`{P : A -> Type} (f g : forall x, P x) (p : f == g) : path_forall _ _ (fun x => (p x)^) = (path_forall _ _ p)^. Proof. transitivity (path_forall _ _ (fun x => (apD10 (path_forall _ _ p) x)^)). - f_ap. symmetry. apply (@ap _ _ (fun h x => (h x)^)). apply eisretr. - transitivity (path_forall _ _ (apD10 (path_forall _ _ p)^)). + apply ap, inverse. apply path_forall; intros x. apply apD10_V. + apply eissect. Defined.
Require Import Basics.Overture Basics.Equivalences Basics.PathGroupoids