{A} {D : A -> Type} `{DHasEquivs A D} {a b : A} {f : a $<~> b} {a' : D a} {b' : D b} (f' : DCatEquiv f a' b') : DGpdHom (compose_cate_idl f) (dcate_fun (did_cate b' $oE' f')) (dcate_fun f'). Proof. refine (dcompose_cate_fun _ f' $@' _ $@' dcat_idl (dcate_fun f')). apply (dcate_buildequiv_fun _ $@R' _). Defined.
Require Import Basics.Overture. Require Import Basics.Tactics. Require Import Basics.Equivalences. Require Import Types.Sigma. Require Import WildCat.Core. Require Import WildCat.Displayed. Require Import WildCat.Equiv.