{A B : Type} {DA : A -> Type} `{DHasEquivs A DA} {DB : B -> Type} `{DHasEquivs B DB} (F : A -> B) `{!Is0Functor F, !Is1Functor F} (F' : forall (a : A), DA a -> DB (F a)) `{!IsD0Functor F F', !IsD1Functor F F'} {a b : A} {f : a $<~> b} {a' : DA a} {b' : DA b} (f' : DCatEquiv f a' b') : DCatEquiv (emap F f) (F' a a') (F' b b') := Build_DCatEquiv (dfmap F F' (dcate_fun f')).
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.