Commit 0ed0d7f9 authored by Jacques-Henri Jourdan's avatar Jacques-Henri Jourdan

Some properties of imap

parent cdb38447
......@@ -1265,6 +1265,21 @@ Proof.
take_app_alt by (rewrite ?app_length, ?take_length, ?Hk; lia).
(** ** Properties of the [imap] function *)
Lemma imap_cons {B} (f : nat → A → B) x l :
imap f (x :: l) = f 0 x :: imap (f ∘ S) l.
unfold imap. simpl. f_equal. generalize 0.
induction l; intros n; simpl; repeat (auto||f_equal).
Lemma imap_ext {B} (f g : nat → A → B) l :
(∀ i x, f i x = g i x) →
imap f l = imap g l.
unfold imap. intro EQ. generalize 0.
induction l; simpl; intros n; f_equal; auto.
(** ** Properties of the [mask] function *)
Lemma mask_nil f βs : mask f βs (@nil A) = [].
Proof. by destruct βs. Qed.
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