Commit 0ac2b4db authored by Ralf Jung's avatar Ralf Jung
Browse files

relate Forall2 and Forall

parent aae110fd
......@@ -2301,6 +2301,7 @@ Qed.
Lemma Forall_Forall2 {A} (Q : A → A → Prop) l :
Forall (λ x, Q x x) l → Forall2 Q l l.
Proof. induction 1; constructor; auto. Qed.
Lemma Forall2_forall `{Inhabited A} B C (Q : A → B → C → Prop) l k :
Forall2 (λ x y, ∀ z, Q z x y) l k ↔ ∀ z, Forall2 (Q z) l k.
......@@ -2310,6 +2311,10 @@ Proof.
- apply IH. intros z. by feed inversion (Hlk z).
Lemma Forall2_Forall {A} P (l1 l2 : list A) :
Forall2 P l1 l2 → Forall (curry P) (zip l1 l2).
Proof. induction 1; constructor; auto. Qed.
Section Forall2.
Context {A B} (P : A → B → Prop).
Implicit Types x : A.
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