matita/matita/contribs/lambdadelta/basic_2/rt_transition/lfpr_fquq.ma

   1 (**************************************************************************)
   2 (*       ___                                                              *)
   3 (*      ||M||                                                             *)
   4 (*      ||A||       A project by Andrea Asperti                           *)
   5 (*      ||T||                                                             *)
   6 (*      ||I||       Developers:                                           *)
   7 (*      ||T||         The HELM team.                                      *)
   8 (*      ||A||         http://helm.cs.unibo.it                             *)
   9 (*      \   /                                                             *)
  10 (*       \ /        This file is distributed under the terms of the       *)
  11 (*        v         GNU General Public License Version 2                  *)
  12 (*                                                                        *)
  13 (**************************************************************************)
  14
  15 include "basic_2/s_transition/fquq.ma".
  16 include "basic_2/rt_transition/cpm_drops.ma".
  17 include "basic_2/rt_transition/cpr.ma".
  18 include "basic_2/rt_transition/lfpr_fqup.ma".
  19
  20 (* PARALLEL R-TRANSITION FOR LOCAL ENV.S ON REFERRED ENTRIES ****************)
  21
  22 (* Properties with supclosure ***********************************************)
  23
  24 lemma fqu_cpr_trans_dx: ∀h,G1,G2,L1,L2,T1,T2. ⦃G1, L1, T1⦄ ⊐ ⦃G2, L2, T2⦄ →
  25                         ∀U2. ⦃G2, L2⦄ ⊢ T2 ➡[h] U2 →
  26                         ∃∃L,U1. ⦃G1, L1⦄ ⊢ ➡[h, T1] L & ⦃G1, L⦄ ⊢ T1 ➡[h] U1 & ⦃G1, L, U1⦄ ⊐ ⦃G2, L2, U2⦄.
  27 #h #G1 #G2 #L1 #L2 #T1 #T2 #H elim H -G1 -G2 -L1 -L2 -T1 -T2
  28 /3 width=5 by lfpr_pair, cpr_pair_sn, cpr_flat, cpm_bind, fqu_lref_O, fqu_pair_sn, fqu_bind_dx, fqu_flat_dx, ex3_2_intro/
  29 #I #G #L #V #U #T #HUT #U2 #HU2 elim (cpm_lifts … HU2 (Ⓣ) … HUT) -U
  30 /3 width=9 by fqu_drop, drops_refl, drops_drop, ex3_2_intro/
  31 qed-.
  32
  33 lemma fqu_cpr_trans_sn: ∀h,G1,G2,L1,L2,T1,T2. ⦃G1, L1, T1⦄ ⊐ ⦃G2, L2, T2⦄ →
  34                         ∀U2. ⦃G2, L2⦄ ⊢ T2 ➡[h] U2 →
  35                         ∃∃L,U1. ⦃G1, L1⦄ ⊢ ➡[h, T1] L & ⦃G1, L1⦄ ⊢ T1 ➡[h] U1 & ⦃G1, L, U1⦄ ⊐ ⦃G2, L2, U2⦄.
  36 #h #G1 #G2 #L1 #L2 #T1 #T2 #H elim H -G1 -G2 -L1 -L2 -T1 -T2
  37 /3 width=5 by lfpr_pair, cpr_pair_sn, cpr_flat, cpm_bind, fqu_lref_O, fqu_pair_sn, fqu_bind_dx, fqu_flat_dx, ex3_2_intro/
  38 #I #G #L #V #U #T #HUT #U2 #HU2 elim (cpm_lifts … HU2 (Ⓣ) … HUT) -U
  39 /3 width=9 by fqu_drop, drops_refl, drops_drop, ex3_2_intro/
  40 qed-.
  41
  42 (* Properties with optional supclosure **************************************)
  43
  44 lemma fquq_cpr_trans_dx: ∀h,G1,G2,L1,L2,T1,T2. ⦃G1, L1, T1⦄ ⊐⸮ ⦃G2, L2, T2⦄ →
  45                          ∀U2. ⦃G2, L2⦄ ⊢ T2 ➡[h] U2 →
  46                          ∃∃L,U1. ⦃G1, L1⦄ ⊢ ➡[h, T1] L & ⦃G1, L⦄ ⊢ T1 ➡[h] U1 & ⦃G1, L, U1⦄ ⊐⸮ ⦃G2, L2, U2⦄.
  47 #h #G1 #G2 #L1 #L2 #T1 #T2 #H elim H -H
  48 [ #HT12 #U2 #HTU2 elim (fqu_cpr_trans_dx … HT12 … HTU2) /3 width=5 by fqu_fquq, ex3_2_intro/
  49 | * #H1 #H2 #H3 destruct /2 width=5 by ex3_2_intro/
  50 ]
  51 qed-.
  52
  53 lemma fquq_cpr_trans_sn: ∀h,G1,G2,L1,L2,T1,T2. ⦃G1, L1, T1⦄ ⊐⸮ ⦃G2, L2, T2⦄ →
  54                          ∀U2. ⦃G2, L2⦄ ⊢ T2 ➡[h] U2 →
  55                          ∃∃L,U1. ⦃G1, L1⦄ ⊢ ➡[h, T1] L & ⦃G1, L1⦄ ⊢ T1 ➡[h] U1 & ⦃G1, L, U1⦄ ⊐⸮ ⦃G2, L2, U2⦄.
  56 #h #G1 #G2 #L1 #L2 #T1 #T2 #H elim H -H
  57 [ #HT12 #U2 #HTU2 elim (fqu_cpr_trans_sn … HT12 … HTU2) /3 width=5 by fqu_fquq, ex3_2_intro/
  58 | * #H1 #H2 #H3 destruct /2 width=5 by ex3_2_intro/
  59 ]
  60 qed-.