Adapt to rocq-prover/rocq#18164 (#103)

Author: Villetaneuse

Bedrock/Word.v

@@ -2,7 +2,6 @@ Require Export Fiat.Common.Coq__8_4__8_5__Compat.
 (** Fixed precision machine words *)
 
 Require Import Coq.Arith.Arith
-        Coq.Arith.Div2
         Coq.NArith.NArith
         Coq.Bool.Bool
         Coq.ZArith.ZArith.

src/ADTRefinement/FixedPoint.v

@@ -1,6 +1,8 @@
 Require Export Fiat.Common.Coq__8_4__8_5__Compat.
 Require Import Fiat.ADT Fiat.ADTNotation.
 Require Export Fiat.Computation.FixComp.
+Require Import Coq.ZArith.ZArith.
+Require Import Coq.Arith.PeanoNat.
 
 Import LeastFixedPointFun.
 
@@ -113,9 +115,8 @@ Lemma length_wf' : forall A len l,
 Proof.
   induction len; simpl; intros;
     constructor; intros.
-  contradiction (NPeano.Nat.nlt_0_r _ H).
+  contradiction (Nat.nlt_0_r _ H).
   apply IHlen.
-  Require Import Coq.ZArith.ZArith.
   omega.
 Qed.
 

src/CertifiedExtraction/Extraction/External/Lists.v

@@ -5,7 +5,7 @@ Require Export Bedrock.Platform.Facade.examples.QsADTs.
 Lemma CompileEmpty_helper {A}:
   forall (lst : list A) (w : W),
     Programming.propToWord (lst = @nil A) w ->
-    ret (bool2w (EqNat.beq_nat (Datatypes.length lst) 0)) ↝ w.
+    ret (bool2w (Nat.eqb (Datatypes.length lst) 0)) ↝ w.
 Proof.
   unfold Programming.propToWord, IF_then_else in *.
   destruct lst; simpl in *; destruct 1; repeat cleanup; try discriminate; fiat_t.
@@ -15,7 +15,7 @@ Hint Resolve CompileEmpty_helper : call_helpers_db.
 
 Lemma ListEmpty_helper :
   forall {A} (seq: list A),
-    (EqNat.beq_nat (Datatypes.length seq) 0) = match seq with
+    (Nat.eqb (Datatypes.length seq) 0) = match seq with
                                                | nil => true
                                                | _ :: _ => false
                                                end.

src/CertifiedExtraction/Extraction/QueryStructures/CallRules/TupleList.v

@@ -123,7 +123,7 @@ Module ADTListCompilation
       GLabelMap.MapsTo fpointer (Axiomatic Empty) env ->
       {{ tenv }}
         Call vtest fpointer (vlst :: nil)
-      {{ [[`vtest ->> (bool2w (EqNat.beq_nat (Datatypes.length lst) 0)) as _]] :: (DropName vtest tenv) }} ∪ {{ ext }} // env.
+      {{ [[`vtest ->> (bool2w (Nat.eqb (Datatypes.length lst) 0)) as _]] :: (DropName vtest tenv) }} ∪ {{ ext }} // env.
   Proof.
     repeat (SameValues_Facade_t_step || facade_cleanup_call || LiftPropertyToTelescope_t || PreconditionSet_t || injections).
 
@@ -144,7 +144,7 @@ Module ADTListCompilation
       GLabelMap.MapsTo fpointer (Axiomatic Empty) env ->
       {{ tenv }}
         Call vtest fpointer (vlst :: nil)
-      {{ [[`vtest ->> (bool2w (EqNat.beq_nat (Datatypes.length (rev lst)) 0)) as _]] :: tenv }} ∪ {{ ext }} // env.
+      {{ [[`vtest ->> (bool2w (Nat.eqb (Datatypes.length (rev lst)) 0)) as _]] :: tenv }} ∪ {{ ext }} // env.
   Proof.
     intros.
     setoid_rewrite rev_length.

src/CertifiedExtraction/Extraction/QueryStructures/QueryStructures.v

@@ -154,7 +154,7 @@ Ltac _compile_length :=
   match_ProgOk
     ltac:(fun prog pre post ext env =>
             match constr:((pre, post)) with
-            | (?pre, Cons ?k (ret (bool2w (EqNat.beq_nat (Datatypes.length (rev ?seq)) 0))) (fun _ => ?pre')) =>
+            | (?pre, Cons ?k (ret (bool2w (Nat.eqb (Datatypes.length (rev ?seq)) 0))) (fun _ => ?pre')) =>
               let vlst := find_fast (wrap (FacadeWrapper := WrapInstance (H := QS_WrapFiatWTupleList)) seq) ext in
               match vlst with
               | Some ?vlst => eapply (WTupleListCompilation.CompileEmpty_spec (idx := 3) (vlst := vlst))

src/Common.v

@@ -1,5 +1,4 @@
 Require Import Coq.Lists.List.
-Require Import Coq.Numbers.Natural.Peano.NPeano.
 Require Import Coq.ZArith.ZArith Coq.Lists.SetoidList.
 Require Export Coq.Setoids.Setoid Coq.Classes.RelationClasses
         Coq.Program.Program Coq.Classes.Morphisms.
@@ -1330,7 +1329,7 @@ Definition path_prod' {A B} {x x' : A} {y y' : B}
 
 Lemma lt_irrefl' {n m} (H : n = m) : ~n < m.
 Proof.
-  subst; apply Lt.lt_irrefl.
+  subst; apply Nat.lt_irrefl.
 Qed.
 
 Lemma or_not_l {A B} (H : A \/ B) (H' : ~A) : B.
@@ -1627,7 +1626,7 @@ Module opt.
   Definition snd {A B} := Eval compute in @snd A B.
   Definition andb := Eval compute in andb.
   Definition orb := Eval compute in orb.
-  Definition beq_nat := Eval compute in EqNat.beq_nat.
+  Definition beq_nat := Eval compute in Nat.eqb.
 
   Module Export Notations.
     Delimit Scope opt_bool_scope with opt_bool.
@@ -1641,7 +1640,7 @@ Module opt2.
   Definition snd {A B} := Eval compute in @snd A B.
   Definition andb := Eval compute in andb.
   Definition orb := Eval compute in orb.
-  Definition beq_nat := Eval compute in EqNat.beq_nat.
+  Definition beq_nat := Eval compute in Nat.eqb.
   Definition leb := Eval compute in Compare_dec.leb.
 
   Module Export Notations.

src/Common/BoundedLookup.v

@@ -141,7 +141,7 @@ Section BoundedIndex.
 
     Fixpoint fin_beq {m n} (p : Fin.t m) (q : Fin.t n) :=
       match p, q with
-      | @Fin.F1 m', @Fin.F1 n' => EqNat.beq_nat m' n'
+      | @Fin.F1 m', @Fin.F1 n' => Nat.eqb m' n'
       | Fin.FS _ _, Fin.F1 _ => false
       | Fin.F1 _, Fin.FS _ _ => false
       | Fin.FS _ p', Fin.FS _ q' => fin_beq p' q'
@@ -153,7 +153,7 @@ Section BoundedIndex.
     Proof.
       intros; pattern n, p, q; eapply Fin.rect2; simpl;
         intuition; try (congruence || discriminate).
-      - symmetry; eapply beq_nat_refl.
+      - eapply Nat.eqb_refl.
       - eauto using Fin.FS_inj.
     Qed.
 

src/Common/Enumerable.v

@@ -20,7 +20,7 @@ Section enum.
 
   Definition enumerate_fun_beq (enumerate : list A) (f g : A -> B)
   : bool
-    := EqNat.beq_nat (List.length (List.filter (fun x => negb (beq (f x) (g x))) enumerate)) 0.
+    := Nat.eqb (List.length (List.filter (fun x => negb (beq (f x) (g x))) enumerate)) 0.
 
   Definition enumerate_fun_bl_in
              (bl : forall x y, beq x y = true -> x = y)
@@ -29,7 +29,7 @@ Section enum.
   Proof.
     unfold enumerate_fun_beq.
     intros H x H'.
-    apply EqNat.beq_nat_true in H.
+    apply Nat.eqb_eq in H.
     apply bl.
     destruct (beq (f x) (g x)) eqn:Heq; [ reflexivity | exfalso ].
     apply Bool.negb_true_iff in Heq.

src/Common/Equality.v

@@ -1,5 +1,6 @@
 Require Import Coq.Lists.List Coq.Lists.SetoidList.
 Require Import Coq.Bool.Bool.
+Require Import Coq.Arith.PeanoNat.
 Require Import Coq.Strings.Ascii.
 Require Import Coq.Strings.String.
 Require Import Coq.Logic.Eqdep_dec.
@@ -379,10 +380,10 @@ Definition internal_prod_dec_lb {A B} eq_A eq_B A_lb B_lb x y
              H
              (surjective_pairing _))).
 
-Global Instance nat_BoolDecR : BoolDecR nat := EqNat.beq_nat.
-Global Instance nat_BoolDec_bl : BoolDec_bl (@eq nat) := @EqNat.beq_nat_true.
+Global Instance nat_BoolDecR : BoolDecR nat := Nat.eqb.
+Global Instance nat_BoolDec_bl : BoolDec_bl (@eq nat) := fun n m => (proj1 (Nat.eqb_eq n m)).
 Global Instance nat_BoolDec_lb : BoolDec_lb (@eq nat) :=
-  fun x y => proj2 (@EqNat.beq_nat_true_iff x y).
+  fun x y => proj2 (@Nat.eqb_eq x y).
 
 Lemma unit_bl {x y} : unit_beq x y = true -> x = y.
 Proof. apply internal_unit_dec_bl. Qed.

src/Common/FixedPoints.v

@@ -62,7 +62,7 @@ Section fixedpoints.
              | _ => omega
              | [ H : forall a, _ -> _ = _ |- _ ] => rewrite H by omega
              | [ H : _ < _ |- _ ] => hnf in H
-             | [ H : S _ <= S _ |- _ ] => apply Le.le_S_n in H
+             | [ H : S _ <= S _ |- _ ] => apply Nat.succ_le_mono in H
              | [ H : sizeof ?x <= ?y, H' : ?y <= sizeof (step ?x) |- _ ]
                => let H'' := fresh in
                   assert (H'' : sizeof (step x) <= sizeof x) by apply step_monotonic;
@@ -95,7 +95,7 @@ Section listpair.
   Lemma step_monotonic lss : sizeof_pair (step lss) <= sizeof_pair lss.
   Proof.
     unfold step, sizeof_pair; simpl;
-      apply Plus.plus_le_compat;
+      apply Nat.add_le_mono;
       apply length_filter.
   Qed.