+++ /dev/null
-(**************************************************************************)
-(* ___ *)
-(* ||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/notation/relations/dpredstar_7.ma".
-include "basic_2/static/da.ma".
-include "basic_2/computation/cprs.ma".
-
-(* STRATIFIED DECOMPOSED PARALLEL COMPUTATION ON TERMS **********************)
-
-definition scpds: ∀h. sd h → nat → relation4 genv lenv term term ≝
- λh,o,d2,G,L,T1,T2.
- ∃∃T,d1. d2 ≤ d1 & ⦃G, L⦄ ⊢ T1 ▪[h, o] d1 & ⦃G, L⦄ ⊢ T1 •*[h, d2] T & ⦃G, L⦄ ⊢ T ➡* T2.
-
-interpretation "stratified decomposed parallel computation (term)"
- 'DPRedStar h o d G L T1 T2 = (scpds h o d G L T1 T2).
-
-(* Basic properties *********************************************************)
-
-lemma sta_cprs_scpds: ∀h,o,G,L,T1,T,T2,d. ⦃G, L⦄ ⊢ T1 ▪[h, o] d+1 → ⦃G, L⦄ ⊢ T1 •*[h, 1] T →
- ⦃G, L⦄ ⊢ T ➡* T2 → ⦃G, L⦄ ⊢ T1 •*➡*[h, o, 1] T2.
-/2 width=6 by ex4_2_intro/ qed.
-
-lemma lstas_scpds: ∀h,o,G,L,T1,T2,d1. ⦃G, L⦄ ⊢ T1 ▪[h, o] d1 →
- ∀d2. d2 ≤ d1 → ⦃G, L⦄ ⊢ T1 •*[h, d2] T2 → ⦃G, L⦄ ⊢ T1 •*➡*[h, o, d2] T2.
-/2 width=6 by ex4_2_intro/ qed.
-
-lemma scpds_strap1: ∀h,o,G,L,T1,T,T2,d.
- ⦃G, L⦄ ⊢ T1 •*➡*[h, o, d] T → ⦃G, L⦄ ⊢ T ➡ T2 → ⦃G, L⦄ ⊢ T1 •*➡*[h, o, d] T2.
-#h #o #G #L #T1 #T #T2 #d * /3 width=8 by cprs_strap1, ex4_2_intro/
-qed.
-
-(* Basic forward lemmas *****************************************************)
-
-lemma scpds_fwd_cprs: ∀h,o,G,L,T1,T2. ⦃G, L⦄ ⊢ T1 •*➡*[h, o, 0] T2 →
- ⦃G, L⦄ ⊢ T1 ➡* T2.
-#h #o #G #L #T1 #T2 * /3 width=3 by cprs_strap2, lstas_cpr/
-qed-.