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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 include "basic_2/rt_transition/lfpx_fqup.ma".
16 include "basic_2/rt_computation/lfpxs.ma".
18 (* UNCOUNTED PARALLEL RT-COMPUTATION FOR LOCAL ENV.S ON REFERRED ENTRIES ****)
20 (* Advanced eliminators *****************************************************)
22 (* Basic_2A1: was just: lpxs_ind *)
23 lemma lfpxs_ind: ∀h,G,L1,T. ∀R:predicate lenv. R L1 →
24 (∀L,L2. ⦃G, L1⦄ ⊢ ⬈*[h, T] L → ⦃G, L⦄ ⊢ ⬈[h, T] L2 → R L → R L2) →
25 ∀L2. ⦃G, L1⦄ ⊢ ⬈*[h, T] L2 → R L2.
26 #h #G #L1 #T #R #HL1 #IHL1 #L2 #HL12
27 @(TC_star_ind … HL1 IHL1 … HL12) //
30 (* Basic_2A1: was just: lpxs_ind_dx *)
31 lemma lfpxs_ind_dx: ∀h,G,L2,T. ∀R:predicate lenv. R L2 →
32 (∀L1,L. ⦃G, L1⦄ ⊢ ⬈[h, T] L → ⦃G, L⦄ ⊢ ⬈*[h, T] L2 → R L → R L1) →
33 ∀L1. ⦃G, L1⦄ ⊢ ⬈*[h, T] L2 → R L1.
34 #h #o #G #L2 #R #HL2 #IHL2 #L1 #HL12
35 @(TC_star_ind_dx … HL2 IHL2 … HL12) //
38 (* Advanced properties ******************************************************)
40 (* Basic_2A1: was just: lpxs_refl *)
41 lemma lfpxs_refl: ∀h,G,L,T. ⦃G, L⦄ ⊢ ⬈*[h, T] L.
42 /2 width=1 by lfpx_lfpxs/ qed.