{J W P : Type} (f : J -> P) (a : J) (jr : W -> J) (jg : forall w, a = jr w) {b c : W} (p : b = c) : ap_trijoin_general f a jr jg p = (1 @@ ap_compose _ f _)^ @ (transport_paths_Fr _ _)^ @ apD (fun x => ap f (jg x)) p. Proof. induction p. unfold ap_trijoin_general; simpl. induction (jg b). reflexivity. Defined.
Require Import Basics Types.Paths WildCat Join.Core HoTT.Tactics.