emap_compose' {A B : Type} `{HasEquivs A} `{HasEquivs B} (F : A -> B) `{!Is0Functor F, !Is1Functor F} {a b c : A} (f : a $<~> b) (g : b $<~> c) : cate_fun (emap F (g $oE f)) $== cate_fun ((emap F g) $oE (emap F f)). Proof. refine (emap_compose F f g $@ _). symmetry. refine (compose_cate_fun _ _ $@ _). exact (cate_buildequiv_fun _ $@@ cate_buildequiv_fun _). Defined.
Require Import Basics.Utf8 Basics.Overture Basics.Tactics Basics.Equivalences. Require Import WildCat.Core. Require Import WildCat.Opposite.