From 6acc16820aceab3f5d9b36c4acf447b1e2ece3b4 Mon Sep 17 00:00:00 2001 From: Robbert Krebbers Date: Mon, 8 Aug 2016 13:44:44 +0200 Subject: [PATCH] Extensionality property for fmap on lists in terms of dist. --- algebra/list.v | 7 +++++-- 1 file changed, 5 insertions(+), 2 deletions(-) diff --git a/algebra/list.v b/algebra/list.v index 3ab4d27c..1c4389ac 100644 --- a/algebra/list.v +++ b/algebra/list.v @@ -81,13 +81,16 @@ End cofe. Arguments listC : clear implicits. (** Functor *) +Lemma list_fmap_ext_ne {A} {B : cofeT} (f g : A → B) (l : list A) n : + (∀ x, f x ≡{n}≡ g x) → f <\$> l ≡{n}≡ g <\$> l. +Proof. intros Hf. by apply Forall2_fmap, Forall_Forall2, Forall_true. Qed. Instance list_fmap_ne {A B : cofeT} (f : A → B) n: Proper (dist n ==> dist n) f → Proper (dist n ==> dist n) (fmap (M:=list) f). -Proof. intros Hf l k ?; by eapply Forall2_fmap, Forall2_impl; eauto. Qed. +Proof. intros Hf l k ?; by eapply Forall2_fmap, Forall2_impl; eauto. Qed. Definition listC_map {A B} (f : A -n> B) : listC A -n> listC B := CofeMor (fmap f : listC A → listC B). Instance listC_map_ne A B n : Proper (dist n ==> dist n) (@listC_map A B). -Proof. intros f f' ? l; by apply Forall2_fmap, Forall_Forall2, Forall_true. Qed. +Proof. intros f g ? l. by apply list_fmap_ext_ne. Qed. Program Definition listCF (F : cFunctor) : cFunctor := {| cFunctor_car A B := listC (cFunctor_car F A B); -- GitLab