{X Y : pType} `{IsCohHSpace Y} (f : X <~>* Y) : IsCohHSpace X. Proof. snrapply Build_IsCohHSpace. - rapply (ishspace_equiv_hspace f). apply ishspace_cohhspace; assumption. - unfold IsCoherent; cbn. refine (_ @@ 1). refine (ap (ap f^-1) _). pelim f. refine (1 @@ _). apply iscoherent. Defined.
Require Import Basics HSpace.Core Pointed.Core Pointed.Loops.