+++ /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/unfold/lstas.ma".
-include "basic_2/computation/cprs.ma".
-
-(* DECOMPOSED EXTENDED PARALLEL COMPUTATION ON TERMS ************************)
-
-definition cpds: ∀h. sd h → nat → relation4 genv lenv term term ≝
- λh,g,l2,G,L,T1,T2.
- ∃∃T,l1. l2 ≤ l1 & ⦃G, L⦄ ⊢ T1 ▪[h, g] l1 & ⦃G, L⦄ ⊢ T1 •*[h, l2] T & ⦃G, L⦄ ⊢ T ➡* T2.
-
-interpretation "decomposed extended parallel computation (term)"
- 'DPRedStar h g l G L T1 T2 = (cpds h g l G L T1 T2).
-
-(* Basic properties *********************************************************)
-
-lemma sta_cprs_cpds: ∀h,g,G,L,T1,T,T2,l. ⦃G, L⦄ ⊢ T1 ▪[h, g] l+1 → ⦃G, L⦄ ⊢ T1 •[h] T →
- ⦃G, L⦄ ⊢ T ➡* T2 → ⦃G, L⦄ ⊢ T1 •*➡*[h, g, 1] T2.
-/3 width=6 by sta_lstas, ex4_2_intro/ qed.
-
-lemma lstas_cpds: ∀h,g,G,L,T1,T2,l1. ⦃G, L⦄ ⊢ T1 ▪[h, g] l1 →
- ∀l2. l2 ≤ l1 → ⦃G, L⦄ ⊢ T1 •*[h, l2] T2 → ⦃G, L⦄ ⊢ T1 •*➡*[h, g, l2] T2.
-/2 width=6 by ex4_2_intro/ qed.
-
-lemma cprs_cpds: ∀h,g,G,L,T1,T2,l. ⦃G, L⦄ ⊢ T1 ▪[h, g] l → ⦃G, L⦄ ⊢ T1 ➡* T2 →
- ⦃G, L⦄ ⊢ T1 •*➡*[h, g, 0] T2.
-/2 width=6 by lstar_O, ex4_2_intro/ qed.
-
-lemma cpds_refl: ∀h,g,G,L,T,l. ⦃G, L⦄ ⊢ T ▪[h, g] l → ⦃G, L⦄ ⊢ T •*➡*[h, g, 0] T.
-/2 width=2 by cprs_cpds/ qed.
-
-lemma cpds_strap1: ∀h,g,G,L,T1,T,T2,l.
- ⦃G, L⦄ ⊢ T1 •*➡*[h, g, l] T → ⦃G, L⦄ ⊢ T ➡ T2 → ⦃G, L⦄ ⊢ T1 •*➡*[h, g, l] T2.
-#h #g #G #L #T1 #T #T2 #l * /3 width=8 by cprs_strap1, ex4_2_intro/
-qed.
-
-(* Basic forward lemmas *****************************************************)
-
-lemma cpds_fwd_cprs: ∀h,g,G,L,T1,T2. ⦃G, L⦄ ⊢ T1 •*➡*[h, g, 0] T2 →
- ⦃G, L⦄ ⊢ T1 ➡* T2.
-#h #g #G #L #T1 #T2 *
-#T #l #_ #_ #H lapply (lstas_inv_O … H) -l -H
-#H destruct //
-qed-.