proposition: Lemma is1natural_γ_l (y : D) : Is1Natural (yon y o F) (yon (G y)) (is0functor_F := is0functor_compose (A:=C^op) (B:=D^op) (C:=Type) _ _) (is0functor_G := is0functor_yon (G y)) (fun x : C^op => γ x y).
proof: Proof. nrapply (is1natural_natequiv (natequiv_inverse (Build_NatEquiv (yon (G y)) (yon y o F) (fun x => (γ x y)^-1$) _))). nrapply is1natural_yoneda. nrapply is1functor_compose. 1: nrapply is1functor_op; exact _. nrapply is1functor_opyon. nrapply hasmorext_op; exact _. Defined.
imports: Basics.Utf8 Basics.Overture Basics.Tactics Basics.Equivalences WildCat.Core WildCat.NatTrans WildCat.Equiv WildCat.Prod WildCat.Opposite WildCat.Yoneda WildCat.FunctorCat WildCat.Universe Types.Prod