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4 (* ||A|| A project by Andrea Asperti *)
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7 (* ||T|| The HELM team. *)
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15 notation "hvbox( ⦃ term 46 L1 , term 46 T1 ⦄ ➡ * break ⦃ term 46 L2 , term 46 T2 ⦄ )"
16 non associative with precedence 45
17 for @{ 'FocalizedPRedStar $L1 $T1 $L2 $T2 }.
19 notation "hvbox( ⦃ term 46 L1 , term 46 T1 ⦄ ➡ ➡ * break ⦃ term 46 L2 , term 46 T2 ⦄ )"
20 non associative with precedence 45
21 for @{ 'FocalizedPRedStarAlt $L1 $T1 $L2 $T2 }.
23 include "basic_2/reducibility/fpr.ma".
25 (* CONTEXT-FREE PARALLEL COMPUTATION ON CLOSURES ****************************)
27 definition fprs: bi_relation lenv term ≝ bi_TC … fpr.
29 interpretation "context-free parallel computation (closure)"
30 'FocalizedPRedStar L1 T1 L2 T2 = (fprs L1 T1 L2 T2).
32 (* Basic eliminators ********************************************************)
34 lemma fprs_ind: ∀L1,T1. ∀R:relation2 lenv term. R L1 T1 →
35 (∀L,L2,T,T2. ⦃L1, T1⦄ ➡* ⦃L, T⦄ → ⦃L, T⦄ ➡ ⦃L2, T2⦄ → R L T → R L2 T2) →
36 ∀L2,T2. ⦃L1, T1⦄ ➡* ⦃L2, T2⦄ → R L2 T2.
37 /3 width=7 by bi_TC_star_ind/ qed-.
39 lemma fprs_ind_dx: ∀L2,T2. ∀R:relation2 lenv term. R L2 T2 →
40 (∀L1,L,T1,T. ⦃L1, T1⦄ ➡ ⦃L, T⦄ → ⦃L, T⦄ ➡* ⦃L2, T2⦄ → R L T → R L1 T1) →
41 ∀L1,T1. ⦃L1, T1⦄ ➡* ⦃L2, T2⦄ → R L1 T1.
42 /3 width=7 by bi_TC_star_ind_dx/ qed-.
44 (* Basic properties *********************************************************)
46 lemma fpr_fprs: ∀L1,L2,T1,T2. ⦃L1, T1⦄ ➡ ⦃L2, T2⦄ → ⦃L1, T1⦄ ➡* ⦃L2, T2⦄.
49 lemma fprs_refl: bi_reflexive … fprs.
52 lemma fprs_strap1: ∀L1,L,L2,T1,T,T2. ⦃L1, T1⦄ ➡* ⦃L, T⦄ → ⦃L, T⦄ ➡ ⦃L2, T2⦄ →
56 lemma fprs_strap2: ∀L1,L,L2,T1,T,T2. ⦃L1, T1⦄ ➡ ⦃L, T⦄ → ⦃L, T⦄ ➡* ⦃L2, T2⦄ →