 | x57 | x58 | x59 | x5a | x5b | x5c | x5d | x5e | x5f | x60 | x61 | x62 | x63 | x64 | x65 | x66 | x67 | x68 | x69 | x6a | x6b | x6c | x6d | x6e | x6f | x70 | x71 | x72 | x73 | x74 | x75 | x76 | x77 | x78 | x79 | x7a | x7b | x7c | x7d | x7e | x7f | x80 | x81 | x82 | x83 | x84 | x85 | x86 | x87 | x88 | x89 | x8a | x8b | x8c | x8d | x8e | x8f | x90 | x91 | x92 | x93 | x94 | x95 | x96 | x97 | x98 | x99 | x9a | x9b | x9c | x9d | x9e | x9f | xa0 | xa1 | xa2 | xa3 | xa4 | xa5 | xa6 | xa7 | xa8 | xa9 | xaa | xab | xac | xad | xae | xaf | xb0 | xb1 | xb2 | xb3 | xb4 | xb5 | xb6 | xb7 | xb8 | xb9 | xba | xbb | xbc | xbd | xbe | xbf | xc0 | xc1 | xc2 | xc3 | xc4 | xc5 | xc6 | xc7 | xc8 | xc9 | xca | xcb | xcc | xcd | xce | xcf | xd0 | xd1 | xd2 | xd3 | xd4 | xd5 | xd6 | xd7 | xd8 | xd9 | xda | xdb | xdc | xdd | xde | xdf | xe0 | xe1 | xe2 | xe3 | xe4 | xe5 | xe6 => Gt
+  | xe7 => Eq
+  | _ => Lt
+  end.
+Definition compare_byte_xe8 (b : byte) :=
+  match b with
+  | x00 | x01 | x02 | x03 | x04 | x05 | x06 | x07 | x08 | x09 | x0a | x0b | x0c | x0d | x0e | x0f | x10 | x11 | x12 | x13 | x14 | x15 | x16 | x17 | x18 | x19 | x1a | x1b | x1c | x1d | x1e | x1f | x20 | x21 | x22 | x23 | x24 | x25 | x26 | x27 | x28 | x29 | x2a | x2b | x2c | x2d | x2e | x2f | x30 | x31 | x32 | x33 | x34 | x35 | x36 | x37 | x38 | x39 | x3a | x3b | x3c | x3d | x3e | x3f | x40 | x41 | x42 | x43 | x44 | x45 | x46 | x47 | x48 | x49 | x4a | x4b | x4c | x4d | x4e | x4f | x50 | x51 | x52 | x53 | x54 | x55 | x56 | x57 | x58 | x59 | x5a | x5b | x5c | x5d | x5e | x5f | x60 | x61 | x62 | x63 | x64 | x65 | x66 | x67 | x68 | x69 | x6a | x6b | x6c | x6d | x6e | x6f | x70 | x71 | x72 | x73 | x74 | x75 | x76 | x77 | x78 | x79 | x7a | x7b | x7c | x7d | x7e | x7f | x80 | x81 | x82 | x83 | x84 | x85 | x86 | x87 | x88 | x89 | x8a | x8b | x8c | x8d | x8e | x8f | x90 | x91 | x92 | x93 | x94 | x95 | x96 | x97 | x98 | x99 | x9a | x9b | x9c | x9d | x9e | x9f | xa0 | xa1 | xa2 | xa3 | xa4 | xa5 | xa6 | xa7 | xa8 | xa9 | xaa | xab | xac | xad | xae | xaf | xb0 | xb1 | xb2 | xb3 | xb4 | xb5 | xb6 | xb7 | xb8 | xb9 | xba | xbb | xbc | xbd | xbe | xbf | xc0 | xc1 | xc2 | xc3 | xc4 | xc5 | xc6 | xc7 | xc8 | xc9 | xca | xcb | xcc | xcd | xce | xcf | xd0 | xd1 | xd2 | xd3 | xd4 | xd5 | xd6 | xd7 | xd8 | xd9 | xda | xdb | xdc | xdd | xde | xdf | xe0 | xe1 | xe2 | xe3 | xe4 | xe5 | xe6 | xe7 => Gt
+  | xe8 => Eq
+  | _ => Lt
+  end.
+Definition compare_byte_xe9 (b : byte) :=
+  match b with
+  | x00 | x01 | x02 | x03 | x04 | x05 | x06 | x07 | x08 | x09 | x0a | x0b | x0c | x0d | x0e | x0f | x10 | x11 | x12 | x13 | x14 | x15 | x16 | x17 | x18 | x19 | x1a | x1b | x1c | x1d | x1e | x1f | x20 | x21 | x22 | x23 | x24 | x25 | x26 | x27 | x28 | x29 | x2a | x2b | x2c | x2d | x2e | x2f | x30 | x31 | x32 | x33 | x34 | x35 | x36 | x37 | x38 | x39 | x3a | x3b | x3c | x3d | x3e | x3f | x40 | x41 | x42 | x43 | x44 | x45 | x46 | x47 | x48 | x49 | x4a | x4b | x4c | x4d | x4e | x4f | x50 | x51 | x52 | x53 | x54 | x55 | x56 | x57 | x58 | x59 | x5a | x5b | x5c | x5d | x5e | x5f | x60 | x61 | x62 | x63 | x64 | x65 | x66 | x67 | x68 | x69 | x6a | x6b | x6c | x6d | x6e | x6f | x70 | x71 | x72 | x73 | x74 | x75 | x76 | x77 | x78 | x79 | x7a | x7b | x7c | x7d | x7e | x7f | x80 | x81 | x82 | x83 | x84 | x85 | x86 | x87 | x88 | x89 | x8a | x8b | x8c | x8d | x8e | x8f | x90 | x91 | x92 | x93 | x94 | x95 | x96 | x97 | x98 | x99 | x9a | x9b | x9c | x9d | x9e | x9f | xa0 | xa1 | xa2 | xa3 | xa4 | xa5 | xa6 | xa7 | xa8 | xa9 | xaa | xab | xac | xad | xae | xaf | xb0 | xb1 | xb2 | xb3 | xb4 | xb5 | xb6 | xb7 | xb8 | xb9 | xba | xbb | xbc | xbd | xbe | xbf | xc0 | xc1 | xc2 | xc3 | xc4 | xc5 | xc6 | xc7 | xc8 | xc9 | xca | xcb | xcc | xcd | xce | xcf | xd0 | xd1 | xd2 | xd3 | xd4 | xd5 | xd6 | xd7 | xd8 | xd9 | xda | xdb | xdc | xdd | xde | xdf | xe0 | xe1 | xe2 | xe3 | xe4 | xe5 | xe6 | xe7 | xe8 => Gt
+  | xe9 => Eq
+  | _ => Lt
+  end.
+Definition compare_byte_xea (b : byte) :=
+  match b with
+  | x00 | x01 | x02 | x03 | x04 | x05 | x06 | x07 | x08 | x09 | x0a | x0b | x0c | x0d | x0e | x0f | x10 | x11 | x12 | x13 | x14 | x15 | x16 | x17 | x18 | x19 | x1a | x1b | x1c | x1d | x1e | x1f | x20 | x21 | x22 | x23 | x24 | x25 | x26 | x27 | x28 | x29 | x2a | x2b | x2c | x2d | x2e | x2f | x30 | x31 | x32 | x33 | x34 | x35 | x36 | x37 | x38 | x39 | x3a | x3b | x3c | x3d | x3e | x3f | x40 | x41 | x42 | x43 | x44 | x45 | x46 | x47 | x48 | x49 | x4a | x4b | x4c | x4d | x4e | x4f | x50 | x51 | x52 | x53 | x54 | x55 | x56 | x57 | x58 | x59 | x5a | x5b | x5c | x5d | x5e | x5f | x60 | x61 | x62 | x63 | x64 | x65 | x66 | x67 | x68 | x69 | x6a | x6b | x6c | x6d | x6e | x6f | x70 | x71 | x72 | x73 | x74 | x75 | x76 | x77 | x78 | x79 | x7a | x7b | x7c | x7d | x7e | x7f | x80 | x81 | x82 | x83 | x84 | x85 | x86 | x87 | x88 | x89 | x8a | x8b | x8c | x8d | x8e | x8f | x90 | x91 | x92 | x93 | x94 | x95 | x96 | x97 | x98 | x99 | x9a | x9b | x9c | x9d | x9e | x9f | xa0 | xa1 | xa2 | xa3 | xa4 | xa5 | xa6 | xa7 | xa8 | xa9 | xaa | xab | xac | xad | xae | xaf | xb0 | xb1 | xb2 | xb3 | xb4 | xb5 | xb6 | xb7 | xb8 | xb9 | xba | xbb | xbc | xbd | xbe | xbf | xc0 | xc1 | xc2 | xc3 | xc4 | xc5 | xc6 | xc7 | xc8 | xc9 | xca | xcb | xcc | xcd | xce | xcf | xd0 | xd1 | xd2 | xd3 | xd4 | xd5 | xd6 | xd7 | xd8 | xd9 | xda | xdb | xdc | xdd | xde | xdf | xe0 | xe1 | xe2 | xe3 | xe4 | xe5 | xe6 | xe7 | xe8 | xe9 => Gt
+  | xea => Eq
+  | _ => Lt
+  end.
+Definition compare_byte_xeb (b : byte) :=
+  match b with
+  | x00 | x01 | x02 | x03 | x04 | x05 | x06 | x07 | x08 | x09 | x0a | x0b | x0c | x0d | x0e | x0f | x10 | x11 | x12 | x13 | x14 | x15 | x16 | x17 | x18 | x19 | x1a | x1b | x1c | x1d | x1e | x1f | x20 | x21 | x22 | x23 | x24 | x25 | x26 | x27 | x28 | x29 | x2a | x2b | x2c | x2d | x2e | x2f | x30 | x31 | x32 | x33 | x34 | x35 | x36 | x37 | x38 | x39 | x3a | x3b | x3c | x3d | x3e | x3f | x40 | x41 | x42 | x43 | x44 | x45 | x46 | x47 | x48 | x49 | x4a | x4b | x4c | x4d | x4e | x4f | x50 | x51 | x52 | x53 | x54 | x55 | x56 | x57 | x58 | x59 | x5a | x5b | x5c | x5d | x5e | x5f | x60 | x61 | x62 | x63 | x64 | x65 | x66 | x67 | x68 | x69 | x6a | x6b | x6c | x6d | x6e | x6f | x70 | x71 | x72 | x73 | x74 | x75 | x76 | x77 | x78 | x79 | x7a | x7b | x7c | x7d | x7e | x7f | x80 | x81 | x82 | x83 | x84 | x85 | x86 | x87 | x88 | x89 | x8a | x8b | x8c | x8d | x8e | x8f | x90 | x91 | x92 | x93 | x94 | x95 | x96 | x97 | x98 | x99 | x9a | x9b | x9c | x9d | x9e | x9f | xa0 | xa1 | xa2 | xa3 | xa4 | xa5 | xa6 | xa7 | xa8 | xa9 | xaa | xab | xac | xad | xae | xaf | xb0 | xb1 | xb2 | xb3 | xb4 | xb5 | xb6 | xb7 | xb8 | xb9 | xba | xbb | xbc | xbd | xbe | xbf | xc0 | xc1 | xc2 | xc3 | xc4 | xc5 | xc6 | xc7 | xc8 | xc9 | xca | xcb | xcc | xcd | xce | xcf | xd0 | xd1 | xd2 | xd3 | xd4 | xd5 | xd6 | xd7 | xd8 | xd9 | xda | xdb | xdc | xdd | xde | xdf | xe0 | xe1 | xe2 | xe3 | xe4 | xe5 | xe6 | xe7 | xe8 | xe9 | xea => Gt
+  | xeb => Eq
+  | _ => Lt
+  end.
+Definition compare_byte_xec (b : byte) :=
+  match b with
+  | x00 | x01 | x02 | x03 | x04 | x05 | x06 | x07 | x08 | x09 | x0a | x0b | x0c | x0d | x0e | x0f | x10 | x11 | x12 | x13 | x14 | x15 | x16 | x17 | x18 | x19 | x1a | x1b | x1c | x1d | x1e | x1f | x20 | x21 | x22 | x23 | x24 | x25 | x26 | x27 | x28 | x29 | x2a | x2b | x2c | x2d | x2e | x2f | x30 | x31 | x32 | x33 | x34 | x35 | x36 | x37 | x38 | x39 | x3a | x3b | x3c | x3d | x3e | x3f | x40 | x41 | x42 | x43 | x44 | x45 | x46 | x47 | x48 | x49 | x4a | x4b | x4c | x4d | x4e | x4f | x50 | x51 | x52 | x53 | x54 | x55 | x56 | x57 | x58 | x59 | x5a | x5b | x5c | x5d | x5e | x5f | x60 | x61 | x62 | x63 | x64 | x65 | x66 | x67 | x68 | x69 | x6a | x6b | x6c | x6d | x6e | x6f | x70 | x71 | x72 | x73 | x74 | x75 | x76 | x77 | x78 | x79 | x7a | x7b | x7c | x7d | x7e | x7f | x80 | x81 | x82 | x83 | x84 | x85 | x86 | x87 | x88 | x89 | x8a | x8b | x8c | x8d | x8e | x8f | x90 | x91 | x92 | x93 | x94 | x95 | x96 | x97 | x98 | x99 | x9a | x9b | x9c | x9d | x9e | x9f | xa0 | xa1 | xa2 | xa3 | xa4 | xa5 | xa6 | xa7 | xa8 | xa9 | xaa | xab | xac | xad | xae | xaf | xb0 | xb1 | xb2 | xb3 | xb4 | xb5 | xb6 | xb7 | xb8 | xb9 | xba | xbb | xbc | xbd | xbe | xbf | xc0 | xc1 | xc2 | xc3 | xc4 | xc5 | xc6 | xc7 | xc8 | xc9 | xca | xcb | xcc | xcd | xce | xcf | xd0 | xd1 | xd2 | xd3 | xd4 | xd5 | xd6 | xd7 | xd8 | xd9 | xda | xdb | xdc | xdd | xde | xdf | xe0 | xe1 | xe2 | xe3 | xe4 | xe5 | xe6 | xe7 | xe8 | xe9 | xea | xeb => Gt
+  | xec => Eq
+  | _ => Lt
+  end.
+Definition compare_byte_xed (b : byte) :=
+  match b with
+  | x00 | x01 | x02 | x03 | x04 | x05 | x06 | x07 | x08 | x09 | x0a | x0b | x0c | x0d | x0e | x0f | x10 | x11 | x12 | x13 | x14 | x15 | x16 | x17 | x18 | x19 | x1a | x1b | x1c | x1d | x1e | x1f | x20 | x21 | x22 | x23 | x24 | x25 | x26 | x27 | x28 | x29 | x2a | x2b | x2c | x2d | x2e | x2f | x30 | x31 | x32 | x33 | x34 | x35 | x36 | x37 | x38 | x39 | x3a | x3b | x3c | x3d | x3e | x3f | x40 | x41 | x42 | x43 | x44 | x45 | x46 | x47 | x48 | x49 | x4a | x4b | x4c | x4d | x4e | x4f | x50 | x51 | x52 | x53 | x54 | x55 | x56 | x57 | x58 | x59 | x5a | x5b | x5c | x5d | x5e | x5f | x60 | x61 | x62 | x63 | x64 | x65 | x66 | x67 | x68 | x69 | x6a | x6b | x6c | x6d | x6e | x6f | x70 | x71 | x72 | x73 | x74 | x75 | x76 | x77 | x78 | x79 | x7a | x7b | x7c | x7d | x7e | x7f | x80 | x81 | x82 | x83 | x84 | x85 | x86 | x87 | x88 | x89 | x8a | x8b | x8c | x8d | x8e | x8f | x90 | x91 | x92 | x93 | x94 | x95 | x96 | x97 | x98 | x99 | x9a | x9b | x9c | x9d | x9e | x9f | xa0 | xa1 | xa2 | xa3 | xa4 | xa5 | xa6 | xa7 | xa8 | xa9 | xaa | xab | xac | xad | xae | xaf | xb0 | xb1 | xb2 | xb3 | xb4 | xb5 | xb6 | xb7 | xb8 | xb9 | xba | xbb | xbc | xbd | xbe | xbf | xc0 | xc1 | xc2 | xc3 | xc4 | xc5 | xc6 | xc7 | xc8 | xc9 | xca | xcb | xcc | xcd | xce | xcf | xd0 | xd1 | xd2 | xd3 | xd4 | xd5 | xd6 | xd7 | xd8 | xd9 | xda | xdb | xdc | xdd | xde | xdf | xe0 | xe1 | xe2 | xe3 | xe4 | xe5 | xe6 | xe7 | xe8 | xe9 | xea | xeb | xec => Gt
+  | xed => Eq
+  | _ => Lt
+  end.
+Definition compare_byte_xee (b : byte) :=
+  match b with
+  | x00 | x01 | x02 | x03 | x04 | x05 | x06 | x07 | x08 | x09 | x0a | x0b | x0c | x0d | x0e | x0f | x10 | x11 | x12 | x13 | x14 | x15 | x16 | x17 | x18 | x19 | x1a | x1b | x1c | x1d | x1e | x1f | x20 | x21 | x22 | x23 | x24 | x25 | x26 | x27 | x28 | x29 | x2a | x2b | x2c | x2d | x2e | x2f | x30 | x31 | x32 | x33 | x34 | x35 | x36 | x37 | x38 | x39 | x3a | x3b | x3c | x3d | x3e | x3f | x40 | x41 | x42 | x43 | x44 | x45 | x46 | x47 | x48 | x49 | x4a | x4b | x4c | x4d | x4e | x4f | x50 | x51 | x52 | x53 | x54 | x55 | x56 | x57 | x58 | x59 | x5a | x5b | x5c | x5d | x5e | x5f | x60 | x61 | x62 | x63 | x64 | x65 | x66 | x67 | x68 | x69 | x6a | x6b | x6c | x6d | x6e | x6f | x70 | x71 | x72 | x73 | x74 | x75 | x76 | x77 | x78 | x79 | x7a | x7b | x7c | x7d | x7e | x7f | x80 | x81 | x82 | x83 | x84 | x85 | x86 | x87 | x88 | x89 | x8a | x8b | x8c | x8d | x8e | x8f | x90 | x91 | x92 | x93 | x94 | x95 | x96 | x97 | x98 | x99 | x9a | x9b | x9c | x9d | x9e | x9f | xa0 | xa1 | xa2 | xa3 | xa4 | xa5 | xa6 | xa7 | xa8 | xa9 | xaa | xab | xac | xad | xae | xaf | xb0 | xb1 | xb2 | xb3 | xb4 | xb5 | xb6 | xb7 | xb8 | xb9 | xba | xbb | xbc | xbd | xbe | xbf | xc0 | xc1 | xc2 | xc3 | xc4 | xc5 | xc6 | xc7 | xc8 | xc9 | xca | xcb | xcc | xcd | xce | xcf | xd0 | xd1 | xd2 | xd3 | xd4 | xd5 | xd6 | xd7 | xd8 | xd9 | xda | xdb | xdc | xdd | xde | xdf | xe0 | xe1 | xe2 | xe3 | xe4 | xe5 | xe6 | xe7 | xe8 | xe9 | xea | xeb | xec | xed => Gt
+  | xee => Eq
+  | _ => Lt
+  end.
+Definition compare_byte_xef (b : byte) :=
+  match b with
+  | x00 | x01 | x02 | x03 | x04 | x05 | x06 | x07 | x08 | x09 | x0a | x0b | x0c | x0d | x0e | x0f | x10 | x11 | x12 | x13 | x14 | x15 | x16 | x17 | x18 | x19 | x1a | x1b | x1c | x1d | x1e | x1f | x20 | x21 | x22 | x23 | x24 | x25 | x26 | x27 | x28 | x29 | x2a | x2b | x2c | x2d | x2e | x2f | x30 | x31 | x32 | x33 | x34 | x35 | x36 | x37 | x38 | x39 | x3a | x3b | x3c | x3d | x3e | x3f | x40 | x41 | x42 | x43 | x44 | x45 | x46 | x47 | x48 | x49 | x4a | x4b | x4c | x4d | x4e | x4f | x50 | x51 | x52 | x53 | x54 | x55 | x56 | x57 | x58 | x59 | x5a | x5b | x5c | x5d | x5e | x5f | x60 | x61 | x62 | x63 | x64 | x65 | x66 | x67 | x68 | x69 | x6a | x6b | x6c | x6d | x6e | x6f | x70 | x71 | x72 | x73 | x74 | x75 | x76 | x77 | x78 | x79 | x7a | x7b | x7c | x7d | x7e | x7f | x80 | x81 | x82 | x83 | x84 | x85 | x86 | x87 | x88 | x89 | x8a | x8b | x8c | x8d | x8e | x8f | x90 | x91 | x92 | x93 | x94 | x95 | x96 | x97 | x98 | x99 | x9a | x9b | x9c | x9d | x9e | x9f | xa0 | xa1 | xa2 | xa3 | xa4 | xa5 | xa6 | xa7 | xa8 | xa9 | xaa | xab | xac | xad | xae | xaf | xb0 | xb1 | xb2 | xb3 | xb4 | xb5 | xb6 | xb7 | xb8 | xb9 | xba | xbb | xbc | xbd | xbe | xbf | xc0 | xc1 | xc2 | xc3 | xc4 | xc5 | xc6 | xc7 | xc8 | xc9 | xca | xcb | xcc | xcd | xce | xcf | xd0 | xd1 | xd2 | xd3 | xd4 | xd5 | xd6 | xd7 | xd8 | xd9 | xda | xdb | xdc | xdd | xde | xdf | xe0 | xe1 | xe2 | xe3 | xe4 | xe5 | xe6 | xe7 | xe8 | xe9 | xea | xeb | xec | xed | xee => Gt
+  | xef => Eq
+  | _ => Lt
+  end.
+Definition compare_byte_xf0 (b : byte) :=
+  match b with
+  | x00 | x01 | x02 | x03 | x04 | x05 | x06 | x07 | x08 | x09 | x0a | x0b | x0c | x0d | x0e | x0f | x10 | x11 | x12 | x13 | x14 | x15 | x16 | x17 | x18 | x19 | x1a | x1b | x1c | x1d | x1e | x1f | x20 | x21 | x22 | x23 | x24 | x25 | x26 | x27 | x28 | x29 | x2a | x2b | x2c | x2d | x2e | x2f | x30 | x31 | x32 | x33 | x34 | x35 | x36 | x37 | x38 | x39 | x3a | x3b | x3c | x3d | x3e | x3f | x40 | x41 | x42 | x43 | x44 | x45 | x46 | x47 | x48 | x49 | x4a | x4b | x4c | x4d | x4e | x4f | x50 | x51 | x52 | x53 | x54 | x55 | x56 | x57 | x58 | x59 | x5a | x5b | x5c | x5d | x5e | x5f | x60 | x61 | x62 | x63 | x64 | x65 | x66 | x67 | x68 | x69 | x6a | x6b | x6c | x6d | x6e | x6f | x70 | x71 | x72 | x73 | x74 | x75 | x76 | x77 | x78 | x79 | x7a | x7b | x7c | x7d | x7e | x7f | x80 | x81 | x82 | x83 | x84 | x85 | x86 | x87 | x88 | x89 | x8a | x8b | x8c | x8d | x8e | x8f | x90 | x91 | x92 | x93 | x94 | x95 | x96 | x97 | x98 | x99 | x9a | x9b | x9c | x9d | x9e | x9f | xa0 | xa1 | xa2 | xa3 | xa4 | xa5 | xa6 | xa7 | xa8 | xa9 | xaa | xab | xac | xad | xae | xaf | xb0 | xb1 | xb2 | xb3 | xb4 | xb5 | xb6 | xb7 | xb8 | xb9 | xba | xbb | xbc | xbd | xbe | xbf | xc0 | xc1 | xc2 | xc3 | xc4 | xc5 | xc6 | xc7 | xc8 | xc9 | xca | xcb | xcc | xcd | xce | xcf | xd0 | xd1 | xd2 | xd3 | xd4 | xd5 | xd6 | xd7 | xd8 | xd9 | xda | xdb | xdc | xdd | xde | xdf | xe0 | xe1 | xe2 | xe3 | xe4 | xe5 | xe6 | xe7 | xe8 | xe9 | xea | xeb | xec | xed | xee | xef => Gt
+  | xf0 => Eq
+  | _ => Lt
+  end.
+Definition compare_byte_xf1 (b : byte) :=
+  match b with
+  | x00 | x01 | x02 | x03 | x04 | x05 | x06 | x07 | x08 | x09 | x0a | x0b | x0c | x0d | x0e | x0f | x10 | x11 | x12 | x13 | x14 | x15 | x16 | x17 | x18 | x19 | x1a | x1b | x1c | x1d | x1e | x1f | x20 | x21 | x22 | x23 | x24 | x25 | x26 | x27 | x28 | x29 | x2a | x2b | x2c | x2d | x2e | x2f | x30 | x31 | x32 | x33 | x34 | x35 | x36 | x37 | x38 | x39 | x3a | x3b | x3c | x3d | x3e | x3f | x40 | x41 | x42 | x43 | x44 | x45 | x46 | x47 | x48 | x49 | x4a | x4b | x4c | x4d | x4e | x4f | x50 | x51 | x52 | x53 | x54 | x55 | x56 | x57 | x58 | x59 | x5a | x5b | x5c | x5d | x5e | x5f | x60 | x61 | x62 | x63 | x64 | x65 | x66 | x67 | x68 | x69 | x6a | x6b | x6c | x6d | x6e | x6f | x70 | x71 | x72 | x73 | x74 | x75 | x76 | x77 | x78 | x79 | x7a | x7b | x7c | x7d | x7e | x7f | x80 | x81 | x82 | x83 | x84 | x85 | x86 | x87 | x88 | x89 | x8a | x8b | x8c | x8d | x8e | x8f | x90 | x91 | x92 | x93 | x94 | x95 | x96 | x97 | x98 | x99 | x9a | x9b | x9c | x9d | x9e | x9f | xa0 | xa1 | xa2 | xa3 | xa4 | xa5 | xa6 | xa7 | xa8 | xa9 | xaa | xab | xac | xad | xae | xaf | xb0 | xb1 | xb2 | xb3 | xb4 | xb5 | xb6 | xb7 | xb8 | xb9 | xba | xbb | xbc | xbd | xbe | xbf | xc0 | xc1 | xc2 | xc3 | xc4 | xc5 | xc6 | xc7 | xc8 | xc9 | xca | xcb | xcc | xcd | xce | xcf | xd0 | xd1 | xd2 | xd3 | xd4 | xd5 | xd6 | xd7 | xd8 | xd9 | xda | xdb | xdc | xdd | xde | xdf | xe0 | xe1 | xe2 | xe3 | xe4 | xe5 | xe6 | xe7 | xe8 | xe9 | xea | xeb | xec | xed | xee | xef | xf0 => Gt
+  | xf1 => Eq
+  | _ => Lt
+  end.
+Definition compare_byte_xf2 (b : byte) :=
+  match b with
+  | x00 | x01 | x02 | x03 | x04 | x05 | x06 | x07 | x08 | x09 | x0a | x0b | x0c | x0d | x0e | x0f | x10 | x11 | x12 | x13 | x14 | x15 | x16 | x17 | x18 | x19 | x1a | x1b | x1c | x1d | x1e | x1f | x20 | x21 | x22 | x23 | x24 | x25 | x26 | x27 | x28 | x29 | x2a | x2b | x2c | x2d | x2e | x2f | x30 | x31 | x32 | x33 | x34 | x35 | x36 | x37 | x38 | x39 | x3a | x3b | x3c | x3d | x3e | x3f | x40 | x41 | x42 | x43 | x44 | x45 | x46 | x47 | x48 | x49 | x4a | x4b | x4c | x4d | x4e | x4f | x50 | x51 | x52 | x53 | x54 | x55 | x56 | x57 | x58 | x59 | x5a | x5b | x5c | x5d | x5e | x5f | x60 | x61 | x62 | x63 | x64 | x65 | x66 | x67 | x68 | x69 | x6a | x6b | x6c | x6d | x6e | x6f | x70 | x71 | x72 | x73 | x74 | x75 | x76 | x77 | x78 | x79 | x7a | x7b | x7c | x7d | x7e | x7f | x80 | x81 | x82 | x83 | x84 | x85 | x86 | x87 | x88 | x89 | x8a | x8b | x8c | x8d | x8e | x8f | x90 | x91 | x92 | x93 | x94 | x95 | x96 | x97 | x98 | x99 | x9a | x9b | x9c | x9d | x9e | x9f | xa0 | xa1 | xa2 | xa3 | xa4 | xa5 | xa6 | xa7 | xa8 | xa9 | xaa | xab | xac | xad | xae | xaf | xb0 | xb1 | xb2 | xb3 | xb4 | xb5 | xb6 | xb7 | xb8 | xb9 | xba | xbb | xbc | xbd | xbe | xbf | xc0 | xc1 | xc2 | xc3 | xc4 | xc5 | xc6 | xc7 | xc8 | xc9 | xca | xcb | xcc | xcd | xce | xcf | xd0 | xd1 | xd2 | xd3 | xd4 | xd5 | xd6 | xd7 | xd8 | xd9 | xda | xdb | xdc | xdd | xde | xdf | xe0 | xe1 | xe2 | xe3 | xe4 | xe5 | xe6 | xe7 | xe8 | xe9 | xea | xeb | xec | xed | xee | xef | xf0 | xf1 => Gt
+  | xf2 => Eq
+  | _ => Lt
+  end.
+Definition compare_byte_xf3 (b : byte) :=
+  match b with
+  | x00 | x01 | x02 | x03 | x04 | x05 | x06 | x07 | x08 | x09 | x0a | x0b | x0c | x0d | x0e | x0f | x10 | x11 | x12 | x13 | x14 | x15 | x16 | x17 | x18 | x19 | x1a | x1b | x1c | x1d | x1e | x1f | x20 | x21 | x22 | x23 | x24 | x25 | x26 | x27 | x28 | x29 | x2a | x2b | x2c | x2d | x2e | x2f | x30 | x31 | x32 | x33 | x34 | x35 | x36 | x37 | x38 | x39 | x3a | x3b | x3c | x3d | x3e | x3f | x40 | x41 | x42 | x43 | x44 | x45 | x46 | x47 | x48 | x49 | x4a | x4b | x4c | x4d | x4e | x4f | x50 | x51 | x52 | x53 | x54 | x55 | x56 | x57 | x58 | x59 | x5a | x5b | x5c | x5d | x5e | x5f | x60 | x61 | x62 | x63 | x64 | x65 | x66 | x67 | x68 | x69 | x6a | x6b | x6c | x6d | x6e | x6f | x70 | x71 | x72 | x73 | x74 | x75 | x76 | x77 | x78 | x79 | x7a | x7b | x7c | x7d | x7e | x7f | x80 | x81 | x82 | x83 | x84 | x85 | x86 | x87 | x88 | x89 | x8a | x8b | x8c | x8d | x8e | x8f | x90 | x91 | x92 | x93 | x94 | x95 | x96 | x97 | x98 | x99 | x9a | x9b | x9c | x9d | x9e | x9f | xa0 | xa1 | xa2 | xa3 | xa4 | xa5 | xa6 | xa7 | xa8 | xa9 | xaa | xab | xac | xad | xae | xaf | xb0 | xb1 | xb2 | xb3 | xb4 | xb5 | xb6 | xb7 | xb8 | xb9 | xba | xbb | xbc | xbd | xbe | xbf | xc0 | xc1 | xc2 | xc3 | xc4 | xc5 | xc6 | xc7 | xc8 | xc9 | xca | xcb | xcc | xcd | xce | xcf | xd0 | xd1 | xd2 | xd3 | xd4 | xd5 | xd6 | xd7 | xd8 | xd9 | xda | xdb | xdc | xdd | xde | xdf | xe0 | xe1 | xe2 | xe3 | xe4 | xe5 | xe6 | xe7 | xe8 | xe9 | xea | xeb | xec | xed | xee | xef | xf0 | xf1 | xf2 => Gt
+  | xf3 => Eq
+  | _ => Lt
+  end.
+Definition compare_byte_xf4 (b : byte) :=
+  match b with
+  | x00 | x01 | x02 | x03 | x04 | x05 | x06 | x07 | x08 | x09 | x0a | x0b | x0c | x0d | x0e | x0f | x10 | x11 | x12 | x13 | x14 | x15 | x16 | x17 | x18 | x19 | x1a | x1b | x1c | x1d | x1e | x1f | x20 | x21 | x22 | x23 | x24 | x25 | x26 | x27 | x28 | x29 | x2a | x2b | x2c | x2d | x2e | x2f | x30 | x31 | x32 | x33 | x34 | x35 | x36 | x37 | x38 | x39 | x3a | x3b | x3c | x3d | x3e | x3f | x40 | x41 | x42 | x43 | x44 | x45 | x46 | x47 | x48 | x49 | x4a | x4b | x4c | x4d | x4e | x4f | x50 | x51 | x52 | x53 | x54 | x55 | x56 | x57 | x58 | x59 | x5a | x5b | x5c | x5d | x5e | x5f | x60 | x61 | x62 | x63 | x64 | x65 | x66 | x67 | x68 | x69 | x6a | x6b | x6c | x6d | x6e | x6f | x70 | x71 | x72 | x73 | x74 | x75 | x76 | x77 | x78 | x79 | x7a | x7b | x7c | x7d | x7e | x7f | x80 | x81 | x82 | x83 | x84 | x85 | x86 | x87 | x88 | x89 | x8a | x8b | x8c | x8d | x8e | x8f | x90 | x91 | x92 | x93 | x94 | x95 | x96 | x97 | x98 | x99 | x9a | x9b | x9c | x9d | x9e | x9f | xa0 | xa1 | xa2 | xa3 | xa4 | xa5 | xa6 | xa7 | xa8 | xa9 | xaa | xab | xac | xad | xae | xaf | xb0 | xb1 | xb2 | xb3 | xb4 | xb5 | xb6 | xb7 | xb8 | xb9 | xba | xbb | xbc | xbd | xbe | xbf | xc0 | xc1 | xc2 | xc3 | xc4 | xc5 | xc6 | xc7 | xc8 | xc9 | xca | xcb | xcc | xcd | xce | xcf | xd0 | xd1 | xd2 | xd3 | xd4 | xd5 | xd6 | xd7 | xd8 | xd9 | xda | xdb | xdc | xdd | xde | xdf | xe0 | xe1 | xe2 | xe3 | xe4 | xe5 | xe6 | xe7 | xe8 | xe9 | xea | xeb | xec | xed | xee | xef | xf0 | xf1 | xf2 | xf3 => Gt
+  | xf4 => Eq
+  | _ => Lt
+  end.
+Definition compare_byte_xf5 (b : byte) :=
+  match b with
+  | x00 | x01 | x02 | x03 | x04 | x05 | x06 | x07 | x08 | x09 | x0a | x0b | x0c | x0d | x0e | x0f | x10 | x11 | x12 | x13 | x14 | x15 | x16 | x17 | x18 | x19 | x1a | x1b | x1c | x1d | x1e | x1f | x20 | x21 | x22 | x23 | x24 | x25 | x26 | x27 | x28 | x29 | x2a | x2b | x2c | x2d | x2e | x2f | x30 | x31 | x32 | x33 | x34 | x35 | x36 | x37 | x38 | x39 | x3a | x3b | x3c | x3d | x3e | x3f | x40 | x41 | x42 | x43 | x44 | x45 | x46 | x47 | x48 | x49 | x4a | x4b | x4c | x4d | x4e | x4f | x50 | x51 | x52 | x53 | x54 | x55 | x56 | x57 | x58 | x59 | x5a | x5b | x5c | x5d | x5e | x5f | x60 | x61 | x62 | x63 | x64 | x65 | x66 | x67 | x68 | x69 | x6a | x6b | x6c | x6d | x6e | x6f | x70 | x71 | x72 | x73 | x74 | x75 | x76 | x77 | x78 | x79 | x7a | x7b | x7c | x7d | x7e | x7f | x80 | x81 | x82 | x83 | x84 | x85 | x86 | x87 | x88 | x89 | x8a | x8b | x8c | x8d | x8e | x8f | x90 | x91 | x92 | x93 | x94 | x95 | x96 | x97 | x98 | x99 | x9a | x9b | x9c | x9d | x9e | x9f | xa0 | xa1 | xa2 | xa3 | xa4 | xa5 | xa6 | xa7 | xa8 | xa9 | xaa | xab | xac | xad | xae | xaf | xb0 | xb1 | xb2 | xb3 | xb4 | xb5 | xb6 | xb7 | xb8 | xb9 | xba | xbb | xbc | xbd | xbe | xbf | xc0 | xc1 | xc2 | xc3 | xc4 | xc5 | xc6 | xc7 | xc8 | xc9 | xca | xcb | xcc | xcd | xce | xcf | xd0 | xd1 | xd2 | xd3 | xd4 | xd5 | xd6 | xd7 | xd8 | xd9 | xda | xdb | xdc | xdd | xde | xdf | xe0 | xe1 | xe2 | xe3 | xe4 | xe5 | xe6 | xe7 | xe8 | xe9 | xea | xeb | xec | xed | xee | xef | xf0 | xf1 | xf2 | xf3 | xf4 => Gt
+  | xf5 => Eq
+  | _ => Lt
+  end.
+Definition compare_byte_xf6 (b : byte) :=
+  match b with
+  | x00 | x01 | x02 | x03 | x04 | x05 | x06 | x07 | x08 | x09 | x0a | x0b | x0c | x0d | x0e | x0f | x10 | x11 | x12 | x13 | x14 | x15 | x16 | x17 | x18 | x19 | x1a | x1b | x1c | x1d | x1e | x1f | x20 | x21 | x22 | x23 | x24 | x25 | x26 | x27 | x28 | x29 | x2a | x2b | x2c | x2d | x2e | x2f | x30 | x31 | x32 | x33 | x34 | x35 | x36 | x37 | x38 | x39 | x3a | x3b | x3c | x3d | x3e | x3f | x40 | x41 | x42 | x43 | x44 | x45 | x46 | x47 | x48 | x49 | x4a | x4b | x4c | x4d | x4e | x4f | x50 | x51 | x52 | x53 | x54 | x55 | x56 | x57 | x58 | x59 | x5a | x5b | x5c | x5d | x5e | x5f | x60 | x61 | x62 | x63 | x64 | x65 | x66 | x67 | x68 | x69 | x6a | x6b | x6c | x6d | x6e | x6f | x70 | x71 | x72 | x73 | x74 | x75 | x76 | x77 | x78 | x79 | x7a | x7b | x7c | x7d | x7e | x7f | x80 | x81 | x82 | x83 | x84 | x85 | x86 | x87 | x88 | x89 | x8a | x8b | x8c | x8d | x8e | x8f | x90 | x91 | x92 | x93 | x94 | x95 | x96 | x97 | x98 | x99 | x9a | x9b | x9c | x9d | x9e | x9f | xa0 | xa1 | xa2 | xa3 | xa4 | xa5 | xa6 | xa7 | xa8 | xa9 | xaa | xab | xac | xad | xae | xaf | xb0 | xb1 | xb2 | xb3 | xb4 | xb5 | xb6 | xb7 | xb8 | xb9 | xba | xbb | xbc | xbd | xbe | xbf | xc0 | xc1 | xc2 | xc3 | xc4 | xc5 | xc6 | xc7 | xc8 | xc9 | xca | xcb | xcc | xcd | xce | xcf | xd0 | xd1 | xd2 | xd3 | xd4 | xd5 | xd6 | xd7 | xd8 | xd9 | xda | xdb | xdc | xdd | xde | xdf | xe0 | xe1 | xe2 | xe3 | xe4 | xe5 | xe6 | xe7 | xe8 | xe9 | xea | xeb | xec | xed | xee | xef | xf0 | xf1 | xf2 | xf3 | xf4 | xf5 => Gt
+  | xf6 => Eq
+  | _ => Lt
+  end.
+Definition compare_byte_xf7 (b : byte) :=
+  match b with
+  | x00 | x01 | x02 | x03 | x04 | x05 | x06 | x07 | x08 | x09 | x0a | x0b | x0c | x0d | x0e | x0f | x10 | x11 | x12 | x13 | x14 | x15 | x16 | x17 | x18 | x19 | x1a | x1b | x1c | x1d | x1e | x1f | x20 | x21 | x22 | x23 | x24 | x25 | x26 | x27 | x28 | x29 | x2a | x2b | x2c | x2d | x2e | x2f | x30 | x31 | x32 | x33 | x34 | x35 | x36 | x37 | x38 | x39 | x3a | x3b | x3c | x3d | x3e | x3f | x40 | x41 | x42 | x43 | x44 | x45 | x46 | x47 | x48 | x49 | x4a | x4b | x4c | x4d | x4e | x4f | x50 | x51 | x52 | x53 | x54 | x55 | x56 | x57 | x58 | x59 | x5a | x5b | x5c | x5d | x5e | x5f | x60 | x61 | x62 | x63 | x64 | x65 | x66 | x67 | x68 | x69 | x6a | x6b | x6c | x6d | x6e | x6f | x70 | x71 | x72 | x73 | x74 | x75 | x76 | x77 | x78 | x79 | x7a | x7b | x7c | x7d | x7e | x7f | x80 | x81 | x82 | x83 | x84 | x85 | x86 | x87 | x88 | x89 | x8a | x8b | x8c | x8d | x8e | x8f | x90 | x91 | x92 | x93 | x94 | x95 | x96 | x97 | x98 | x99 | x9a | x9b | x9c | x9d | x9e | x9f | xa0 | xa1 | xa2 | xa3 | xa4 | xa5 | xa6 | xa7 | xa8 | xa9 | xaa | xab | xac | xad | xae | xaf | xb0 | xb1 | xb2 | xb3 | xb4 | xb5 | xb6 | xb7 | xb8 | xb9 | xba | xbb | xbc | xbd | xbe | xbf | xc0 | xc1 | xc2 | xc3 | xc4 | xc5 | xc6 | xc7 | xc8 | xc9 | xca | xcb | xcc | xcd | xce | xcf | xd0 | xd1 | xd2 | xd3 | xd4 | xd5 | xd6 | xd7 | xd8 | xd9 | xda | xdb | xdc | xdd | xde | xdf | xe0 | xe1 | xe2 | xe3 | xe4 | xe5 | xe6 | xe7 | xe8 | xe9 | xea | xeb | xec | xed | xee | xef | xf0 | xf1 | xf2 | xf3 | xf4 | xf5 | xf6 => Gt
+  | xf7 => Eq
+  | _ => Lt
+  end.
+Definition compare_byte_xf8 (b : byte) :=
+  match b with
+  | x00 | x01 | x02 | x03 | x04 | x05 | x06 | x07 | x08 | x09 | x0a | x0b | x0c | x0d | x0e | x0f | x10 | x11 | x12 | x13 | x14 | x15 | x16 | x17 | x18 | x19 | x1a | x1b | x1c | x1d | x1e | x1f | x20 | x21 | x22 | x23 | x24 | x25 | x26 | x27 | x28 | x29 | x2a | x2b | x2c | x2d | x2e | x2f | x30 | x31 | x32 | x33 | x34 | x35 | x36 | x37 | x38 | x39 | x3a | x3b | x3c | x3d | x3e | x3f | x40 | x41 | x42 | x43 | x44 | x45 | x46 | x47 | x48 | x49 | x4a | x4b | x4c | x4d | x4e | x4f | x50 | x51 | x52 | x53 | x54 | x55 | x56 | x57 | x58 | x59 | x5a | x5b | x5c | x5d | x5e | x5f | x60 | x61 | x62 | x63 | x64 | x65 | x66 | x67 | x68 | x69 | x6a | x6b | x6c | x6d | x6e | x6f | x70 | x71 | x72 | x73 | x74 | x75 | x76 | x77 | x78 | x79 | x7a | x7b | x7c | x7d | x7e | x7f | x80 | x81 | x82 | x83 | x84 | x85 | x86 | x87 | x88 | x89 | x8a | x8b | x8c | x8d | x8e | x8f | x90 | x91 | x92 | x93 | x94 | x95 | x96 | x97 | x98 | x99 | x9a | x9b | x9c | x9d | x9e | x9f | xa0 | xa1 | xa2 | xa3 | xa4 | xa5 | xa6 | xa7 | xa8 | xa9 | xaa | xab | xac | xad | xae | xaf | xb0 | xb1 | xb2 | xb3 | xb4 | xb5 | xb6 | xb7 | xb8 | xb9 | xba | xbb | xbc | xbd | xbe | xbf | xc0 | xc1 | xc2 | xc3 | xc4 | xc5 | xc6 | xc7 | xc8 | xc9 | xca | xcb | xcc | xcd | xce | xcf | xd0 | xd1 | xd2 | xd3 | xd4 | xd5 | xd6 | xd7 | xd8 | xd9 | xda | xdb | xdc | xdd | xde | xdf | xe0 | xe1 | xe2 | xe3 | xe4 | xe5 | xe6 | xe7 | xe8 | xe9 | xea | xeb | xec | xed | xee | xef | xf0 | xf1 | xf2 | xf3 | xf4 | xf5 | xf6 | xf7 => Gt
+  | xf8 => Eq
+  | _ => Lt
+  end.
+Definition compare_byte_xf9 (b : byte) :=
+  match b with
+  | x00 | x01 | x02 | x03 | x04 | x05 | x06 | x07 | x08 | x09 | x0a | x0b | x0c | x0d | x0e | x0f | x10 | x11 | x12 | x13 | x14 | x15 | x16 | x17 | x18 | x19 | x1a | x1b | x1c | x1d | x1e | x1f | x20 | x21 | x22 | x23 | x24 | x25 | x26 | x27 | x28 | x29 | x2a | x2b | x2c | x2d | x2e | x2f | x30 | x31 | x32 | x33 | x34 | x35 | x36 | x37 | x38 | x39 | x3a | x3b | x3c | x3d | x3e | x3f | x40 | x41 | x42 | x43 | x44 | x45 | x46 | x47 | x48 | x49 | x4a | x4b | x4c | x4d | x4e | x4f | x50 | x51 | x52 | x53 | x54 | x55 | x56 | x57 | x58 | x59 | x5a | x5b | x5c | x5d | x5e | x5f | x60 | x61 | x62 | x63 | x64 | x65 | x66 | x67 | x68 | x69 | x6a | x6b | x6c | x6d | x6e | x6f | x70 | x71 | x72 | x73 | x74 | x75 | x76 | x77 | x78 | x79 | x7a | x7b | x7c | x7d | x7e | x7f | x80 | x81 | x82 | x83 | x84 | x85 | x86 | x87 | x88 | x89 | x8a | x8b | x8c | x8d | x8e | x8f | x90 | x91 | x92 | x93 | x94 | x95 | x96 | x97 | x98 | x99 | x9a | x9b | x9c | x9d | x9e | x9f | xa0 | xa1 | xa2 | xa3 | xa4 | xa5 | xa6 | xa7 | xa8 | xa9 | xaa | xab | xac | xad | xae | xaf | xb0 | xb1 | xb2 | xb3 | xb4 | xb5 | xb6 | xb7 | xb8 | xb9 | xba | xbb | xbc | xbd | xbe | xbf | xc0 | xc1 | xc2 | xc3 | xc4 | xc5 | xc6 | xc7 | xc8 | xc9 | xca | xcb | xcc | xcd | xce | xcf | xd0 | xd1 | xd2 | xd3 | xd4 | xd5 | xd6 | xd7 | xd8 | xd9 | xda | xdb | xdc | xdd | xde | xdf | xe0 | xe1 | xe2 | xe3 | xe4 | xe5 | xe6 | xe7 | xe8 | xe9 | xea | xeb | xec | xed | xee | xef | xf0 | xf1 | xf2 | xf3 | xf4 | xf5 | xf6 | xf7 | xf8 => Gt
+  | xf9 => Eq
+  | _ => Lt
+  end.
+Definition compare_byte_xfa (b : byte) :=
+  match b with
+  | x00 | x01 | x02 | x03 | x04 | x05 | x06 | x07 | x08 | x09 | x0a | x0b | x0c | x0d | x0e | x0f | x10 | x11 | x12 | x13 | x14 | x15 | x16 | x17 | x18 | x19 | x1a | x1b | x1c | x1d | x1e | x1f | x20 | x21 | x22 | x23 | x24 | x25 | x26 | x27 | x28 | x29 | x2a | x2b | x2c | x2d | x2e | x2f | x30 | x31 | x32 | x33 | x34 | x35 | x36 | x37 | x38 | x39 | x3a | x3b | x3c | x3d | x3e | x3f | x40 | x41 | x42 | x43 | x44 | x45 | x46 | x47 | x48 | x49 | x4a | x4b | x4c | x4d | x4e | x4f | x50 | x51 | x52 | x53 | x54 | x55 | x56 | x57 | x58 | x59 | x5a | x5b | x5c | x5d | x5e | x5f | x60 | x61 | x62 | x63 | x64 | x65 | x66 | x67 | x68 | x69 | x6a | x6b | x6c | x6d | x6e | x6f | x70 | x71 | x72 | x73 | x74 | x75 | x76 | x77 | x78 | x79 | x7a | x7b | x7c | x7d | x7e | x7f | x80 | x81 | x82 | x83 | x84 | x85 | x86 | x87 | x88 | x89 | x8a | x8b | x8c | x8d | x8e | x8f | x90 | x91 | x92 | x93 | x94 | x95 | x96 | x97 | x98 | x99 | x9a | x9b | x9c | x9d | x9e | x9f | xa0 | xa1 | xa2 | xa3 | xa4 | xa5 | xa6 | xa7 | xa8 | xa9 | xaa | xab | xac | xad | xae | xaf | xb0 | xb1 | xb2 | xb3 | xb4 | xb5 | xb6 | xb7 | xb8 | xb9 | xba | xbb | xbc | xbd | xbe | xbf | xc0 | xc1 | xc2 | xc3 | xc4 | xc5 | xc6 | xc7 | xc8 | xc9 | xca | xcb | xcc | xcd | xce | xcf | xd0 | xd1 | xd2 | xd3 | xd4 | xd5 | xd6 | xd7 | xd8 | xd9 | xda | xdb | xdc | xdd | xde | xdf | xe0 | xe1 | xe2 | xe3 | xe4 | xe5 | xe6 | xe7 | xe8 | xe9 | xea | xeb | xec | xed | xee | xef | xf0 | xf1 | xf2 | xf3 | xf4 | xf5 | xf6 | xf7 | xf8 | xf9 => Gt
+  | xfa => Eq
+  | _ => Lt
+  end.
+Definition compare_byte_xfb (b : byte) :=
+  match b with
+  | x00 | x01 | x02 | x03 | x04 | x05 | x06 | x07 | x08 | x09 | x0a | x0b | x0c | x0d | x0e | x0f | x10 | x11 | x12 | x13 | x14 | x15 | x16 | x17 | x18 | x19 | x1a | x1b | x1c | x1d | x1e | x1f | x20 | x21 | x22 | x23 | x24 | x25 | x26 | x27 | x28 | x29 | x2a | x2b | x2c | x2d | x2e | x2f | x30 | x31 | x32 | x33 | x34 | x35 | x36 | x37 | x38 | x39 | x3a | x3b | x3c | x3d | x3e | x3f | x40 | x41 | x42 | x43 | x44 | x45 | x46 | x47 | x48 | x49 | x4a | x4b | x4c | x4d | x4e | x4f | x50 | x51 | x52 | x53 | x54 | x55 | x56 | x57 | x58 | x59 | x5a | x5b | x5c | x5d | x5e | x5f | x60 | x61 | x62 | x63 | x64 | x65 | x66 | x67 | x68 | x69 | x6a | x6b | x6c | x6d | x6e | x6f | x70 | x71 | x72 | x73 | x74 | x75 | x76 | x77 | x78 | x79 | x7a | x7b | x7c | x7d | x7e | x7f | x80 | x81 | x82 | x83 | x84 | x85 | x86 | x87 | x88 | x89 | x8a | x8b | x8c | x8d | x8e | x8f | x90 | x91 | x92 | x93 | x94 | x95 | x96 | x97 | x98 | x99 | x9a | x9b | x9c | x9d | x9e | x9f | xa0 | xa1 | xa2 | xa3 | xa4 | xa5 | xa6 | xa7 | xa8 | xa9 | xaa | xab | xac | xad | xae | xaf | xb0 | xb1 | xb2 | xb3 | xb4 | xb5 | xb6 | xb7 | xb8 | xb9 | xba | xbb | xbc | xbd | xbe | xbf | xc0 | xc1 | xc2 | xc3 | xc4 | xc5 | xc6 | xc7 | xc8 | xc9 | xca | xcb | xcc | xcd | xce | xcf | xd0 | xd1 | xd2 | xd3 | xd4 | xd5 | xd6 | xd7 | xd8 | xd9 | xda | xdb | xdc | xdd | xde | xdf | xe0 | xe1 | xe2 | xe3 | xe4 | xe5 | xe6 | xe7 | xe8 | xe9 | xea | xeb | xec | xed | xee | xef | xf0 | xf1 | xf2 | xf3 | xf4 | xf5 | xf6 | xf7 | xf8 | xf9 | xfa => Gt
+  | xfb => Eq
+  | _ => Lt
+  end.
+Definition compare_byte_xfc (b : byte) :=
+  match b with
+  | x00 | x01 | x02 | x03 | x04 | x05 | x06 | x07 | x08 | x09 | x0a | x0b | x0c | x0d | x0e | x0f | x10 | x11 | x12 | x13 | x14 | x15 | x16 | x17 | x18 | x19 | x1a | x1b | x1c | x1d | x1e | x1f | x20 | x21 | x22 | x23 | x24 | x25 | x26 | x27 | x28 | x29 | x2a | x2b | x2c | x2d | x2e | x2f | x30 | x31 | x32 | x33 | x34 | x35 | x36 | x37 | x38 | x39 | x3a | x3b | x3c | x3d | x3e | x3f | x40 | x41 | x42 | x43 | x44 | x45 | x46 | x47 | x48 | x49 | x4a | x4b | x4c | x4d | x4e | x4f | x50 | x51 | x52 | x53 | x54 | x55 | x56 | x57 | x58 | x59 | x5a | x5b | x5c | x5d | x5e | x5f | x60 | x61 | x62 | x63 | x64 | x65 | x66 | x67 | x68 | x69 | x6a | x6b | x6c | x6d | x6e | x6f | x70 | x71 | x72 | x73 | x74 | x75 | x76 | x77 | x78 | x79 | x7a | x7b | x7c | x7d | x7e | x7f | x80 | x81 | x82 | x83 | x84 | x85 | x86 | x87 | x88 | x89 | x8a | x8b | x8c | x8d | x8e | x8f | x90 | x91 | x92 | x93 | x94 | x95 | x96 | x97 | x98 | x99 | x9a | x9b | x9c | x9d | x9e | x9f | xa0 | xa1 | xa2 | xa3 | xa4 | xa5 | xa6 | xa7 | xa8 | xa9 | xaa | xab | xac | xad | xae | xaf | xb0 | xb1 | xb2 | xb3 | xb4 | xb5 | xb6 | xb7 | xb8 | xb9 | xba | xbb | xbc | xbd | xbe | xbf | xc0 | xc1 | xc2 | xc3 | xc4 | xc5 | xc6 | xc7 | xc8 | xc9 | xca | xcb | xcc | xcd | xce | xcf | xd0 | xd1 | xd2 | xd3 | xd4 | xd5 | xd6 | xd7 | xd8 | xd9 | xda | xdb | xdc | xdd | xde | xdf | xe0 | xe1 | xe2 | xe3 | xe4 | xe5 | xe6 | xe7 | xe8 | xe9 | xea | xeb | xec | xed | xee | xef | xf0 | xf1 | xf2 | xf3 | xf4 | xf5 | xf6 | xf7 | xf8 | xf9 | xfa | xfb => Gt
+  | xfc => Eq
+  | _ => Lt
+  end.
+Definition compare_byte_xfd (b : byte) :=
+  match b with
+  | x00 | x01 | x02 | x03 | x04 | x05 | x06 | x07 | x08 | x09 | x0a | x0b | x0c | x0d | x0e | x0f | x10 | x11 | x12 | x13 | x14 | x15 | x16 | x17 | x18 | x19 | x1a | x1b | x1c | x1d | x1e | x1f | x20 | x21 | x22 | x23 | x24 | x25 | x26 | x27 | x28 | x29 | x2a | x2b | x2c | x2d | x2e | x2f | x30 | x31 | x32 | x33 | x34 | x35 | x36 | x37 | x38 | x39 | x3a | x3b | x3c | x3d | x3e | x3f | x40 | x41 | x42 | x43 | x44 | x45 | x46 | x47 | x48 | x49 | x4a | x4b | x4c | x4d | x4e | x4f | x50 | x51 | x52 | x53 | x54 | x55 | x56 | x57 | x58 | x59 | x5a | x5b | x5c | x5d | x5e | x5f | x60 | x61 | x62 | x63 | x64 | x65 | x66 | x67 | x68 | x69 | x6a | x6b | x6c | x6d | x6e | x6f | x70 | x71 | x72 | x73 | x74 | x75 | x76 | x77 | x78 | x79 | x7a | x7b | x7c | x7d | x7e | x7f | x80 | x81 | x82 | x83 | x84 | x85 | x86 | x87 | x88 | x89 | x8a | x8b | x8c | x8d | x8e | x8f | x90 | x91 | x92 | x93 | x94 | x95 | x96 | x97 | x98 | x99 | x9a | x9b | x9c | x9d | x9e | x9f | xa0 | xa1 | xa2 | xa3 | xa4 | xa5 | xa6 | xa7 | xa8 | xa9 | xaa | xab | xac | xad | xae | xaf | xb0 | xb1 | xb2 | xb3 | xb4 | xb5 | xb6 | xb7 | xb8 | xb9 | xba | xbb | xbc | xbd | xbe | xbf | xc0 | xc1 | xc2 | xc3 | xc4 | xc5 | xc6 | xc7 | xc8 | xc9 | xca | xcb | xcc | xcd | xce | xcf | xd0 | xd1 | xd2 | xd3 | xd4 | xd5 | xd6 | xd7 | xd8 | xd9 | xda | xdb | xdc | xdd | xde | xdf | xe0 | xe1 | xe2 | xe3 | xe4 | xe5 | xe6 | xe7 | xe8 | xe9 | xea | xeb | xec | xed | xee | xef | xf0 | xf1 | xf2 | xf3 | xf4 | xf5 | xf6 | xf7 | xf8 | xf9 | xfa | xfb | xfc => Gt
+  | xfd => Eq
+  | _ => Lt
+  end.
+Definition compare_byte_xfe (b : byte) :=
+  match b with
+  | x00 | x01 | x02 | x03 | x04 | x05 | x06 | x07 | x08 | x09 | x0a | x0b | x0c | x0d | x0e | x0f | x10 | x11 | x12 | x13 | x14 | x15 | x16 | x17 | x18 | x19 | x1a | x1b | x1c | x1d | x1e | x1f | x20 | x21 | x22 | x23 | x24 | x25 | x26 | x27 | x28 | x29 | x2a | x2b | x2c | x2d | x2e | x2f | x30 | x31 | x32 | x33 | x34 | x35 | x36 | x37 | x38 | x39 | x3a | x3b | x3c | x3d | x3e | x3f | x40 | x41 | x42 | x43 | x44 | x45 | x46 | x47 | x48 | x49 | x4a | x4b | x4c | x4d | x4e | x4f | x50 | x51 | x52 | x53 | x54 | x55 | x56 | x57 | x58 | x59 | x5a | x5b | x5c | x5d | x5e | x5f | x60 | x61 | x62 | x63 | x64 | x65 | x66 | x67 | x68 | x69 | x6a | x6b | x6c | x6d | x6e | x6f | x70 | x71 | x72 | x73 | x74 | x75 | x76 | x77 | x78 | x79 | x7a | x7b | x7c | x7d | x7e | x7f | x80 | x81 | x82 | x83 | x84 | x85 | x86 | x87 | x88 | x89 | x8a | x8b | x8c | x8d | x8e | x8f | x90 | x91 | x92 | x93 | x94 | x95 | x96 | x97 | x98 | x99 | x9a | x9b | x9c | x9d | x9e | x9f | xa0 | xa1 | xa2 | xa3 | xa4 | xa5 | xa6 | xa7 | xa8 | xa9 | xaa | xab | xac | xad | xae | xaf | xb0 | xb1 | xb2 | xb3 | xb4 | xb5 | xb6 | xb7 | xb8 | xb9 | xba | xbb | xbc | xbd | xbe | xbf | xc0 | xc1 | xc2 | xc3 | xc4 | xc5 | xc6 | xc7 | xc8 | xc9 | xca | xcb | xcc | xcd | xce | xcf | xd0 | xd1 | xd2 | xd3 | xd4 | xd5 | xd6 | xd7 | xd8 | xd9 | xda | xdb | xdc | xdd | xde | xdf | xe0 | xe1 | xe2 | xe3 | xe4 | xe5 | xe6 | xe7 | xe8 | xe9 | xea | xeb | xec | xed | xee | xef | xf0 | xf1 | xf2 | xf3 | xf4 | xf5 | xf6 | xf7 | xf8 | xf9 | xfa | xfb | xfc | xfd => Gt
+  | xfe => Eq
+  | _ => Lt
+  end.
+Definition compare_byte_xff (b : byte) :=
+  match b with
+  | x00 | x01 | x02 | x03 | x04 | x05 | x06 | x07 | x08 | x09 | x0a | x0b | x0c | x0d | x0e | x0f | x10 | x11 | x12 | x13 | x14 | x15 | x16 | x17 | x18 | x19 | x1a | x1b | x1c | x1d | x1e | x1f | x20 | x21 | x22 | x23 | x24 | x25 | x26 | x27 | x28 | x29 | x2a | x2b | x2c | x2d | x2e | x2f | x30 | x31 | x32 | x33 | x34 | x35 | x36 | x37 | x38 | x39 | x3a | x3b | x3c | x3d | x3e | x3f | x40 | x41 | x42 | x43 | x44 | x45 | x46 | x47 | x48 | x49 | x4a | x4b | x4c | x4d | x4e | x4f | x50 | x51 | x52 | x53 | x54 | x55 | x56 | x57 | x58 | x59 | x5a | x5b | x5c | x5d | x5e | x5f | x60 | x61 | x62 | x63 | x64 | x65 | x66 | x67 | x68 | x69 | x6a | x6b | x6c | x6d | x6e | x6f | x70 | x71 | x72 | x73 | x74 | x75 | x76 | x77 | x78 | x79 | x7a | x7b | x7c | x7d | x7e | x7f | x80 | x81 | x82 | x83 | x84 | x85 | x86 | x87 | x88 | x89 | x8a | x8b | x8c | x8d | x8e | x8f | x90 | x91 | x92 | x93 | x94 | x95 | x96 | x97 | x98 | x99 | x9a | x9b | x9c | x9d | x9e | x9f | xa0 | xa1 | xa2 | xa3 | xa4 | xa5 | xa6 | xa7 | xa8 | xa9 | xaa | xab | xac | xad | xae | xaf | xb0 | xb1 | xb2 | xb3 | xb4 | xb5 | xb6 | xb7 | xb8 | xb9 | xba | xbb | xbc | xbd | xbe | xbf | xc0 | xc1 | xc2 | xc3 | xc4 | xc5 | xc6 | xc7 | xc8 | xc9 | xca | xcb | xcc | xcd | xce | xcf | xd0 | xd1 | xd2 | xd3 | xd4 | xd5 | xd6 | xd7 | xd8 | xd9 | xda | xdb | xdc | xdd | xde | xdf | xe0 | xe1 | xe2 | xe3 | xe4 | xe5 | xe6 | xe7 | xe8 | xe9 | xea | xeb | xec | xed | xee | xef | xf0 | xf1 | xf2 | xf3 | xf4 | xf5 | xf6 | xf7 | xf8 | xf9 | xfa | xfb | xfc | xfd | xfe => Gt
+  | xff => Eq
+  end.
+Definition compare (b b' : byte) :=
+  match b with
+  | x00 => compare_byte_x00 b'
+  | x01 => compare_byte_x01 b'
+  | x02 => compare_byte_x02 b'
+  | x03 => compare_byte_x03 b'
+  | x04 => compare_byte_x04 b'
+  | x05 => compare_byte_x05 b'
+  | x06 => compare_byte_x06 b'
+  | x07 => compare_byte_x07 b'
+  | x08 => compare_byte_x08 b'
+  | x09 => compare_byte_x09 b'
+  | x0a => compare_byte_x0a b'
+  | x0b => compare_byte_x0b b'
+  | x0c => compare_byte_x0c b'
+  | x0d => compare_byte_x0d b'
+  | x0e => compare_byte_x0e b'
+  | x0f => compare_byte_x0f b'
+  | x10 => compare_byte_x10 b'
+  | x11 => compare_byte_x11 b'
+  | x12 => compare_byte_x12 b'
+  | x13 => compare_byte_x13 b'
+  | x14 => compare_byte_x14 b'
+  | x15 => compare_byte_x15 b'
+  | x16 => compare_byte_x16 b'
+  | x17 => compare_byte_x17 b'
+  | x18 => compare_byte_x18 b'
+  | x19 => compare_byte_x19 b'
+  | x1a => compare_byte_x1a b'
+  | x1b => compare_byte_x1b b'
+  | x1c => compare_byte_x1c b'
+  | x1d => compare_byte_x1d b'
+  | x1e => compare_byte_x1e b'
+  | x1f => compare_byte_x1f b'
+  | x20 => compare_byte_x20 b'
+  | x21 => compare_byte_x21 b'
+  | x22 => compare_byte_x22 b'
+  | x23 => compare_byte_x23 b'
+  | x24 => compare_byte_x24 b'
+  | x25 => compare_byte_x25 b'
+  | x26 => compare_byte_x26 b'
+  | x27 => compare_byte_x27 b'
+  | x28 => compare_byte_x28 b'
+  | x29 => compare_byte_x29 b'
+  | x2a => compare_byte_x2a b'
+  | x2b => compare_byte_x2b b'
+  | x2c => compare_byte_x2c b'
+  | x2d => compare_byte_x2d b'
+  | x2e => compare_byte_x2e b'
+  | x2f => compare_byte_x2f b'
+  | x30 => compare_byte_x30 b'
+  | x31 => compare_byte_x31 b'
+  | x32 => compare_byte_x32 b'
+  | x33 => compare_byte_x33 b'
+  | x34 => compare_byte_x34 b'
+  | x35 => compare_byte_x35 b'
+  | x36 => compare_byte_x36 b'
+  | x37 => compare_byte_x37 b'
+  | x38 => compare_byte_x38 b'
+  | x39 => compare_byte_x39 b'
+  | x3a => compare_byte_x3a b'
+  | x3b => compare_byte_x3b b'
+  | x3c => compare_byte_x3c b'
+  | x3d => compare_byte_x3d b'
+  | x3e => compare_byte_x3e b'
+  | x3f => compare_byte_x3f b'
+  | x40 => compare_byte_x40 b'
+  | x41 => compare_byte_x41 b'
+  | x42 => compare_byte_x42 b'
+  | x43 => compare_byte_x43 b'
+  | x44 => compare_byte_x44 b'
+  | x45 => compare_byte_x45 b'
+  | x46 => compare_byte_x46 b'
+  | x47 => compare_byte_x47 b'
+  | x48 => compare_byte_x48 b'
+  | x49 => compare_byte_x49 b'
+  | x4a => compare_byte_x4a b'
+  | x4b => compare_byte_x4b b'
+  | x4c => compare_byte_x4c b'
+  | x4d => compare_byte_x4d b'
+  | x4e => compare_byte_x4e b'
+  | x4f => compare_byte_x4f b'
+  | x50 => compare_byte_x50 b'
+  | x51 => compare_byte_x51 b'
+  | x52 => compare_byte_x52 b'
+  | x53 => compare_byte_x53 b'
+  | x54 => compare_byte_x54 b'
+  | x55 => compare_byte_x55 b'
+  | x56 => compare_byte_x56 b'
+  | x57 => compare_byte_x57 b'
+  | x58 => compare_byte_x58 b'
+  | x59 => compare_byte_x59 b'
+  | x5a => compare_byte_x5a b'
+  | x5b => compare_byte_x5b b'
+  | x5c => compare_byte_x5c b'
+  | x5d => compare_byte_x5d b'
+  | x5e => compare_byte_x5e b'
+  | x5f => compare_byte_x5f b'
+  | x60 => compare_byte_x60 b'
+  | x61 => compare_byte_x61 b'
+  | x62 => compare_byte_x62 b'
+  | x63 => compare_byte_x63 b'
+  | x64 => compare_byte_x64 b'
+  | x65 => compare_byte_x65 b'
+  | x66 => compare_byte_x66 b'
+  | x67 => compare_byte_x67 b'
+  | x68 => compare_byte_x68 b'
+  | x69 => compare_byte_x69 b'
+  | x6a => compare_byte_x6a b'
+  | x6b => compare_byte_x6b b'
+  | x6c => compare_byte_x6c b'
+  | x6d => compare_byte_x6d b'
+  | x6e => compare_byte_x6e b'
+  | x6f => compare_byte_x6f b'
+  | x70 => compare_byte_x70 b'
+  | x71 => compare_byte_x71 b'
+  | x72 => compare_byte_x72 b'
+  | x73 => compare_byte_x73 b'
+  | x74 => compare_byte_x74 b'
+  | x75 => compare_byte_x75 b'
+  | x76 => compare_byte_x76 b'
+  | x77 => compare_byte_x77 b'
+  | x78 => compare_byte_x78 b'
+  | x79 => compare_byte_x79 b'
+  | x7a => compare_byte_x7a b'
+  | x7b => compare_byte_x7b b'
+  | x7c => compare_byte_x7c b'
+  | x7d => compare_byte_x7d b'
+  | x7e => compare_byte_x7e b'
+  | x7f => compare_byte_x7f b'
+  | x80 => compare_byte_x80 b'
+  | x81 => compare_byte_x81 b'
+  | x82 => compare_byte_x82 b'
+  | x83 => compare_byte_x83 b'
+  | x84 => compare_byte_x84 b'
+  | x85 => compare_byte_x85 b'
+  | x86 => compare_byte_x86 b'
+  | x87 => compare_byte_x87 b'
+  | x88 => compare_byte_x88 b'
+  | x89 => compare_byte_x89 b'
+  | x8a => compare_byte_x8a b'
+  | x8b => compare_byte_x8b b'
+  | x8c => compare_byte_x8c b'
+  | x8d => compare_byte_x8d b'
+  | x8e => compare_byte_x8e b'
+  | x8f => compare_byte_x8f b'
+  | x90 => compare_byte_x90 b'
+  | x91 => compare_byte_x91 b'
+  | x92 => compare_byte_x92 b'
+  | x93 => compare_byte_x93 b'
+  | x94 => compare_byte_x94 b'
+  | x95 => compare_byte_x95 b'
+  | x96 => compare_byte_x96 b'
+  | x97 => compare_byte_x97 b'
+  | x98 => compare_byte_x98 b'
+  | x99 => compare_byte_x99 b'
+  | x9a => compare_byte_x9a b'
+  | x9b => compare_byte_x9b b'
+  | x9c => compare_byte_x9c b'
+  | x9d => compare_byte_x9d b'
+  | x9e => compare_byte_x9e b'
+  | x9f => compare_byte_x9f b'
+  | xa0 => compare_byte_xa0 b'
+  | xa1 => compare_byte_xa1 b'
+  | xa2 => compare_byte_xa2 b'
+  | xa3 => compare_byte_xa3 b'
+  | xa4 => compare_byte_xa4 b'
+  | xa5 => compare_byte_xa5 b'
+  | xa6 => compare_byte_xa6 b'
+  | xa7 => compare_byte_xa7 b'
+  | xa8 => compare_byte_xa8 b'
+  | xa9 => compare_byte_xa9 b'
+  | xaa => compare_byte_xaa b'
+  | xab => compare_byte_xab b'
+  | xac => compare_byte_xac b'
+  | xad => compare_byte_xad b'
+  | xae => compare_byte_xae b'
+  | xaf => compare_byte_xaf b'
+  | xb0 => compare_byte_xb0 b'
+  | xb1 => compare_byte_xb1 b'
+  | xb2 => compare_byte_xb2 b'
+  | xb3 => compare_byte_xb3 b'
+  | xb4 => compare_byte_xb4 b'
+  | xb5 => compare_byte_xb5 b'
+  | xb6 => compare_byte_xb6 b'
+  | xb7 => compare_byte_xb7 b'
+  | xb8 => compare_byte_xb8 b'
+  | xb9 => compare_byte_xb9 b'
+  | xba => compare_byte_xba b'
+  | xbb => compare_byte_xbb b'
+  | xbc => compare_byte_xbc b'
+  | xbd => compare_byte_xbd b'
+  | xbe => compare_byte_xbe b'
+  | xbf => compare_byte_xbf b'
+  | xc0 => compare_byte_xc0 b'
+  | xc1 => compare_byte_xc1 b'
+  | xc2 => compare_byte_xc2 b'
+  | xc3 => compare_byte_xc3 b'
+  | xc4 => compare_byte_xc4 b'
+  | xc5 => compare_byte_xc5 b'
+  | xc6 => compare_byte_xc6 b'
+  | xc7 => compare_byte_xc7 b'
+  | xc8 => compare_byte_xc8 b'
+  | xc9 => compare_byte_xc9 b'
+  | xca => compare_byte_xca b'
+  | xcb => compare_byte_xcb b'
+  | xcc => compare_byte_xcc b'
+  | xcd => compare_byte_xcd b'
+  | xce => compare_byte_xce b'
+  | xcf => compare_byte_xcf b'
+  | xd0 => compare_byte_xd0 b'
+  | xd1 => compare_byte_xd1 b'
+  | xd2 => compare_byte_xd2 b'
+  | xd3 => compare_byte_xd3 b'
+  | xd4 => compare_byte_xd4 b'
+  | xd5 => compare_byte_xd5 b'
+  | xd6 => compare_byte_xd6 b'
+  | xd7 => compare_byte_xd7 b'
+  | xd8 => compare_byte_xd8 b'
+  | xd9 => compare_byte_xd9 b'
+  | xda => compare_byte_xda b'
+  | xdb => compare_byte_xdb b'
+  | xdc => compare_byte_xdc b'
+  | xdd => compare_byte_xdd b'
+  | xde => compare_byte_xde b'
+  | xdf => compare_byte_xdf b'
+  | xe0 => compare_byte_xe0 b'
+  | xe1 => compare_byte_xe1 b'
+  | xe2 => compare_byte_xe2 b'
+  | xe3 => compare_byte_xe3 b'
+  | xe4 => compare_byte_xe4 b'
+  | xe5 => compare_byte_xe5 b'
+  | xe6 => compare_byte_xe6 b'
+  | xe7 => compare_byte_xe7 b'
+  | xe8 => compare_byte_xe8 b'
+  | xe9 => compare_byte_xe9 b'
+  | xea => compare_byte_xea b'
+  | xeb => compare_byte_xeb b'
+  | xec => compare_byte_xec b'
+  | xed => compare_byte_xed b'
+  | xee => compare_byte_xee b'
+  | xef => compare_byte_xef b'
+  | xf0 => compare_byte_xf0 b'
+  | xf1 => compare_byte_xf1 b'
+  | xf2 => compare_byte_xf2 b'
+  | xf3 => compare_byte_xf3 b'
+  | xf4 => compare_byte_xf4 b'
+  | xf5 => compare_byte_xf5 b'
+  | xf6 => compare_byte_xf6 b'
+  | xf7 => compare_byte_xf7 b'
+  | xf8 => compare_byte_xf8 b'
+  | xf9 => compare_byte_xf9 b'
+  | xfa => compare_byte_xfa b'
+  | xfb => compare_byte_xfb b'
+  | xfc => compare_byte_xfc b'
+  | xfd => compare_byte_xfd b'
+  | xfe => compare_byte_xfe b'
+  | xff => compare_byte_xff b'
+  end.
diff --git a/template-coq/theories/utils/MCCompare.v b/template-coq/theories/utils/MCCompare.v
index 250387de3..99c8eea34 100644
--- a/template-coq/theories/utils/MCCompare.v
+++ b/template-coq/theories/utils/MCCompare.v
@@ -1,4 +1,4 @@
-From Coq Require Import ssreflect Extraction OrderedType Orders Ascii String.
+From Coq Require Import ssreflect Extraction OrderedType Orders.
 From Equations Require Import Equations.
 
 Lemma CompareSpec_Proper : Proper (iff ==> iff ==> iff ==> Logic.eq ==> iff) CompareSpec.
@@ -109,296 +109,6 @@ Notation bool_compare := BoolOT.compare.
 
 Local Ltac trd := cbn in *; try reflexivity; try discriminate.
 
-Module AsciiOT <: UsualOrderedType.
-  Definition t := ascii.
-
-  Definition eq : t -> t -> Prop := eq.
-  Definition eq_equiv : Equivalence eq := _.
-
-  Definition compare x y :=
-    let 'Ascii a b c d e f g h := x in
-    let 'Ascii a' b' c' d' e' f' g' h' := y in
-    bool_compare a a'
-      ?? bool_compare b b'
-      ?? bool_compare c c'
-      ?? bool_compare d d'
-      ?? bool_compare e e'
-      ?? bool_compare f f'
-      ?? bool_compare g g'
-      ?? bool_compare h h'.
-
-  Ltac tryone a a' H :=
-    destruct a, a'; simpl in H; try (reflexivity || discriminate).
-
-  Lemma compare_eq : forall x y, compare x y = Eq <-> x = y.
-  Proof.
-    destruct x as [a b c d e f g h].
-    destruct y as [a' b' c' d' e' f' g' h'].
-    split. intros H.
-    tryone a a' H;
-      tryone b b' H;
-      tryone c c' H;
-      tryone d d' H;
-      tryone e e' H;
-      tryone f f' H;
-      tryone g g' H;
-      tryone h h' H; reflexivity.
-    intros H; injection H. intros; subst.
-    destruct a', b', c', d', e', f', g', h'; reflexivity.
-  Qed.
-
-  Lemma compare_refl x : compare x x = Eq.
-  Proof.
-    now apply compare_eq.
-  Qed.
-
-  Lemma compare_Lt x y : compare x y = Gt <-> compare y x = Lt.
-  Proof.
-    destruct x as [a b c d e f g h].
-    destruct y as [a' b' c' d' e' f' g' h'].
-    split.
-    intros H.
-    tryone a a' H;
-      tryone b b' H;
-      tryone c c' H;
-      tryone d d' H;
-      tryone e e' H;
-      tryone f f' H;
-      tryone g g' H;
-      tryone h h' H; try reflexivity.
-    intros H.
-    tryone a a' H;
-      tryone b b' H;
-      tryone c c' H;
-      tryone d d' H;
-      tryone e e' H;
-      tryone f f' H;
-      tryone g g' H;
-      tryone h h' H; try reflexivity.
-  Qed.
-
-  Definition lt x y := compare x y = Lt.
-
-  Definition compare_spec (x y : t) : CompareSpec (eq x y) (lt x y) (lt y x) (compare x y).
-  Proof.
-    case_eq (compare x y).
-    intros.
-    - constructor 1.
-      now apply compare_eq.
-    - intros. apply CompLt.
-      destruct x as [a b c d e f g h].
-      destruct y as [a' b' c' d' e' f' g' h'].
-      unfold lt. apply H.
-    - intros. apply CompGt. red. now apply compare_Lt.
-  Qed.
-  
-  Lemma compare_sym (x y : t) : compare x y = CompOpp (compare y x).
-  Proof.
-    destruct (compare_spec x y).
-    - red in H; subst. now rewrite compare_refl.
-    - symmetry. rewrite (proj2 (compare_Lt _ _)); auto.
-    - symmetry. rewrite (proj1 (compare_Lt _ _)); auto.
-      now apply compare_Lt.
-  Qed.
-  
-  Lemma lt_irreflexive : Irreflexive lt.
-  Proof.
-    intro x. destruct x. unfold complement, lt; cbn.
-    destruct b, b0, b1, b2, b3, b4, b5, b6; cbn; discriminate.
-  Qed.
-  
-  Lemma lt_transitive : Transitive lt.
-  Proof.
-    intros [a b c d e f g h] [a' b' c' d' e' f' g' h']
-          [a'' b'' c'' d'' e'' f'' g'' h''].
-    unfold lt, compare.
-    intros H1 H2.
-    destruct a, a', a''; trd;
-    destruct b, b', b''; trd;
-    destruct c, c', c''; trd;
-    destruct d, d', d''; trd;
-    destruct e, e', e''; trd;
-    destruct f, f', f''; trd;
-    destruct g, g', g''; trd;
-    destruct h, h', h''; trd;
-    eapply transitive_bool_lt; eassumption.
-  Qed.
-
-  Global Instance lt_strorder : StrictOrder lt.
-  Proof.
-    split.
-    - apply lt_irreflexive.
-    - apply lt_transitive.
-  Qed.
-
-  Definition lt_compat : Proper (eq ==> eq ==> iff) lt.
-  Proof.
-    unfold eq. intros x y e z t e'. subst; reflexivity.
-  Qed.
- 
-  (* Bonus *)
- Definition eqb (l1 l2 : t) : bool
- := match compare l1 l2 with Eq => true | _ => false end.
-
-  Definition eq_leibniz (x y : t) : eq x y -> x = y := id.
-
-  Definition eq_dec (l1 l2 : t) : {l1 = l2}+{l1 <> l2}.
-  Proof.
-    destruct (compare l1 l2) eqn:e.
-    apply compare_eq in e. now left.
-    right; intros eq. destruct (compare_spec l1 l2); try discriminate. subst. now apply irreflexivity in H.
-    right; intros eq. destruct (compare_spec l1 l2); try discriminate. subst. now apply irreflexivity in H.
-  Defined.
-
-End AsciiOT.
-
-Notation ascii_compare := AsciiOT.compare.
-
-Module StringOT <: UsualOrderedType.
-  Definition t := string.
-
-  Definition eq : t -> t -> Prop := eq.
-  Definition eq_equiv : Equivalence eq := _.
-
-  Fixpoint compare x y :=
-    match x, y with
-    | EmptyString, EmptyString => Eq
-    | String a s, String b s' =>
-      match ascii_compare a b with
-      | Eq => compare s s'
-      | Lt => Lt
-      | Gt => Gt
-      end
-    | EmptyString, String _ _ => Lt
-    | String _ _, EmptyString => Gt
-    end.
-  
-  Definition lt x y : Prop := compare x y = Lt.
-  
-  Lemma compare_eq : forall x y : string, compare x y = Eq <-> eq x y.
-  Proof.
-    split.
-    induction x in y |- *.
-    + destruct y. reflexivity.
-      discriminate.
-    + destruct y. discriminate.
-      simpl. destruct (AsciiOT.compare_spec a a0); red in H; subst; try discriminate.
-      intros eq. red. f_equal; auto. now apply IHx.
-    + intros ->.
-      induction y. reflexivity.
-      simpl. now rewrite AsciiOT.compare_refl.
-  Qed.
-  
-  Lemma compare_refl x : compare x x = Eq.
-  Proof.
-    now apply compare_eq.
-  Qed.
-
-  Lemma compare_lt : forall x y : string, compare x y = Lt <-> compare y x = Gt.
-  Proof.
-    split.
-    - induction x in y |- *.
-      + destruct y. discriminate.
-        reflexivity.
-      + destruct y. discriminate.
-        simpl. destruct (AsciiOT.compare_spec a a0); intros H'; red in H; subst; try discriminate.
-        rewrite AsciiOT.compare_refl //; auto.
-        apply AsciiOT.compare_Lt in H. now rewrite H.
-    - induction x in y |- *.
-      + destruct y. discriminate.
-        reflexivity.
-      + destruct y. discriminate.
-        simpl. rewrite (AsciiOT.compare_sym a a0).
-        destruct (AsciiOT.compare_spec a0 a); cbn; try congruence.
-        auto.
-  Qed.
-
-  Definition compare_spec (x y : t) : CompareSpec (eq x y) (lt x y) (lt y x) (compare x y).
-  Proof.
-    case_eq (compare x y); intros H.
-    - apply CompEq. now apply compare_eq.
-    - apply CompLt; assumption.
-    - apply CompGt. red. now apply compare_lt.
-  Qed.
-  
-  #[local] Instance lt_transitive : Transitive lt.
-  Proof.
-    red. unfold lt.
-    intro s; induction s.
-    - induction y; cbn.
-      + intuition.
-      + intros [|]. discriminate. reflexivity.
-    - intros [|y1 y2]. discriminate.
-      intros [|z1 z2]. discriminate.
-      cbn. case_eq (ascii_compare a y1); try discriminate.
-      + intro Ha; apply AsciiOT.compare_eq in Ha; subst.
-        destruct (ascii_compare y1 z1); try discriminate.
-        intros; eauto. reflexivity.
-      + intros Ha _. case_eq (ascii_compare y1 z1); try discriminate.
-        intros Hy1; apply AsciiOT.compare_eq in Hy1; subst. now rewrite Ha.
-        intro Hy1. eapply AsciiOT.lt_transitive in Ha.
-        specialize (Ha Hy1). now rewrite Ha.
-  Qed.
-  
-  Lemma compare_sym (x y : string) : compare x y = CompOpp (compare y x).
-  Proof.
-    destruct (compare_spec x y).
-    - red in H; subst.
-      rewrite (proj2 (compare_eq _ _)); auto. reflexivity.
-    - rewrite (proj1 (compare_lt _ _)); auto.
-    - rewrite (proj2 (compare_lt _ _)); auto.
-      red in H.
-      now apply compare_lt.
-  Qed.
-  
-  Lemma compare_trans (x y z : string) c : compare x y = c -> compare y z = c -> compare x z = c.
-  Proof.
-    destruct (compare_spec x y); subst; intros <-;
-    destruct (compare_spec y z); subst; try congruence.
-    eapply transitivity in H0. 2:eassumption. red in H0. subst. now rewrite compare_refl.
-    eapply transitivity in H0. 2:eassumption. now red in H0.
-    eapply transitivity in H. 2:eassumption.
-    now apply compare_lt in H.
-  Qed.
-  
-  Definition lt_irreflexive : Irreflexive lt.
-  Proof.
-    intro x. red; unfold lt.
-    now rewrite compare_refl.
-  Qed.
-
-  Global Instance lt_strorder : StrictOrder lt.
-  Proof.
-    split.
-    - apply lt_irreflexive.
-    - apply lt_transitive.
-  Qed.
-
-  Definition lt_compat : Proper (eq ==> eq ==> iff) lt.
-  Proof.
-    unfold eq. intros x y e z t e'. subst; reflexivity.
-  Qed.
- 
-  (* Bonus *)
-  Definition eqb (l1 l2 : t) : bool := 
-    match compare l1 l2 with Eq => true | _ => false end.
-
-  Definition eq_leibniz (x y : t) : eq x y -> x = y := id.
-
-  Definition eq_dec (l1 l2 : t) : {l1 = l2}+{l1 <> l2}.
-  Proof.
-    destruct (compare l1 l2) eqn:e.
-    apply compare_eq in e. now left.
-    right; intros eq. destruct (compare_spec l1 l2); try discriminate. subst. now apply irreflexivity in H.
-    right; intros eq. destruct (compare_spec l1 l2); try discriminate. subst. now apply irreflexivity in H.
-  Defined.
-
-End StringOT.
-
-Notation string_compare := StringOT.compare.
-Notation string_compare_eq := StringOT.compare_eq.
-Notation CompareSpec_string := StringOT.compare_spec.
-
 Module ListOrderedType (A : UsualOrderedType) <: UsualOrderedType. 
   Definition t := list A.t.
   Import List. Import ListNotations.
@@ -413,12 +123,7 @@ Module ListOrderedType (A : UsualOrderedType) <: UsualOrderedType.
 
   Definition eq : t -> t -> Prop := eq.
   Definition eq_equiv : Equivalence eq := _.
-
-  Definition eq_dec (l1 l2 : t) : {l1 = l2}+{l1 <> l2}.
-  Proof.
-    decide equality. apply A.eq_dec.
-  Defined.
-
+  
   Inductive lt_ : t -> t -> Prop :=
   | lt_nil_cons hd tl : lt_ [] (hd :: tl)
   | lt_cons_cons_hd hd tl hd' tl' : A.lt hd hd' -> lt_ (hd :: tl) (hd' :: tl')
@@ -511,5 +216,22 @@ Module ListOrderedType (A : UsualOrderedType) <: UsualOrderedType.
   
   Definition eq_leibniz (x y : t) : eq x y -> x = y := id.
 
+  Program Definition eqb_dec (x y : t) : { x = y } + { x <> y } := 
+    match eqb x y with
+    | true => left _
+    | false => right _
+    end.
+  Next Obligation.
+    unfold eqb in Heq_anonymous.
+    destruct (compare x y) eqn:hc; try congruence.
+    now eapply compare_eq in hc.
+  Qed.
+  Next Obligation.
+    unfold eqb in Heq_anonymous.
+    rewrite compare_refl in Heq_anonymous. now discriminate.
+  Qed.
+
+  Global Instance eq_dec : EqDec t := { eq_dec := eqb_dec }.
+
 End ListOrderedType.
 
diff --git a/template-coq/theories/utils/MCString.v b/template-coq/theories/utils/MCString.v
index 1ec07e68b..c5d6ef402 100644
--- a/template-coq/theories/utils/MCString.v
+++ b/template-coq/theories/utils/MCString.v
@@ -1,11 +1,12 @@
-From Coq Require Import String Decimal DecimalString ZArith.
-From MetaCoq.Template Require Import MCCompare.
+From Coq Require Import ssreflect ssrbool Decimal DecimalString ZArith.
+From MetaCoq.Template Require Import MCCompare bytestring ReflectEq.
 
-Local Open Scope string_scope.
+Local Open Scope bs.
+Notation string := String.t.
 
 (** When defining [Show] instance for your own datatypes, you sometimes need to
     start a new line for better printing. [nl] is a shorthand for it. *)
-Definition nl : string := String (Ascii.ascii_of_nat 10) EmptyString.
+Definition nl : string := String.String "010"%byte String.EmptyString.
 
 Definition string_of_list_aux {A} (f : A -> string) (sep : string) (l : list A) : string :=
   let fix aux l :=
@@ -25,8 +26,23 @@ Definition print_list {A} (f : A -> string) (sep : string) (l : list A) : string
 Definition parens (top : bool) (s : string) :=
   if top then s else "(" ++ s ++ ")".
 
+Fixpoint string_of_uint n := 
+  match n with
+  | Nil => ""
+  | D0 n => "0" ++ string_of_uint n
+  | D1 n => "1" ++ string_of_uint n
+  | D2 n => "2" ++ string_of_uint n
+  | D3 n => "3" ++ string_of_uint n
+  | D4 n => "4" ++ string_of_uint n
+  | D5 n => "5" ++ string_of_uint n
+  | D6 n => "6" ++ string_of_uint n
+  | D7 n => "7" ++ string_of_uint n
+  | D8 n => "8" ++ string_of_uint n
+  | D9 n => "9" ++ string_of_uint n
+  end.
+
 Definition string_of_nat n : string :=
-  DecimalString.NilEmpty.string_of_uint (Nat.to_uint n).
+  string_of_uint (Nat.to_uint n).
 
 #[global]
 Hint Resolve String.string_dec : eq_dec.
@@ -40,15 +56,3 @@ Definition string_of_Z (z : Z) : string :=
   | Zpos p => string_of_positive p
   | Zneg p => "-" ++ string_of_positive p
   end.
-
-Definition eq_string s s' :=
-  match string_compare s s' with
-  | Eq => true
-  | _ => false
-  end.
-
-Lemma eq_string_refl x : is_true (eq_string x x).
-Proof.
-  unfold eq_string.
-  now rewrite (proj2 (string_compare_eq x x) eq_refl).
-Qed.
diff --git a/template-coq/theories/utils/MCUtils.v b/template-coq/theories/utils/MCUtils.v
index c36249ab3..95e65de6e 100644
--- a/template-coq/theories/utils/MCUtils.v
+++ b/template-coq/theories/utils/MCUtils.v
@@ -12,6 +12,8 @@ Require Export MCPrelude
         MCSquash
         MCRelations
         MCString
+        ReflectEq
+        bytestring
 .
 
 Tactic Notation "destruct" "?" :=
@@ -186,8 +188,8 @@ Proof.
   destruct q. apply Eqdep_dec.UIP_refl_bool.
 Qed.
 
-Axiom todo : String.string -> forall {A}, A.
+Axiom todo : string -> forall {A}, A.
 Ltac todo s := exact (todo s).
 
 From Coq Require Import Extraction.
-Extract Constant todo => "fun s -> failwith (String.concat """" (List.map (String.make 1) s))".
+Extract Constant todo => "fun s -> failwith (Caml_bytestring.caml_string_of_bytestring s)".
diff --git a/template-coq/theories/utils/ReflectEq.v b/template-coq/theories/utils/ReflectEq.v
new file mode 100644
index 000000000..5dc72dfbe
--- /dev/null
+++ b/template-coq/theories/utils/ReflectEq.v
@@ -0,0 +1,205 @@
+From Coq Require Import ssreflect ssrbool List.
+From Equations Require Import Equations.
+Import ListNotations.
+
+(* Some reflection / EqDec lemmata *)
+
+Inductive reflectProp (P : Prop) : bool -> Prop :=
+ | reflectP : P -> reflectProp P true
+ | reflectF : ~ P -> reflectProp P false.
+Derive Signature for reflectProp.
+
+Lemma elimP {T} {b} : reflectProp T b -> b -> T.
+Proof. intros [] => //. Qed.
+Coercion elimP : reflectProp >-> Funclass.
+
+Lemma introP {T} {b} : reflectProp T b -> T -> b.
+Proof. intros [] => //. Qed.
+
+Hint View for move/ introP|2.
+Hint View for apply/ introP|2.
+
+Lemma reflect_reflectProp {P b} : reflect P b -> reflectProp P b.
+Proof.
+  intros []; constructor; auto.
+Qed.
+
+(** If one really wants a computational version. *)
+Remark reflectProp_reflect {P b} : reflectProp P b -> reflect P b.
+Proof.
+  now destruct b; intros H; constructor; depelim H.
+Defined.
+
+Lemma reflect_reflectProp_1 {A} {P : A -> Prop} {b} : (forall x, reflect (P x) (b x)) -> (forall x, reflectProp (P x) (b x)).
+Proof.
+  intros f x. now apply reflect_reflectProp.
+Qed.
+
+Lemma reflect_reflectProp_2 {A B} {P : A -> B -> Prop} {b} : (forall x y, reflect (P x y) (b x y)) -> (forall x y, reflectProp (P x y) (b x y)).
+Proof.
+  intros f x y. now apply reflect_reflectProp.
+Qed.
+
+Class ReflectEq A := {
+  eqb : A -> A -> bool ;
+  eqb_spec : forall x y : A, reflectProp (x = y) (eqb x y) (* Prevent using reflect in computational content *)
+}.
+Arguments eqb : simpl never.
+Infix "==" := eqb (at level 70).
+
+(* If one needs to eliminate a decidable equality in Type, e.g. when working with PCUIC derivations. *)
+Lemma eqb_specT {A} {HR : ReflectEq A} (x y : A) : reflect (x = y) (x == y).
+Proof.
+  eapply reflectProp_reflect. apply eqb_spec.
+Qed.
+
+Lemma eqb_eq {A} `{ReflectEq A} (x y : A) : x == y -> x = y.
+Proof.
+  elim: eqb_spec; auto.
+  discriminate.
+Qed.
+
+Lemma eqb_refl {A} {R : ReflectEq A} (x : A) : x == x.
+Proof.
+  destruct (eqb_spec x x); auto.
+Qed.
+
+Lemma neqb {A} {R : ReflectEq A} (x y : A) : ~~ (x == y) <-> x <> y.
+Proof.
+  destruct (eqb_spec x y); auto; subst; intuition auto.
+Qed.
+
+#[global, program] Instance ReflectEq_EqDec {A} (R : ReflectEq A) : EqDec A := {
+  eq_dec := fun x y => 
+    match eqb x y with
+    | true => left _
+    | false => right _
+    end }.
+Next Obligation.
+  now apply eqb_eq.
+Qed.
+Next Obligation.
+  rewrite eqb_refl in Heq_anonymous.
+  discriminate.
+Qed.
+
+Definition eq_dec_to_bool {A} `{EqDec A} x y :=
+  match eq_dec x y with
+  | left _ => true
+  | right _ => false
+  end.
+
+(* Not an instance to avoid loops and making boolean definitions depend on sumbool ones *)
+#[global, program]
+Definition EqDec_ReflectEq A {E : EqDec A} : ReflectEq A := 
+  {| eqb := eq_dec_to_bool |}.
+Next Obligation.
+Proof.
+  unfold eq_dec_to_bool.
+  destruct (eq_dec x y).
+  all: constructor ; assumption.
+Qed.
+
+Ltac nodec :=
+  let bot := fresh "bot" in
+  try solve [ constructor ; intro bot ; inversion bot ; subst ; tauto ].
+
+Definition eq_option {A} (eqA : A -> A -> bool) (u v : option A) : bool :=
+  match u, v with
+  | Some u, Some v => eqA u v
+  | None, None => true
+  | _, _ => false
+  end.
+
+#[global] Instance reflect_option : forall {A}, ReflectEq A -> ReflectEq (option A).
+Proof.
+  intros A RA. refine {| eqb := eq_option eqb |}.
+  intros x y. destruct x, y.
+  all: cbn.
+  all: try solve [ constructor ; easy ].
+  destruct (eqb_spec a a0) ; nodec.
+  constructor. f_equal. assumption.
+Defined.
+
+Fixpoint eq_list {A} (eqA : A -> A -> bool) (l l' : list A) : bool :=
+  match l, l' with
+  | a :: l, a' :: l' =>
+    if eqA a a' then eq_list eqA l l'
+    else false
+  | [], [] => true
+  | _, _ => false
+  end.
+
+#[global] Instance reflect_list : forall {A}, ReflectEq A -> ReflectEq (list A).
+Proof.
+  intros A RA. refine {| eqb := eq_list eqb |}.
+  intro x. induction x ; intro y ; destruct y.
+  - cbn. constructor. reflexivity.
+  - cbn. constructor. discriminate.
+  - cbn. constructor. discriminate.
+  - cbn. destruct (eqb_spec a a0) ; nodec.
+    destruct (IHx y) ; nodec.
+    subst. constructor. reflexivity.
+Defined.
+
+#[global] Instance reflect_nat : ReflectEq nat := {
+  eqb_spec := reflect_reflectProp_2 PeanoNat.Nat.eqb_spec
+}.
+
+
+Definition eq_bool b1 b2 : bool :=
+  if b1 then b2 else negb b2.
+
+Local Obligation Tactic := idtac.
+
+#[global, program] Instance reflect_bool : ReflectEq bool := {
+  eqb := eq_bool
+}.
+Next Obligation.
+  intros x y. unfold eq_bool.
+  destruct x, y.
+  all: constructor.
+  all: try reflexivity.
+  all: discriminate.
+Defined.
+
+Definition eq_sig_true {A f} `{ReflectEq A} (x y : { z : A | f z = true }) : bool :=
+  proj1_sig x == proj1_sig y.
+
+#[global, program] Instance reflect_sig_true {A f} `{ReflectEq A} : ReflectEq ({ z : A | f z = true }) := {
+  eqb := eq_sig_true
+}.
+Next Obligation.
+  intros A f RA. intros [x hx] [y hy]. unfold eq_sig_true; cbn.
+  destruct (eqb_spec x y) ; nodec. subst.
+  constructor. pose proof (uip hx hy). subst. reflexivity.
+Defined.
+
+
+Definition eq_prod {A B} (eqA : A -> A -> bool) (eqB : B -> B -> bool) x y :=
+  let '(a1, b1) := x in
+  let '(a2, b2) := y in
+  if eqA a1 a2 then eqB b1 b2
+  else false.
+
+#[global, program] Instance reflect_prod : forall {A B}, ReflectEq A -> ReflectEq B -> ReflectEq (A * B) := {
+  eqb := eq_prod eqb eqb
+}.
+Next Obligation.
+  intros A B RA RB [x y] [u v].
+  unfold eq_prod.
+  destruct (eqb_spec x u) ; nodec.
+  destruct (eqb_spec y v) ; nodec.
+  subst. constructor. reflexivity.
+Defined.
+
+Lemma eq_prod_refl :
+  forall A B (eqA : A -> A -> bool) (eqB : B -> B -> bool),
+    (forall a, eqA a a) ->
+    (forall b, eqB b b) ->
+    forall p, eq_prod eqA eqB p p.
+Proof.
+  intros A B eqA eqB eqA_refl eqB_refl [a b].
+  simpl. rewrite eqA_refl. apply eqB_refl.
+Qed.
+
diff --git a/template-coq/theories/utils/bytestring.v b/template-coq/theories/utils/bytestring.v
new file mode 100644
index 000000000..d8f0cad4b
--- /dev/null
+++ b/template-coq/theories/utils/bytestring.v
@@ -0,0 +1,499 @@
+(**
+ * Copyright (C) 2020 BedRock Systems, Inc.
+ * All rights reserved.
+ *
+ * SPDX-License-Identifier: LGPL-2.1 WITH BedRock Exception for use over network,
+ * see repository root for details.
+ *)
+ 
+Require Coq.Strings.String ssrbool.
+Require Import ssreflect.
+Require Import Coq.NArith.NArith.
+Require Import Coq.micromega.Lia.
+From Equations Require Import Equations. 
+Set Primitive Projections.
+Set Default Proof Using "Type".
+From MetaCoq.Template Require Import MCCompare ReflectEq.
+From MetaCoq.Template Require ByteCompare ByteCompareSpec.
+(** bytes *)
+
+Definition byte_parse (b : Byte.byte) : Byte.byte := b.
+Definition byte_print (b : Byte.byte) : Byte.byte := b.
+
+Delimit Scope byte_scope with byte.
+String Notation Byte.byte byte_parse byte_print : byte_scope.
+Bind Scope byte_scope with Byte.byte.
+
+Declare Scope bs_scope.
+Delimit Scope bs_scope with bs.
+
+(** bytestrings *)
+Module String.
+  Inductive t : Set :=
+  | EmptyString
+  | String (_ : Byte.byte) (_ : t).
+  Bind Scope bs_scope with t.
+
+  Fixpoint print (b : t) : list Byte.byte :=
+    match b with
+    | EmptyString => nil
+    | String b bs => b :: print bs
+    end.
+
+  Fixpoint parse (b : list Byte.byte) : t :=
+    match b with
+    | nil => EmptyString
+    | List.cons b bs => String b (parse bs)
+    end.
+
+  Lemma print_parse_inv:
+    forall x : t, parse (print x) = x.
+  Proof.
+    induction x; simpl; intros; auto.
+    f_equal; auto.
+  Qed.
+
+  Fixpoint append (x y : t) : t :=
+    match x with
+    | EmptyString => y
+    | String x xs => String x (append xs y)
+    end.
+  
+  Notation "x ++ y" := (append x y) : bs_scope.
+  
+  Fixpoint to_string (b : t) : String.string :=
+    match b with
+    | EmptyString => Strings.String.EmptyString
+    | String x xs => Strings.String.String (Ascii.ascii_of_byte x) (to_string xs)
+    end.
+  
+  Fixpoint of_string (b : String.string) : t :=
+    match b with
+    | Strings.String.EmptyString => EmptyString
+    | Strings.String.String x xs => String (Ascii.byte_of_ascii x) (of_string xs)
+    end%bs.
+  
+  Fixpoint rev (acc s : t) : t :=
+    match s with
+    | EmptyString => acc
+    | String s ss => rev (String s acc) ss
+    end.
+    
+  (** *** Substrings *)
+
+  (** [substring n m s] returns the substring of [s] that starts
+      at position [n] and of length [m];
+      if this does not make sense it returns [""] *)
+  
+  Fixpoint substring (n m : nat) (s : t) : t :=
+    match n, m, s with
+    | O, O, _ => EmptyString
+    | O, S m', EmptyString => s
+    | O, S m', String c s' => String c (substring 0 m' s')
+    | S n', _, EmptyString => s
+    | S n', _, String c s' => substring n' m s'
+    end.
+  
+  Fixpoint prefix (s1 s2 : t) {struct s1} : bool :=
+    match s1 with
+    | EmptyString => true
+    | String x xs =>
+      match s2 with
+      | EmptyString => false
+      | String y ys =>
+        if Byte.eqb x y then prefix xs ys
+        else false
+      end
+    end%bs.
+  
+  Fixpoint index (n : nat) (s1 s2 : t) {struct s2} : option nat :=
+    match s2 with
+    | EmptyString =>
+        match n with
+        | 0 => match s1 with
+              | EmptyString => Some 0
+              | String _ _ => None
+              end
+        | S _ => None
+        end
+    | String _ s2' =>
+        match n with
+        | 0 =>
+            if prefix s1 s2
+            then Some 0
+            else match index 0 s1 s2' with
+                | Some n0 => Some (S n0)
+                | None => None
+                end
+        | S n' => match index n' s1 s2' with
+                  | Some n0 => Some (S n0)
+                  | None => None
+                  end
+        end
+    end%bs.
+  
+  Fixpoint length (l : t) : nat :=
+    match l with
+    | EmptyString => 0
+    | String _ l => S (length l)
+    end.
+  
+  Local Fixpoint contains (start: nat) (keys: list t) (fullname: t) :bool :=
+    match keys with
+    | List.cons kh ktl =>
+      match index start kh fullname with
+      | Some n => contains (n + length kh) ktl fullname
+      | None => false
+      end
+    | List.nil => true
+    end.
+  
+  Fixpoint eqb (a b : t) : bool :=
+    match a , b with
+    | EmptyString , EmptyString => true
+    | String x xs , String y ys =>
+      if ByteCompare.eqb x y then eqb xs ys else false
+    | _ , _ => false
+    end.
+    
+  Fixpoint compare (xs ys : t) : comparison :=
+    match xs , ys with
+    | EmptyString , EmptyString => Eq
+    | EmptyString , _ => Lt
+    | _ , EmptyString => Gt
+    | String x xs , String y ys =>
+      match ByteCompare.compare x y with
+      | Eq => compare xs ys
+      | x => x
+      end
+    end.
+
+  Lemma eqb_compare xs ys : eqb xs ys = match compare xs ys with Eq => true | _ => false end.
+  Proof.
+    induction xs in ys |- *; destruct ys => /= //.
+    rewrite ByteCompareSpec.eqb_compare.
+    destruct ByteCompare.compare => //.
+  Qed.
+
+  Fixpoint concat (sep : t) (s : list t) : t :=
+    match s with
+    | nil => EmptyString
+    | cons s nil => s
+    | cons s xs => s ++ sep ++ concat sep xs
+    end.
+
+End String.
+
+Definition bs := String.t.
+Notation string := String.t.
+
+Bind Scope bs_scope with bs.
+
+String Notation String.t String.parse String.print : bs_scope.
+
+Notation "x ++ y" := (String.append x y) : bs_scope.
+  
+Import String.
+
+(** comparison *)
+Require Import Orders Coq.Structures.OrderedType.
+
+Lemma to_N_inj : forall x y, Byte.to_N x = Byte.to_N y <-> x = y.
+Proof.
+  split.
+  2: destruct 1; reflexivity.
+  intros.
+  assert (Some x = Some y).
+  { do 2 rewrite <- Byte.of_to_N.
+    destruct H. reflexivity. }
+  injection H0. auto.
+Qed.
+
+Module OT_byte <: OrderedType.OrderedType with Definition t := Byte.byte.
+  Definition t := Byte.byte.
+  Definition eq := @Logic.eq t.
+  Definition lt := fun l r => ByteCompare.compare l r = Lt.
+  Theorem eq_refl : forall x : t, eq x x.
+  Proof.
+    intros; apply eq_refl.
+  Qed.
+  Theorem eq_sym : forall x y : t, eq x y -> eq y x.
+  Proof.
+    apply eq_sym.
+  Qed.
+  Theorem eq_trans : forall x y z : t, eq x y -> eq y z -> eq x z.
+  Proof.
+    apply eq_trans.
+  Qed.
+  Theorem lt_trans : forall x y z : t, lt x y -> lt y z -> lt x z.
+  Proof.
+    exact ByteCompareSpec.lt_trans.
+  Qed.
+  Theorem lt_not_eq : forall x y : t, lt x y -> not (eq x y).
+  Proof.
+    apply ByteCompareSpec.lt_not_eq.
+  Qed.
+  Definition compare (x y : t) : OrderedType.Compare lt eq x y.
+    refine  (
+    match ByteCompare.compare x y as X return ByteCompare.compare x y = X -> OrderedType.Compare lt eq x y  with
+    | Eq => fun pf => OrderedType.EQ _
+    | Lt => fun pf => OrderedType.LT pf
+    | Gt => fun pf => OrderedType.GT _
+    end (Logic.eq_refl)).
+    now apply ByteCompareSpec.compare_eq in pf.
+    rewrite ByteCompareSpec.compare_opp in pf.
+    apply CompOpp_iff in pf. apply pf.
+  Defined.
+
+  Definition eq_dec : forall x y : t, {eq x y} + {not (eq x y)} := Classes.eq_dec.
+End OT_byte.
+
+Global Instance byte_eqdec : Classes.EqDec Byte.byte := _.
+
+Module StringOT <: UsualOrderedType.
+  Definition t := string.
+
+  Definition eq : t -> t -> Prop := eq.
+  Definition eq_equiv : Equivalence eq := _.
+
+  Definition compare := String.compare.
+  Definition lt x y : Prop := compare x y = Lt.
+
+  Theorem compare_spec : forall x y, CompareSpec (x = y) (lt x y) (lt y x) (compare x y).
+  Proof.
+    induction x; destruct y; simpl.
+    - constructor; reflexivity.
+    - constructor. reflexivity.
+    - constructor. reflexivity.
+    - unfold lt; simpl. destruct (ByteCompareSpec.compare_spec b b0); simpl.
+      + subst. destruct (IHx y); constructor; eauto.
+        congruence. now rewrite ByteCompareSpec.compare_eq_refl.
+      + constructor; auto.
+      + red in H. rewrite H. constructor; auto.
+  Qed.
+  
+  Theorem eq_refl : forall x : t, eq x x.
+  Proof.
+    reflexivity.
+  Qed.
+  Theorem eq_sym : forall x y : t, eq x y -> eq y x.
+  Proof.
+    eapply eq_sym.
+  Qed.
+  Theorem eq_trans : forall x y z : t, eq x y -> eq y z -> eq x z.
+  Proof.
+    eapply eq_trans.
+  Qed.
+  Theorem lt_trans : forall x y z : t, lt x y -> lt y z -> lt x z.
+  Proof.
+    unfold lt.
+    induction x; destruct y; simpl; try congruence.
+    - destruct z; congruence.
+    - destruct (ByteCompareSpec.compare_spec b b0); subst.
+      + destruct z; auto.
+        destruct (ByteCompare.compare b0 b); auto.
+        eauto.
+      + destruct z; auto.
+        red in H.
+        destruct (ByteCompareSpec.compare_spec b0 b1).
+        * subst. intros _. now rewrite H.
+        * generalize (OT_byte.lt_trans _ _ _ H H0). unfold OT_byte.lt.
+          intro X; rewrite X. auto.
+        * congruence.
+      + congruence.
+  Qed.
+  Theorem lt_not_eq : forall x y : t, lt x y -> not (eq x y).
+  Proof.
+    unfold lt, eq.
+    intros. intro. subst.
+    induction y; simpl in *; try congruence.
+    rewrite ByteCompareSpec.compare_eq_refl in H. auto.
+  Qed.
+
+  #[global] Program Instance reflect_eq_string : ReflectEq t := {
+    eqb := eqb
+  }.
+  Next Obligation.
+    rename x into s, y into s'.
+    destruct (eqb s s') eqn:e; constructor.
+    - rewrite String.eqb_compare in e. fold (compare s s') in e.
+      now destruct (compare_spec s s').
+    - rewrite String.eqb_compare in e.
+      fold (compare s s') in e.
+      destruct (compare_spec s s') => //.
+      now apply lt_not_eq. now apply not_eq_sym, lt_not_eq.
+  Qed.
+
+  Definition eq_dec : forall x y : t, {eq x y} + {not (eq x y)} := Classes.eq_dec.
+
+  Lemma compare_eq : forall x y : string, compare x y = Eq <-> eq x y.
+  Proof.
+    intros.
+    destruct (compare_spec x y); intuition auto; try congruence.
+    - apply lt_not_eq in H; contradiction.
+    - apply lt_not_eq in H. symmetry in H0. contradiction.
+  Qed.
+  
+  Lemma compare_refl x : compare x x = Eq.
+  Proof.
+    now apply compare_eq.
+  Qed.
+
+  Lemma compare_lt : forall x y : string, compare x y = Lt <-> compare y x = Gt.
+  Proof.
+    intros x y.
+    destruct (compare_spec x y).
+    all:split; try congruence; subst.
+    - intros hc.
+      fold (compare y y) in hc. now rewrite compare_refl in hc.
+    - intros _.
+      destruct (compare_spec y x); subst.
+      * eapply lt_not_eq in H. elim H; reflexivity.
+      * eapply lt_trans in H; try eassumption.
+        eapply lt_not_eq in H. elim H; reflexivity.
+      * reflexivity.
+  Qed.
+  
+  #[local] Instance lt_transitive : Transitive lt.
+  Proof.
+    red. eapply lt_trans.
+  Qed.
+  
+  Lemma compare_sym (x y : string) : compare x y = CompOpp (compare y x).
+  Proof.
+    destruct (compare_spec x y).
+    - subst.
+      rewrite (proj2 (compare_eq _ _)); auto. reflexivity.
+    - rewrite (proj1 (compare_lt _ _)); auto.
+    - rewrite (proj2 (compare_lt _ _)); auto.
+      red in H.
+      now apply compare_lt.
+  Qed.
+  
+  Lemma compare_trans (x y z : string) c : compare x y = c -> compare y z = c -> compare x z = c.
+  Proof.
+    destruct (compare_spec x y); subst; intros <-;
+    destruct (compare_spec y z); subst; try congruence.
+    eapply transitivity in H0. 2:eassumption. intros; apply H0.
+    eapply transitivity in H. 2:eassumption.
+    now apply compare_lt in H.
+  Qed.
+  
+  Definition lt_irreflexive : Irreflexive lt.
+  Proof.
+    intro x. red; unfold lt.
+    now rewrite compare_refl.
+  Qed.
+
+  Global Instance lt_strorder : StrictOrder lt.
+  Proof.
+    split.
+    - apply lt_irreflexive.
+    - apply lt_transitive.
+  Qed.
+
+  Definition lt_compat : Proper (eq ==> eq ==> iff) lt.
+  Proof.
+    unfold eq. intros x y e z t e'. subst; reflexivity.
+  Qed.
+ 
+  Definition eq_leibniz (x y : t) : eq x y -> x = y := id.
+
+End StringOT.
+
+Notation string_compare := StringOT.compare.
+Notation string_compare_eq := StringOT.compare_eq.
+Notation CompareSpec_string := StringOT.compare_spec.
+
+(** To perform efficient pretty printing, one needs to use a tree structure 
+  to avoid quadratic overhead of appending strings. *)
+Module Tree.
+  Local Open Scope bs_scope.
+  Inductive t := 
+  | string : String.t -> t
+  | append : t -> t -> t.
+
+  Coercion string : String.t >-> t.
+
+  Infix "++" := append.
+
+  Fixpoint to_rev_list_aux t acc :=
+    match t with
+    | string s => cons s acc
+    | append s s' => to_rev_list_aux s' (to_rev_list_aux s acc)
+    end.
+  
+  Fixpoint to_string_acc acc l := 
+    match l with
+    | nil => acc
+    | cons s xs => to_string_acc (String.append s acc) xs
+    end.
+
+  Definition to_string t := 
+    let l := to_rev_list_aux t nil in
+    to_string_acc "" l.
+  
+  (* Definition test := "a" ++ "b" ++ "v" ++ "c".
+  Eval compute in to_string test. *)
+
+  (* Fixpoint to_string_acc t acc := 
+    match t with
+    | string s => String.append s acc
+    | append s s' => to_string_acc s (to_string_acc s' acc)
+    end.
+
+  Definition to_string t := to_string_acc t "". *)
+
+  Definition string_of_list_aux {A} (f : A -> t) (sep : t) (l : list A) :=
+    let fix aux l :=
+        match l return t with
+        | nil => ""
+        | cons a nil => f a
+        | cons a l => f a ++ sep ++ aux l
+      end
+    in aux l.
+
+  Definition string_of_list {A} (f : A -> t) l :=
+    "[" ++ string_of_list_aux f "," l ++ "]".
+
+  Definition print_list {A} (f : A -> t) (sep : t) (l : list A) : t :=
+    string_of_list_aux f sep l.
+    
+  Fixpoint concat (sep : t) (s : list t) : t :=
+    match s with
+    | nil => EmptyString
+    | cons s nil => s
+    | cons s xs => s ++ sep ++ concat sep xs
+    end.
+
+  Definition parens (top : bool) (s : t) :=
+    if top then s else "(" ++ s ++ ")".
+    
+End Tree.
+
+(* Tests *)
+(*
+
+Local Open Scope bs_scope.
+Import String.
+Definition x := Eval compute in Tree.to_string (Tree.concat (Tree.string "") (List.repeat (Tree.string "frliqhgrnvcrlkejflqrjfljkl") 10000)).
+Definition y := Eval compute in String.concat "" (List.repeat "frliqhgrnvcrlkejflqrjfljkl" 10000) ++ "'".
+
+Time Eval compute in String.compare x y. (* 0.02s *)
+
+Import String.
+Fixpoint String.compare' (xs ys : bs) : comparison :=
+  match xs , ys with
+  | EmptyString, EmptyString => Eq
+  | EmptyString , _ => Lt
+  | _ , EmptyString => Gt
+  | String x xs , String y ys =>
+    match compare x y with
+    | Eq => String.compare' xs ys
+    | x => x
+    end
+  end.
+
+Time Eval vm_compute in String.compare x y. (* 0.14s *)
+Time Eval vm_compute in String.compare' x y. (* 0.03s~0.04s, i.e. more than 3 times faster *)
+*)
\ No newline at end of file
diff --git a/template-coq/update_plugin.sh b/template-coq/update_plugin.sh
index ee9c2afba..171799dd3 100755
--- a/template-coq/update_plugin.sh
+++ b/template-coq/update_plugin.sh
@@ -1,6 +1,8 @@
 #!/usr/bin/env bash
 SED=`which gsed || which sed`
-TOCOPY="ast_denoter.ml ast_quoter.ml denoter.ml plugin_core.ml plugin_core.mli reification.ml quoter.ml run_extractable.ml run_extractable.mli tm_util.ml"
+TOCOPY="ast_denoter.ml ast_quoter.ml denoter.ml plugin_core.ml plugin_core.mli reification.ml quoter.ml run_extractable.ml run_extractable.mli tm_util.ml \
+  caml_nat.mli caml_nat.ml caml_byte.ml caml_byte.mli caml_bytestring.ml"
+SED=`which gsed || which sed`
 
 # Test if gen-src is older than src
 if [[ ! -f "gen-src/denoter.ml" ||
diff --git a/test-suite/bug6.v b/test-suite/bug6.v
index 59070a02e..45e724e4e 100644
--- a/test-suite/bug6.v
+++ b/test-suite/bug6.v
@@ -1,4 +1,5 @@
 Require Import MetaCoq.Template.Loader.
+Import bytestring.
 
 Definition I (t:Type) (x:t) : t := x.
 Definition II := I (forall t:Type, t -> t) I.
diff --git a/test-suite/bugkncst.v b/test-suite/bugkncst.v
index ef0767b26..e00e73606 100644
--- a/test-suite/bugkncst.v
+++ b/test-suite/bugkncst.v
@@ -13,8 +13,6 @@ Function Plus1 (n: nat) {measure id n} : nat :=
 Defined.
 
 Require Import Coq.Lists.List.
-Require Import Coq.Strings.String.
-Require Import Coq.Strings.Ascii.
 Require Import Coq.Bool.Bool.
 Require Import MetaCoq.Template.Loader.
 Require Import MetaCoq.Template.All.
@@ -41,7 +39,7 @@ Fixpoint pocc_term (n:nat) (t:term): bool :=
         | tLambda _ ty t => pocc_term n t || pocc_term n ty
         | tLetIn _ dfn ty t => pocc_term n dfn || pocc_term n t || pocc_term n ty
         | tApp fn args => pocc_term n fn || fold_left orb (map (pocc_term n) args) false
-        | tConst nm _ => if kername_eq_dec str nm then true else false
+        | tConst nm _ => if eqb str nm then true else false
         | tCase _ ty mch brs =>
           existsb (pocc_term n) (pparams ty) || pocc_term n (preturn ty) || 
           pocc_term n mch ||
@@ -55,7 +53,7 @@ Fixpoint pocc_term (n:nat) (t:term): bool :=
   (** does [tConst str] occur anywhere in a program? **)
 
 Definition bound_global_decl (d : kername * global_decl) : bool :=
-  if kername_eq_dec str (fst d) then true else false.
+  if eq_kername str (fst d) then true else false.
 
 Definition bound_program (p : program) := List.existsb bound_global_decl (fst p).(declarations).
 
@@ -70,7 +68,7 @@ Definition pocc_program p := pocc_term 2000 (snd p) || List.existsb pocc_global_
 
 End occ_term_Sec.
 
-Require Import List String. Import ListNotations. Open Scope string_scope.
+Require Import List. Import ListNotations. Open Scope bs_scope.
 (* MetaCoq Test Unquote (tConst (MPfile ["Nat"; "PeanoNat"; "Arith"; "Coq"], "pred") []) . *)
 
 Eval vm_compute in (eq_refl : pocc_program (MPfile ["Nat"; "PeanoNat"; "Arith"; "Coq"], "pred") p_Plus1 = false).
diff --git a/test-suite/extractable.v b/test-suite/extractable.v
index c101ac890..458c4f6bd 100644
--- a/test-suite/extractable.v
+++ b/test-suite/extractable.v
@@ -5,7 +5,7 @@ From MetaCoq.Template Require Import
 From MetaCoq.Template.TemplateMonad Require Import
      Common Extractable.
 
-Local Open Scope string_scope.
+Local Open Scope bs_scope.
 Import MCMonadNotation.
 
 Notation "<% x %>" := (ltac:(let p y := exact y in quote_term x p))
@@ -24,7 +24,7 @@ MetaCoq Run
             (fun t => tmPrint t)).
 
 MetaCoq Run
-    (tmBind (tmDefinition "two" None <% 1 + 1 %>)
+    (tmBind (tmDefinition "two"%bs None <% 1 + 1 %>)
             (fun kn => tmPrint (Ast.tConst kn nil))).
 
 MetaCoq Run
diff --git a/test-suite/issue27.v b/test-suite/issue27.v
index e95fb3c1c..8414b0fa4 100644
--- a/test-suite/issue27.v
+++ b/test-suite/issue27.v
@@ -1,4 +1,4 @@
 Require Import MetaCoq.Template.All.
-Require Export String List.
-Open Scope string.
+Require Export List.
+Open Scope bs_scope.
 MetaCoq Run (tmLemma "test" (@nil nat = @nil nat)).
diff --git a/test-suite/issue28.v b/test-suite/issue28.v
index a488c0160..efa3baea4 100644
--- a/test-suite/issue28.v
+++ b/test-suite/issue28.v
@@ -1,6 +1,6 @@
-Require Import MetaCoq.Template.All MetaCoq.Template.Pretty.
-Require Export String List.
-Open Scope string.
+Require Import MetaCoq.Template.All MetaCoq.Template.utils.bytestring MetaCoq.Template.Pretty.
+Require Export List.
+Open Scope bs_scope.
 Import ListNotations.
 Import MCMonadNotation.
 
diff --git a/test-suite/opaque.v b/test-suite/opaque.v
index 001f4a692..5c76a50ef 100644
--- a/test-suite/opaque.v
+++ b/test-suite/opaque.v
@@ -1,11 +1,11 @@
-From Coq Require Import String List PeanoNat.
+From Coq Require Import List Nat.
 From MetaCoq.Template Require Import All.
 
-Import MCMonadNotation String ListNotations.
+Import MCMonadNotation ListNotations.
 
 Definition foo : nat. exact 0. Qed.
 
-Local Open Scope string_scope.
+Local Open Scope bs_scope.
 MetaCoq Quote Recursively Definition foo_syn := foo.
 MetaCoq Quote Recursively Definition comm_syn := PeanoNat.Nat.add_comm.
 
diff --git a/test-suite/plugin-demo/src/g_demo_plugin.mlg b/test-suite/plugin-demo/src/g_demo_plugin.mlg
index 7f9797c32..1cc2ca482 100644
--- a/test-suite/plugin-demo/src/g_demo_plugin.mlg
+++ b/test-suite/plugin-demo/src/g_demo_plugin.mlg
@@ -13,12 +13,12 @@ END
 
 VERNAC COMMAND EXTEND Make_lens_vernac CLASSIFIED AS SIDEFF STATE program
 | [ "Make" "Lens" ident(name) ] ->
-     { Run_extractable.run_vernac (genLensN (Tm_util.string_to_list (Names.Id.to_string name))) }
+     { Run_extractable.run_vernac (genLensN (Caml_bytestring.bytestring_of_caml_string (Names.Id.to_string name))) }
 END
 
 
 VERNAC COMMAND EXTEND Unquote_vernac CLASSIFIED AS SIDEFF STATE program
 | [ "LookupPrint" ident(name) ] ->
      { let nstr = Names.Id.to_string name in
-       Run_extractable.run_vernac (lookupPrint (Tm_util.string_to_list nstr)) }
+       Run_extractable.run_vernac (lookupPrint (Caml_bytestring.bytestring_of_caml_string nstr)) }
 END
diff --git a/test-suite/plugin-demo/theories/MyPlugin.v b/test-suite/plugin-demo/theories/MyPlugin.v
index 6d455f49c..07b73fe52 100644
--- a/test-suite/plugin-demo/theories/MyPlugin.v
+++ b/test-suite/plugin-demo/theories/MyPlugin.v
@@ -1,11 +1,12 @@
 Require Import Coq.Lists.List.
 From MetaCoq.Template Require Import
-     Ast
+     bytestring Ast
      Loader
      TemplateMonad.Extractable.
 Import TemplateMonad.Extractable.
 From MetaCoq Require Import Template.BasicAst Template.AstUtils Ast.
 
+Open Scope bs_scope.
 
 Notation TemplateMonad := TM.
 Fixpoint mconcat (ls : list (TemplateMonad unit)) : TM unit :=
@@ -45,7 +46,7 @@ Notation "<% x %>" := (ltac:(let p y := exact y in quote_term x p))
 (*   | ConstructRef ind _ => ind.(inductive_mind) *)
 (*   end. *)
 
-Definition tmResolve (nm : String.string) : TM (option kername) :=
+Definition tmResolve (nm : String.t) : TM (option kername) :=
   tmBind (tmLocate nm)
          (fun gr =>
             match gr with
@@ -76,9 +77,7 @@ Fixpoint countTo (n : nat) : list nat :=
   | S m => countTo m ++ (m :: nil)
   end.
 
-Require Import String.
-Open Scope string_scope.
-Definition prepend (ls : string) (i : ident) : ident :=
+Definition prepend (ls : String.t) (i : ident) : ident :=
   ls ++ i.
 
 Definition cBuild_Lens := <% Build_Lens %>.
@@ -155,14 +154,14 @@ Definition opBind {A B} (a: option A) (f: A -> option B) : option B :=
   | None  => None
   end.
 
-Definition genLensN (baseName : String.string) : TM unit :=
+Definition genLensN (baseName : String.t) : TM unit :=
   tmBind (tmLocate baseName) (fun gr =>
     match gr with
     | (IndRef kn) :: _ =>
       let name := kn.(inductive_mind) in
       let ty := Ast.tInd
-        {| BasicAst.inductive_mind := name
-         ; BasicAst.inductive_ind := 0 (* TODO: fix for mutual records *) |} List.nil in
+        {| Kernames.inductive_mind := name
+         ; Kernames.inductive_ind := 0 (* TODO: fix for mutual records *) |} List.nil in
       tmBind (tmQuoteInductive name) (fun ind =>
           match getFields ind with
           | Some info =>
@@ -182,7 +181,7 @@ Definition genLensN (baseName : String.string) : TM unit :=
     end).
 
 
-Definition tmQuoteConstantR (nm : String.string) (bypass : bool) : TM _ :=
+Definition tmQuoteConstantR (nm : String.t) (bypass : bool) : TM _ :=
   tmBind (tmLocate nm)
          (fun gr =>
             match gr with
@@ -192,7 +191,7 @@ Definition tmQuoteConstantR (nm : String.string) (bypass : bool) : TM _ :=
             | _ => tmReturn None
             end).
 
-Definition lookupPrint (baseName : String.string) : TM unit :=
+Definition lookupPrint (baseName : String.t) : TM unit :=
   tmBind (tmQuoteConstantR baseName true)
          (fun b =>
             match b with
diff --git a/test-suite/proj.v b/test-suite/proj.v
index fc04ec8d5..a8d08ab60 100644
--- a/test-suite/proj.v
+++ b/test-suite/proj.v
@@ -23,7 +23,7 @@ Proof.
    |- ?T => quote_term T (fun x => pose (qgoal:=x))
   end.
   match goal with
-    H:= context [Ast.tProj (BasicAst.mkInd _ 0, 1, 0) _] |- _ => idtac
+    H:= context [Ast.tProj (Kernames.mkInd _ 0, 1, 0) _] |- _ => idtac
   end.
   reflexivity.
 Qed.
diff --git a/test-suite/tmFreshName.v b/test-suite/tmFreshName.v
index f5ce13c68..bf76fb57e 100644
--- a/test-suite/tmFreshName.v
+++ b/test-suite/tmFreshName.v
@@ -1,15 +1,15 @@
-Require Import List Arith String.
+Require Import List Arith.
 Require Import MetaCoq.Template.All.
 Import ListNotations MCMonadNotation.
 
 
-MetaCoq Run (x <- tmFreshName ("x" ++ "y")%string ;;
+MetaCoq Run (x <- tmFreshName ("x" ++ "y")%bs ;;
              tmDefinition x 0).
 
 Check (eq_refl : xy = 0).
 
 
-MetaCoq Run (x <- tmFreshName ("x" ++ "y")%string ;;
+MetaCoq Run (x <- tmFreshName ("x" ++ "y")%bs ;;
              tmDefinition x 1).
 
 Check (eq_refl : xy0 = 1).
diff --git a/test-suite/unfold.v b/test-suite/unfold.v
index 898588aa3..f5eb695c5 100644
--- a/test-suite/unfold.v
+++ b/test-suite/unfold.v
@@ -1,4 +1,5 @@
 From MetaCoq.Template Require Import utils All.
+Import MCMonadNotation.
 
 MetaCoq Test Quote negb.
 MetaCoq Run (tmBind (tmEval (unfold (MPfile ["Datatypes"; "Init"; "Coq"], "negb")) negb) tmPrint).
diff --git a/test-suite/univ.v b/test-suite/univ.v
index e55ed11cf..e3dc6ec46 100644
--- a/test-suite/univ.v
+++ b/test-suite/univ.v
@@ -1,7 +1,7 @@
 From MetaCoq.Template Require Import All.
-Require Import String List Arith.
+Require Import List Arith.
 Import ListNotations MCMonadNotation.
-Open Scope string.
+Open Scope bs_scope.
 
 Notation "'unfolded' d" :=
   ltac:(let y := eval unfold d in d in exact y) (at level 100, only parsing).
diff --git a/translations/translation_utils.v b/translations/translation_utils.v
index 2756bfe92..5d2dee521 100644
--- a/translations/translation_utils.v
+++ b/translations/translation_utils.v
@@ -18,11 +18,10 @@ Fixpoint lookup_tsl_table (E : tsl_table) (gr : global_reference)
   match E with
   | nil => None
   | hd :: tl =>
-    if gref_eq_dec gr (fst hd) then Some (snd hd)
+    if gref_eqb gr (fst hd) then Some (snd hd)
     else lookup_tsl_table tl gr
   end.
 
-
 Definition tsl_context := (global_env_ext * tsl_table)%type.
 
 Definition emptyTC : tsl_context := (empty_ext empty_global_env, []).
@@ -91,9 +90,9 @@ Definition nNamed n := {| binder_name := nNamed n; binder_relevance := Relevant
 Definition tsl_name f := map_binder_annot (tsl_name0 f).
 
 
-Definition tmDebug {A} : A -> TemplateMonad unit
-  (* := tmPrint. *)
-  := fun _ => ret tt.
+Definition tmDebug {A} : A -> TemplateMonad unit :=
+  fun _ => ret tt.
+  (* fun x => tmPrint x ;; ret tt. *)
 
 
 Definition add_global_decl d (Σ : global_env_ext) : global_env_ext