{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 (ap f) (ap_V jr p) @ ap_V f _)) @ moveR_pV _ _ _ (ap_trijoin_general f a jr jg p)^. Proof. induction p. unfold ap_trijoin_general; cbn. by induction (jg b). Defined.
Require Import Basics Types.Paths WildCat Join.Core HoTT.Tactics.