+(**************************************************************************)
+(* ___ *)
+(* ||M|| *)
+(* ||A|| A project by Andrea Asperti *)
+(* ||T|| *)
+(* ||I|| Developers: *)
+(* ||T|| The HELM team. *)
+(* ||A|| http://helm.cs.unibo.it *)
+(* \ / *)
+(* \ / This file is distributed under the terms of the *)
+(* v GNU General Public License Version 2 *)
+(* *)
+(**************************************************************************)
+
+include "basic_2/computation/yprs_csups.ma".
+include "basic_2/computation/ysteps.ma".
+
+(* ITERATED STEP OF HYPER PARALLEL COMPUTATION ON CLOSURES ******************)
+
+(* Properties on iterated supclosure ****************************************)
+
+lemma csups_ysteps: ∀h,g,L1,L2,T1,T2. ⦃L1, T1⦄ >* ⦃L2, T2⦄ →
+ h ⊢ ⦃L1, T1⦄ •⭃*[g] ⦃L2, T2⦄.
+#h #g #L1 #L2 #T1 #T2 #H
+lapply (csups_fwd_cw … H) #H1
+@ysteps_intro /2 width=1/ -H #H2 #H3 destruct
+elim (lt_refl_false … H1)
+qed.