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

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   5 (*      ||T||                                                             *)
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  10 (*       \ /        This file is distributed under the terms of the       *)
  11 (*        v         GNU General Public License Version 2                  *)
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  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_sn … HU2 (Ⓣ) … HUT) -U
  30 /3 width=9 by fqu_drop, drops_refl, drops_drop, ex3_2_intro/
  31 qed-.
  32
  33 (* Basic_2A1: uses: fqu_lpr_trans *)
  34 lemma fqu_cpr_trans_sn: ∀h,G1,G2,L1,L2,T1,T2. ⦃G1, L1, T1⦄ ⊐ ⦃G2, L2, T2⦄ →
  35                         ∀U2. ⦃G2, L2⦄ ⊢ T2 ➡[h] U2 →
  36                         ∃∃L,U1. ⦃G1, L1⦄ ⊢ ➡[h, T1] L & ⦃G1, L1⦄ ⊢ T1 ➡[h] U1 & ⦃G1, L, U1⦄ ⊐ ⦃G2, L2, U2⦄.
  37 #h #G1 #G2 #L1 #L2 #T1 #T2 #H elim H -G1 -G2 -L1 -L2 -T1 -T2
  38 /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/
  39 #I #G #L #V #U #T #HUT #U2 #HU2 elim (cpm_lifts_sn … HU2 (Ⓣ) … HUT) -U
  40 /3 width=9 by fqu_drop, drops_refl, drops_drop, ex3_2_intro/
  41 qed-.
  42
  43 (* Properties with optional supclosure **************************************)
  44
  45 lemma fquq_cpr_trans_dx: ∀h,G1,G2,L1,L2,T1,T2. ⦃G1, L1, T1⦄ ⊐⸮ ⦃G2, L2, T2⦄ →
  46                          ∀U2. ⦃G2, L2⦄ ⊢ T2 ➡[h] U2 →
  47                          ∃∃L,U1. ⦃G1, L1⦄ ⊢ ➡[h, T1] L & ⦃G1, L⦄ ⊢ T1 ➡[h] U1 & ⦃G1, L, U1⦄ ⊐⸮ ⦃G2, L2, U2⦄.
  48 #h #G1 #G2 #L1 #L2 #T1 #T2 #H elim H -H
  49 [ #HT12 #U2 #HTU2 elim (fqu_cpr_trans_dx … HT12 … HTU2) /3 width=5 by fqu_fquq, ex3_2_intro/
  50 | * #H1 #H2 #H3 destruct /2 width=5 by ex3_2_intro/
  51 ]
  52 qed-.
  53
  54 (* Basic_2A1: uses: fquq_lpr_trans *)
  55 lemma fquq_cpr_trans_sn: ∀h,G1,G2,L1,L2,T1,T2. ⦃G1, L1, T1⦄ ⊐⸮ ⦃G2, L2, T2⦄ →
  56                          ∀U2. ⦃G2, L2⦄ ⊢ T2 ➡[h] U2 →
  57                          ∃∃L,U1. ⦃G1, L1⦄ ⊢ ➡[h, T1] L & ⦃G1, L1⦄ ⊢ T1 ➡[h] U1 & ⦃G1, L, U1⦄ ⊐⸮ ⦃G2, L2, U2⦄.
  58 #h #G1 #G2 #L1 #L2 #T1 #T2 #H elim H -H
  59 [ #HT12 #U2 #HTU2 elim (fqu_cpr_trans_sn … HT12 … HTU2) /3 width=5 by fqu_fquq, ex3_2_intro/
  60 | * #H1 #H2 #H3 destruct /2 width=5 by ex3_2_intro/
  61 ]
  62 qed-.