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4 (* ||A|| A project by Andrea Asperti *)
6 (* ||I|| Developers: *)
7 (* ||T|| The HELM team. *)
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15 include "basic_2/notation/relations/dpredstar_5.ma".
16 include "basic_2/unfold/sstas.ma".
17 include "basic_2/computation/cprs.ma".
19 (* DECOMPOSED EXTENDED PARALLEL COMPUTATION ON TERMS ************************)
21 definition cpds: ∀h. sd h → lenv → relation term ≝ λh,g,L,T1,T2.
22 ∃∃T. ⦃G, L⦄ ⊢ T1 •*[h, g] T & ⦃G, L⦄ ⊢ T ➡* T2.
24 interpretation "decomposed extended parallel computation (term)"
25 'DPRedStar h g L T1 T2 = (cpds h g L T1 T2).
27 (* Basic properties *********************************************************)
29 lemma cpds_refl: ∀h,g,L. reflexive … (cpds h g L).
32 lemma sstas_cpds: ∀h,g,L,T1,T2. ⦃G, L⦄ ⊢ T1 •*[h, g] T2 → ⦃G, L⦄ ⊢ T1 •*➡*[h, g] T2.
35 lemma cprs_cpds: ∀h,g,L,T1,T2. ⦃G, L⦄ ⊢ T1 ➡* T2 → ⦃G, L⦄ ⊢ T1 •*➡*[h, g] T2.
38 lemma cpds_strap1: ∀h,g,L,T1,T,T2.
39 ⦃G, L⦄ ⊢ T1 •*➡*[h, g] T → ⦃G, L⦄ ⊢ T ➡ T2 → ⦃G, L⦄ ⊢ T1 •*➡*[h, g] T2.
40 #h #g #L #T1 #T #T2 * /3 width=5/
43 lemma cpds_strap2: ∀h,g,L,T1,T,T2,l.
44 ⦃G, L⦄ ⊢ T1 •[h, g] ⦃l+1, T⦄ → ⦃G, L⦄ ⊢ T •*➡*[h, g] T2 → ⦃G, L⦄ ⊢ T1 •*➡*[h, g] T2.
45 #h #g #L #T1 #T #T2 #l #HT1 * /3 width=4/
48 lemma ssta_cprs_cpds: ∀h,g,L,T1,T,T2,l. ⦃G, L⦄ ⊢ T1 •[h, g] ⦃l+1, T⦄ →
49 ⦃G, L⦄ ⊢ T ➡* T2 → ⦃G, L⦄ ⊢ T1 •*➡*[h, g] T2.