-interpretation "extended parallel computation (local environment, sn variant)"
- 'PRedSnStar h o G L1 L2 = (lpxs h o G L1 L2).
-
-(* Basic eliminators ********************************************************)
-
-lemma lpxs_ind: ∀h,o,G,L1. ∀R:predicate lenv. R L1 →
- (∀L,L2. ⦃G, L1⦄ ⊢ ➡*[h, o] L → ⦃G, L⦄ ⊢ ➡[h, o] L2 → R L → R L2) →
- ∀L2. ⦃G, L1⦄ ⊢ ➡*[h, o] L2 → R L2.
-#h #o #G #L1 #R #HL1 #IHL1 #L2 #HL12
-@(TC_star_ind … HL1 IHL1 … HL12) //
-qed-.
-
-lemma lpxs_ind_dx: ∀h,o,G,L2. ∀R:predicate lenv. R L2 →
- (∀L1,L. ⦃G, L1⦄ ⊢ ➡[h, o] L → ⦃G, L⦄ ⊢ ➡*[h, o] L2 → R L → R L1) →
- ∀L1. ⦃G, L1⦄ ⊢ ➡*[h, o] L2 → R L1.
-#h #o #G #L2 #R #HL2 #IHL2 #L1 #HL12
-@(TC_star_ind_dx … HL2 IHL2 … HL12) //
-qed-.