`{H0 : Funext} {A : pType} {P : pFam A} {k : pForall A P} (Q : forall (k' : pForall A P), (k ==* k') -> Type) (q : Q k (reflexivity k)) : phomotopy_ind Q q k (reflexivity k) = q. Proof. change (reflexivity k) with ((equiv_path_pforall k k)^-1%equiv (idpath k)). apply equiv_ind_comp. Defined.
Require Import Basics Types. Require Import Homotopy.IdentitySystems. Require Import WildCat. Require Import Truncations.Core. Require Import ReflectiveSubuniverse. Require Import Extensions.