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15 include "basic_2/reducibility/lfpr.ma".
17 (* FOCALIZED PARALLEL COMPUTATION ON LOCAL ENVIRONMENTS *********************)
19 definition lfprs: relation lenv ≝ TC … lfpr.
22 "focalized parallel computation (environment)"
23 'FocalizedPRedStar L1 L2 = (lfprs L1 L2).
25 (* Basic eliminators ********************************************************)
27 lemma lfprs_ind: ∀L1. ∀R:predicate lenv. R L1 →
28 (∀L,L2. ⦃L1⦄ ➡* ⦃L⦄ → ⦃L⦄ ➡ ⦃L2⦄ → R L → R L2) →
29 ∀L2. ⦃L1⦄ ➡* ⦃L2⦄ → R L2.
30 #L1 #R #HL1 #IHL1 #L2 #HL12
31 @(TC_star_ind … HL1 IHL1 … HL12) //
34 lemma lfprs_ind_dx: ∀L2. ∀R:predicate lenv. R L2 →
35 (∀L1,L. ⦃L1⦄ ➡ ⦃L⦄ → ⦃L⦄ ➡* ⦃L2⦄ → R L → R L1) →
36 ∀L1. ⦃L1⦄ ➡* ⦃L2⦄ → R L1.
37 #L2 #R #HL2 #IHL2 #L1 #HL12
38 @(TC_star_ind_dx … HL2 IHL2 … HL12) //
41 (* Basic properties *********************************************************)
43 lemma lfprs_refl: ∀L. ⦃L⦄ ➡* ⦃L⦄.
46 lemma lfprs_strap1: ∀L1,L,L2. ⦃L1⦄ ➡* ⦃L⦄ → ⦃L⦄ ➡ ⦃L2⦄ → ⦃L1⦄ ➡* ⦃L2⦄.
49 lemma lfprs_strap2: ∀L1,L,L2. ⦃L1⦄ ➡ ⦃L⦄ → ⦃L⦄ ➡* ⦃L2⦄ → ⦃L1⦄ ➡* ⦃L2⦄.