{A} {D : A -> Type} `{DHasEquivs A D} {a b : A} {f : a $-> b} {g : b $-> a} {r : f $o g $== Id b} {s : g $o f $== Id a} {a' : D a} {b' : D b} (f' : DHom f a' b') (g' : DHom g b' a') (r' : DGpdHom r (f' $o' g') (DId b')) (s' : DGpdHom s (g' $o' f') (DId a')) : DGpdHom (cate_inv_adjointify f g r s) (dcate_fun (dcate_adjointify f' g' r' s')^-1$') g'. Proof. apply dcate_inverse_sect. exact ((dcate_buildequiv_fun f' $@R' _) $@' 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.