{A U V : Type} (w : U <~> V) : forall f : U -> A, transport (fun E : Type => E -> A) (path_universe w) f = (f o w^-1). Proof. intros f. funext y. refine (transport_arrow_toconst _ _ _ @ _). apply ap. apply transport_path_universe_V. Defined.
Require Import HoTT.Basics. Require Import Types.Sigma Types.Forall Types.Arrow Types.Paths Types.Equiv Types.Bool Types.Prod.