Fixed Coq realizations of list.why

lib/coq/list/NumOcc.v

@@ -38,9 +38,9 @@ change ((if why_decidable_eq x y then 1 else 0) + num_occ x r = 0 + num_occ x r)
 now case why_decidable_eq.
 Qed.
 
-Lemma Num_Occ_pos : forall {a:Type} {a_WT:WhyType a}, forall (x:a)
-  (l:(list a)), (0 <= (num_occ x l))%Z.
-Proof.
+(* Why3 goal *)
+Lemma Num_Occ_NonNeg : forall {a:Type} {a_WT:WhyType a}, forall (x:a)
+  (l:(list a)), (0%Z <= (num_occ x l))%Z.
 intros a a_WT x l.
 induction l as [|lh lt IHl].
 easy.
@@ -61,7 +61,7 @@ simpl.
 case why_decidable_eq ; intros H ; split.
 intros _.
 clear.
-generalize (Num_Occ_pos x lt).
+generalize (Num_Occ_NonNeg x lt).
 omega.
 now left.
 intros [H'|H'] ; try easy.

lib/coq/list/Permut.v

@@ -128,7 +128,7 @@ induction l1 as [|l1h l1t IHl1].
   contradict H.
   simpl.
   case why_decidable_eq ; intros H.
-  generalize (NumOcc.Num_Occ_pos l2h l2t).
+  generalize (NumOcc.Num_Occ_NonNeg l2h l2t).
   omega.
   now elim H.
 - intros l2 H.
@@ -138,7 +138,7 @@ induction l1 as [|l1h l1t IHl1].
     simpl in H.
     destruct (why_decidable_eq l1h l1h) as [_|H'].
     2: now elim H'.
-    generalize (NumOcc.Num_Occ_pos l1h l1t).
+    generalize (NumOcc.Num_Occ_NonNeg l1h l1t).
     omega.
   destruct (Append.mem_decomp _ _ H') as [l2a [l2b Hl2]].
   rewrite Hl2.

lib/coq/list/RevAppend.v

@@ -32,20 +32,6 @@ easy.
 now simpl.
 Qed.
 
-(* Why3 goal *)
-Lemma rev_append_append_r : forall {a:Type} {a_WT:WhyType a},
-  forall (r:(list a)) (s:(list a)) (t:(list a)),
-  ((Lists.List.rev_append r (Init.Datatypes.app s t)) = (Lists.List.rev_append (Lists.List.rev_append s r) t)).
-Proof.
-intros a a_WT r s t.
-revert r.
-induction s as [|sh st IHs].
-easy.
-intros r.
-simpl.
-now rewrite <- IHs.
-Qed.
-
 (* Why3 goal *)
 Lemma rev_append_length : forall {a:Type} {a_WT:WhyType a},
   forall (s:(list a)) (t:(list a)),
@@ -74,3 +60,17 @@ rewrite <- Append.Append_assoc.
 simpl. reflexivity.
 Qed.
 
+(* Why3 goal *)
+Lemma rev_append_append_r : forall {a:Type} {a_WT:WhyType a},
+  forall (r:(list a)) (s:(list a)) (t:(list a)),
+  ((Lists.List.rev_append r (Init.Datatypes.app s t)) = (Lists.List.rev_append (Lists.List.rev_append s r) t)).
+Proof.
+intros a a_WT r s t.
+revert r.
+induction s as [|sh st IHs].
+easy.
+intros r.
+simpl.
+now rewrite <- IHs.
+Qed.
+

lib/coq/list/Reverse.v

@@ -38,6 +38,14 @@ simpl.
 auto.
 Qed.
 
+(* Why3 goal *)
+Lemma cons_reverse : forall {a:Type} {a_WT:WhyType a}, forall (l:(list a))
+  (x:a),
+  ((Init.Datatypes.cons x (Lists.List.rev l)) = (Lists.List.rev (Init.Datatypes.app l (Init.Datatypes.cons x Init.Datatypes.nil)))).
+intros a a_WT l x.
+now rewrite List.rev_unit.
+Qed.
+
 (* Why3 goal *)
 Lemma reverse_reverse : forall {a:Type} {a_WT:WhyType a},
   forall (l:(list a)), ((Lists.List.rev (Lists.List.rev l)) = l).