proposition: Lemma equiv_into_hprop `{Funext} {A B P : Type} `{IsHProp P} (f : A -> P) : (Join A B -> P) <~> (B -> P).
proof: Proof. apply equiv_iff_hprop. 1: exact (fun f => f o joinr). intros g. snrapply Join_rec. 1,2: assumption. intros a b. apply path_ishprop. Defined.
imports: Basics Types Cubical NullHomotopy Extensions Colimits.Pushout Truncations.Core Truncations.Connectedness Pointed.Core WildCat Spaces.Nat.Core