Commit 6acc1682 authored by Robbert Krebbers's avatar Robbert Krebbers

Extensionality property for fmap on lists in terms of dist.

parent b5e8ab4e
......@@ -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.
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);
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