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4 (* ||A|| A project by Andrea Asperti *)
6 (* ||I|| Developers: *)
7 (* ||T|| The HELM team. *)
8 (* ||A|| http://helm.cs.unibo.it *)
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15 include "basic_2/static/ffdeq_lfeq.ma".
16 include "basic_2/rt_computation/lfpxs_lpxs.ma".
17 include "basic_2/rt_computation/fpbs_lfpxs.ma".
19 (* PARALLEL RST-COMPUTATION FOR CLOSURES ************************************)
21 (* Properties with unbound parallel rt-computation on local environments ****)
23 (* Basic_2A1: uses: fpbs_intro_alt *)
24 lemma fpbs_intro_star: ∀h,o,G1,L1,T1,T. ⦃G1, L1⦄ ⊢ T1 ⬈*[h] T →
25 ∀G,L,T0. ⦃G1, L1, T⦄ ⊐* ⦃G, L, T0⦄ →
26 ∀L0. ⦃G, L⦄ ⊢ ⬈*[h] L0 →
27 ∀G2,L2,T2. ⦃G, L0, T0⦄ ≛[h, o] ⦃G2, L2, T2⦄ → ⦃G1, L1, T1⦄ ≥[h, o] ⦃G2, L2, T2⦄ .
28 /3 width=9 by fpbs_intro_fstar, lfpxs_lpxs/ qed.
30 (* Eliminators with unbound parallel rt-computation on local environments ***)
32 (* Basic_2A1: uses: fpbs_inv_alt *)
33 lemma fpbs_inv_star: ∀h,o,G1,G2,L1,L2,T1,T2. ⦃G1, L1, T1⦄ ≥[h, o] ⦃G2, L2, T2⦄ →
34 ∃∃G,L,L0,T,T0. ⦃G1, L1⦄ ⊢ T1 ⬈*[h] T & ⦃G1, L1, T⦄ ⊐* ⦃G, L, T0⦄
35 & ⦃G, L⦄ ⊢ ⬈*[h] L0 & ⦃G, L0, T0⦄ ≛[h, o] ⦃G2, L2, T2⦄.
36 #h #o #G1 #G2 #L1 #L2 #T1 #T2 #H
37 elim (fpbs_inv_fstar … H) -H #G #L #L0 #T #T0 #HT1 #H10 #HL0 #H02
38 elim (lfpxs_inv_lpxs_lfeq … HL0) -HL0 #L3 #HL3 #HL30
39 /3 width=11 by lfeq_lfdeq_trans, ex4_5_intro/