{A B C P : Type} {f g : TriJoin A B C -> P} (h : TriJoinRecPath (trijoin_rec_inv f) (trijoin_rec_inv g)) : f == g. Proof. snrapply trijoin_ind. 1: apply (h1 h). 1: apply (h2 h). 1: apply (h3 h). 1, 2, 3: intros; nrapply transport_paths_FlFr'. 1: apply (h12 h). 1: apply (h13 h). 1: apply (h23 h). intros a b c; cbn beta. apply isinj_trijoin_rec_inv_helper. exact (h123 h a b c). Defined.
Require Import Basics Types.Paths WildCat Join.Core HoTT.Tactics.