-(**************************************************************************)
-(* ___ *)
-(* ||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/reducibility/ypr.ma".
-
-(* HYPER PARALLEL COMPUTATION ON CLOSURES ***********************************)
-
-definition yprs: ∀h. sd h → bi_relation lenv term ≝
- λh,g. bi_TC … (ypr h g).
-
-interpretation "hyper parallel computation (closure)"
- 'YPRedStar h g L1 T1 L2 T2 = (yprs h g L1 T1 L2 T2).
-
-(* Basic eliminators ********************************************************)
-
-lemma yprs_ind: ∀h,g,L1,T1. ∀R:relation2 lenv term. R L1 T1 →
- (∀L,L2,T,T2. h ⊢ ⦃L1, T1⦄ •⥸*[g] ⦃L, T⦄ → h ⊢ ⦃L, T⦄ •⥸[g] ⦃L2, T2⦄ → R L T → R L2 T2) →
- ∀L2,T2. h ⊢ ⦃L1, T1⦄ •⥸*[g] ⦃L2, T2⦄ → R L2 T2.
-/3 width=7 by bi_TC_star_ind/ qed-.
-
-lemma yprs_ind_dx: ∀h,g,L2,T2. ∀R:relation2 lenv term. R L2 T2 →
- (∀L1,L,T1,T. h ⊢ ⦃L1, T1⦄ •⥸[g] ⦃L, T⦄ → h ⊢ ⦃L, T⦄ •⥸*[g] ⦃L2, T2⦄ → R L T → R L1 T1) →
- ∀L1,T1. h ⊢ ⦃L1, T1⦄ •⥸*[g] ⦃L2, T2⦄ → R L1 T1.
-/3 width=7 by bi_TC_star_ind_dx/ qed-.
-
-(* Basic properties *********************************************************)
-
-lemma yprs_refl: ∀h,g. bi_reflexive … (yprs h g).
-/2 width=1/ qed.
-
-lemma yprs_strap1: ∀h,g,L1,L,L2,T1,T,T2. h ⊢ ⦃L1, T1⦄ •⥸*[g] ⦃L, T⦄ →
- h ⊢ ⦃L, T⦄ •⥸[g] ⦃L2, T2⦄ → h ⊢ ⦃L1, T1⦄ •⥸*[g] ⦃L2, T2⦄.
-/2 width=4/ qed.
-
-lemma yprs_strap2: ∀h,g,L1,L,L2,T1,T,T2. h ⊢ ⦃L1, T1⦄ •⥸[g] ⦃L, T⦄ →
- h ⊢ ⦃L, T⦄ •⥸*[g] ⦃L2, T2⦄ → h ⊢ ⦃L1, T1⦄ •⥸*[g] ⦃L2, T2⦄.
-/2 width=4/ qed.