{z : A} : prod_0gpd I (fun i => yon_0gpd z (x i)) $<~> yon_0gpd z (cat_coprod I x) := cate_cat_prod_corec I (A:=A^op) (x:=x).
Require Import Basics.Overture Basics.Tactics Basics.Decidable. Require Import Types.Bool. Require Import WildCat.Core WildCat.Equiv WildCat.Forall WildCat.NatTrans