matita/matita/contribs/lambdadelta/basic_2/rt_computation/fpbs_lpxs.ma

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  14
  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".
  18
  19 (* PARALLEL RST-COMPUTATION FOR CLOSURES ************************************)
  20
  21 (* Properties with unbound parallel rt-computation on local environments ****)
  22
  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.
  29
  30 (* Eliminators with unbound parallel rt-computation on local environments ***)
  31
  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/
  40 qed-.