matita/matita/contribs/lambdadelta/basic_2/etc/referred/lfpr_fquq.etc

   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/cpm_lsubr.ma".
  18 include "basic_2/rt_transition/cpr.ma".
  19 include "basic_2/rt_transition/lfpr_fqup.ma".
  20
  21 (* PARALLEL R-TRANSITION FOR LOCAL ENV.S ON REFERRED ENTRIES ****************)
  22
  23 (* Properties with supclosure ***********************************************)
  24
  25 lemma fqu_cpr_trans_dx: ∀h,b,G1,G2,L1,L2,T1,T2. ⦃G1, L1, T1⦄ ⊐[b] ⦃G2, L2, T2⦄ →
  26                         ∀U2. ⦃G2, L2⦄ ⊢ T2 ➡[h] U2 →
  27                         ∃∃L,U1. ⦃G1, L1⦄ ⊢ ➡[h, T1] L & ⦃G1, L⦄ ⊢ T1 ➡[h] U1 & ⦃G1, L, U1⦄ ⊐[b] ⦃G2, L2, U2⦄.
  28 #h #b #G1 #G2 #L1 #L2 #T1 #T2 #H elim H -G1 -G2 -L1 -L2 -T1 -T2
  29 /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/
  30 [ /5 width=5 by lsubr_cpm_trans, cpm_bind, lsubr_unit, fqu_clear, ex3_2_intro/
  31 | #I #G #L #U #T #HUT #U2 #HU2 elim (cpm_lifts_sn … HU2 (Ⓣ) … HUT) -U
  32   /3 width=9 by fqu_drop, drops_refl, drops_drop, ex3_2_intro/
  33 ]
  34 qed-.
  35
  36 (* Basic_2A1: uses: fqu_lpr_trans *)
  37 lemma fqu_cpr_trans_sn: ∀h,b,G1,G2,L1,L2,T1,T2. ⦃G1, L1, T1⦄ ⊐[b] ⦃G2, L2, T2⦄ →
  38                         ∀U2. ⦃G2, L2⦄ ⊢ T2 ➡[h] U2 →
  39                         ∃∃L,U1. ⦃G1, L1⦄ ⊢ ➡[h, T1] L & ⦃G1, L1⦄ ⊢ T1 ➡[h] U1 & ⦃G1, L, U1⦄ ⊐[b] ⦃G2, L2, U2⦄.
  40 #h #b #G1 #G2 #L1 #L2 #T1 #T2 #H elim H -G1 -G2 -L1 -L2 -T1 -T2
  41 /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/
  42 [ /5 width=5 by lsubr_cpm_trans, cpm_bind, lsubr_unit, fqu_clear, ex3_2_intro/
  43 | #I #G #L #U #T #HUT #U2 #HU2 elim (cpm_lifts_sn … HU2 (Ⓣ) … HUT) -U
  44   /3 width=9 by fqu_drop, drops_refl, drops_drop, ex3_2_intro/
  45 ]
  46 qed-.
  47
  48 (* Properties with optional supclosure **************************************)
  49
  50 lemma fquq_cpr_trans_dx: ∀h,b,G1,G2,L1,L2,T1,T2. ⦃G1, L1, T1⦄ ⊐⸮[b] ⦃G2, L2, T2⦄ →
  51                          ∀U2. ⦃G2, L2⦄ ⊢ T2 ➡[h] U2 →
  52                          ∃∃L,U1. ⦃G1, L1⦄ ⊢ ➡[h, T1] L & ⦃G1, L⦄ ⊢ T1 ➡[h] U1 & ⦃G1, L, U1⦄ ⊐⸮[b] ⦃G2, L2, U2⦄.
  53 #h #b #G1 #G2 #L1 #L2 #T1 #T2 #H elim H -H
  54 [ #HT12 #U2 #HTU2 elim (fqu_cpr_trans_dx … HT12 … HTU2) /3 width=5 by fqu_fquq, ex3_2_intro/
  55 | * #H1 #H2 #H3 destruct /2 width=5 by ex3_2_intro/
  56 ]
  57 qed-.
  58
  59 (* Basic_2A1: uses: fquq_lpr_trans *)
  60 lemma fquq_cpr_trans_sn: ∀h,b,G1,G2,L1,L2,T1,T2. ⦃G1, L1, T1⦄ ⊐⸮[b] ⦃G2, L2, T2⦄ →
  61                          ∀U2. ⦃G2, L2⦄ ⊢ T2 ➡[h] U2 →
  62                          ∃∃L,U1. ⦃G1, L1⦄ ⊢ ➡[h, T1] L & ⦃G1, L1⦄ ⊢ T1 ➡[h] U1 & ⦃G1, L, U1⦄ ⊐⸮[b] ⦃G2, L2, U2⦄.
  63 #h #b #G1 #G2 #L1 #L2 #T1 #T2 #H elim H -H
  64 [ #HT12 #U2 #HTU2 elim (fqu_cpr_trans_sn … HT12 … HTU2) /3 width=5 by fqu_fquq, ex3_2_intro/
  65 | * #H1 #H2 #H3 destruct /2 width=5 by ex3_2_intro/
  66 ]
  67 qed-.