`{Funext} A B `{IsHProp A} `{IsHProp B} : Join A B <~> hor A B. Proof. apply equiv_iff_hprop. - exact (Join_rec (fun a => tr (inl a)) (fun b => tr (inr b)) (fun _ _ => path_ishprop _ _)). - apply Trunc_rec, push. 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.