A B : join_sym A B o join_sym B A == idmap. Proof. snrapply (Join_ind_FFlr (join_sym B A)). - reflexivity. - reflexivity. - intros a b; cbn beta. apply equiv_p1_1q. refine (ap _ (join_rec_beta_jg _ a b) @ _); cbn. refine (ap_V _ (jglue b a) @ _). refine (ap inverse (join_rec_beta_jg _ b a) @ _). apply inv_V. Defined.
Require Import Basics Types. Require Import Cubical.DPath Cubical.PathSquare. Require Import NullHomotopy. Require Import Extensions. Require Import Colimits.Pushout. Require Import Truncations.Core Truncations.Connectedness. Require Import Pointed.Core. Require Import WildCat. Require Import Spaces.Nat.Core.