{I A : Type} `{Is1Cat A} (coprod : A) (x : I -> A) (z : A) (inj : forall i, x i $-> coprod) : yon_0gpd z coprod $-> prod_0gpd I (fun i => yon_0gpd z (x i)) := cat_prod_corec_inv (coprod : A^op) x z inj.
Require Import Basics.Overture Basics.Tactics Basics.Decidable. Require Import Types.Bool. Require Import WildCat.Core WildCat.Equiv WildCat.Forall WildCat.NatTrans