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4 (* ||A|| A project by Andrea Asperti *)
6 (* ||I|| Developers: *)
7 (* ||T|| The HELM team. *)
8 (* ||A|| http://helm.cs.unibo.it *)
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15 notation "hvbox( ⦃ term 46 h , break term 46 L ⦄ ⊢ break term 46 T1 • ➡ * break [ term 46 g ] break term 46 T2 )"
16 non associative with precedence 45
17 for @{ 'XPRedStar $h $g $L $T1 $T2 }.
19 notation "hvbox( ⦃ term 46 h , break term 46 L ⦄ ⊢ • ⬊ * break [ term 46 g ] break term 46 T2 )"
20 non associative with precedence 45
21 for @{ 'XSN $h $g $L $T }.
23 include "basic_2/static/lsubss.ma".
24 include "basic_2/reducibility/xpr.ma".
26 include "basic_2/reducibility/cnf.ma".
28 (* EXTENDED PARALLEL COMPUTATION ON TERMS ***********************************)
30 definition xprs: ∀h. sd h → lenv → relation term ≝
31 λh,g,L. TC … (xpr h g L).
33 interpretation "extended parallel computation (term)"
34 'XPRedStar h g L T1 T2 = (xprs h g L T1 T2).
36 (* Basic eliminators ********************************************************)
38 lemma xprs_ind: ∀h,g,L,T1. ∀R:predicate term. R T1 →
39 (∀T,T2. ⦃h, L⦄ ⊢ T1 •➡*[g] T → ⦃h, L⦄ ⊢ T •➡[g] T2 → R T → R T2) →
40 ∀T2. ⦃h, L⦄ ⊢ T1 •➡*[g] T2 → R T2.
41 #h #g #L #T1 #R #HT1 #IHT1 #T2 #HT12
42 @(TC_star_ind … HT1 IHT1 … HT12) //
45 lemma xprs_ind_dx: ∀h,g,L,T2. ∀R:predicate term. R T2 →
46 (∀T1,T. ⦃h, L⦄ ⊢ T1 •➡[g] T → ⦃h, L⦄ ⊢ T •➡*[g] T2 → R T → R T1) →
47 ∀T1. ⦃h, L⦄ ⊢ T1 •➡*[g] T2 → R T1.
48 #h #g #L #T2 #R #HT2 #IHT2 #T1 #HT12
49 @(TC_star_ind_dx … HT2 IHT2 … HT12) //
52 (* Basic properties *********************************************************)
54 lemma xprs_refl: ∀h,g,L. reflexive … (xprs h g L).
57 lemma xprs_strap1: ∀h,g,L,T1,T,T2.
58 ⦃h, L⦄ ⊢ T1 •➡*[g] T → ⦃h, L⦄ ⊢ T •➡[g] T2 → ⦃h, L⦄ ⊢ T1 •➡*[g] T2.
61 lemma xprs_strap2: ∀h,g,L,T1,T,T2.
62 ⦃h, L⦄ ⊢ T1 •➡[g] T → ⦃h, L⦄ ⊢ T •➡*[g] T2 → ⦃h, L⦄ ⊢ T1 •➡*[g] T2.
65 (* Basic inversion lemmas ***************************************************)
67 axiom xprs_inv_cnf1: ∀L,T,U. L ⊢ T ➡* U → L ⊢ 𝐍⦃T⦄ → T = U.
68 #L #T #U #H @(xprs_ind_dx … H) -T //
69 #T0 #T #H1T0 #_ #IHT #H2T0
70 lapply (H2T0 … H1T0) -H1T0 #H destruct /2 width=1/