matita/matita/contribs/lambdadelta/basic_2/equivalence/cpcs_lpss.ma

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  14
  15 include "basic_2/substitution/lpss_lpss.ma".
  16 include "basic_2/computation/cprs_lpss.ma".
  17 include "basic_2/equivalence/cpcs_cpcs.ma".
  18
  19 (* CONTEXT-SENSITIVE PARALLEL EQUIVALENCE ON TERMS **************************)
  20
  21 (* Properties on sn parallel substitution for local environments ************)
  22
  23 lemma cpcs_lpss_conf: ∀L1,L2. L1 ⊢ ▶* L2 → ∀T1,T2. L1 ⊢ T1 ⬌* T2 → L2 ⊢ T1 ⬌* T2.
  24 #L1 #L2 #HL12 #T1 #T2 #H
  25 elim (cpcs_inv_cprs … H) -H #T #HT1 #HT2
  26 elim (cprs_lpss_conf_dx … HT1 … HL12) -HT1 #U1 #H1 #HTU1
  27 elim (cprs_lpss_conf_dx … HT2 … HL12) -L1 #U2 #H2 #HTU2
  28 elim (cpss_conf … H1 … H2) -T #U #HU1 #HU2
  29 lapply (cprs_cpss_trans … HTU1 … HU1) -U1
  30 lapply (cprs_cpss_trans … HTU2 … HU2) -U2 /2 width=3/
  31 qed-.
  32
  33 lemma cpcs_lpss_cpss_conf: ∀L1,L2. L1 ⊢ ▶* L2 →
  34                            ∀T,T2. L1 ⊢ T ⬌* T2 →
  35                            ∀T1. L2 ⊢ T ▶* T1 →
  36                            L2 ⊢ T1 ⬌* T2.
  37 #L1 #L2 #HL12 #T #T2 #HT2 #T1 #HT1
  38 lapply (cpcs_lpss_conf … HL12 … HT2) -L1 #HT2
  39 lapply (cpcs_cpss_conf … HT1 … HT2) -T //
  40 qed-.
  41
  42 lemma cpcs_lpss_cpss2_conf: ∀L1,L2. L1 ⊢ ▶* L2 → ∀T1,T2. L1 ⊢ T1 ⬌* T2 →
  43                             ∀T3. L2 ⊢ T1 ▶* T3 → ∀T4. L2 ⊢ T2 ▶* T4 →
  44                             L2 ⊢ T3 ⬌* T4.
  45 #L1 #L2 #HL12 #T1 #T2 #HT12 #T3 #HT13 #T4 #HT24
  46 lapply (cpcs_lpss_cpss_conf … HL12 … HT12 … HT13) -L1 -T1 #HT32
  47 lapply (cpcs_cpss_strap1 … HT32 … HT24) -T2 //
  48 qed-.