{A:Type} (B:A -> Type) (C:forall a, B a -> Type) (x1 x2:A) (p:x1=x2) (f:forall y1:B x1, C x1 y1) (g:forall (y2:B x2), C x2 y2) : (forall (y1:B x1), transportD B C p y1 (f y1) = g (transport B p y1)) <~> (transport (fun x => forall y:B x, C x y) p f = g). Proof. destruct p. apply equiv_path_forall. Defined.
Require Import Basics.Overture Basics.Equivalences Basics.PathGroupoids