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15 include "basic_2/reducibility/fpr.ma".
17 (* CONTEXT-FREE PARALLEL COMPUTATION ON CLOSURES ****************************)
19 definition fprs: bi_relation lenv term ≝ bi_TC … fpr.
21 interpretation "context-free parallel computation (closure)"
22 'FocalizedPRedStar L1 T1 L2 T2 = (fprs L1 T1 L2 T2).
24 (* Basic eliminators ********************************************************)
26 lemma fprs_ind: ∀L1,T1. ∀R:relation2 lenv term. R L1 T1 →
27 (∀L,L2,T,T2. ⦃L1, T1⦄ ➡* ⦃L, T⦄ → ⦃L, T⦄ ➡ ⦃L2, T2⦄ → R L T → R L2 T2) →
28 ∀L2,T2. ⦃L1, T1⦄ ➡* ⦃L2, T2⦄ → R L2 T2.
29 /3 width=7 by bi_TC_star_ind/ qed-.
31 lemma fprs_ind_dx: ∀L2,T2. ∀R:relation2 lenv term. R L2 T2 →
32 (∀L1,L,T1,T. ⦃L1, T1⦄ ➡ ⦃L, T⦄ → ⦃L, T⦄ ➡* ⦃L2, T2⦄ → R L T → R L1 T1) →
33 ∀L1,T1. ⦃L1, T1⦄ ➡* ⦃L2, T2⦄ → R L1 T1.
34 /3 width=7 by bi_TC_star_ind_dx/ qed-.
36 (* Basic properties *********************************************************)
38 lemma fprs_refl: bi_reflexive … fprs.
41 lemma fprs_strap1: ∀L1,L,L2,T1,T,T2. ⦃L1, T1⦄ ➡* ⦃L, T⦄ → ⦃L, T⦄ ➡ ⦃L2, T2⦄ →
45 lemma fprs_strap2: ∀L1,L,L2,T1,T,T2. ⦃L1, T1⦄ ➡ ⦃L, T⦄ → ⦃L, T⦄ ➡* ⦃L2, T2⦄ →