Wtil A B f g C D <~> sWtil. Proof. refine (equiv_adjointify (Wtil_rec _ scct sppt) (sWtil_rec _ cct ppt) _ _). - refine (sWtil_ind _ (fun a x => 1) _). intros b y. apply dpath_path_FFlr. rewrite concat_1p, concat_p1. rewrite sWtil_rec_beta_ppt. by symmetry; apply (@Wtil_rec_beta_ppt A B f g C D). - refine (Wtil_ind _ (fun a x => 1) _). intros b y. apply dpath_path_FFlr. rewrite concat_1p, concat_p1. rewrite Wtil_rec_beta_ppt. by symmetry; apply sWtil_rec_beta_ppt. Defined.
Require Import HoTT.Basics. Require Import Types.Paths Types.Forall Types.Sigma Types.Arrow Types.Universe. Require Import HoTT.Colimits.Coeq.