(A B C : Type) : NatEquiv (trijoinrecdata_0gpd_fun A B C) (trijoinrecdata_0gpd_fun B A C). Proof. snrapply Build_NatEquiv. - intro P. snrapply cate_adjointify. 1, 2: apply trijoinrecdata_twist. 1, 2: apply trijoinrecdata_twist_inv. - snrapply Build_Is1Natural. intros P Q g f; simpl. bundle_trijoinrecpath. all: intros; cbn. + symmetry; apply ap_V. + reflexivity. + reflexivity. + by triangle_ind f b a c. Defined.
Require Import Basics Types WildCat Join.Core Join.TriJoin Spaces.Nat.Core.