trijoin_rec_beta' {A B C P : Type} (f : TriJoinRecData A B C P) : TriJoinRecPath' (unbundle_trijoinrecdata (trijoin_rec_inv (trijoin_rec f))) (unbundle_trijoinrecdata f). Proof. snrapply Build_TriJoinRecPath'; cbn. - apply trijoin_rec_beta_join12. - apply trijoin_rec_beta_join13. - apply trijoin_rec_beta_join23. - intros a b c. unfold prism'. apply moveR_pM. nrapply trijoin_rec_beta_join123. Defined.
Require Import Basics Types.Paths WildCat Join.Core HoTT.Tactics.