matita/matita/contribs/lambdadelta/basic_2A/etc/delift/cpcs_delift.etc

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  14
  15 include "basic_2/unfold/delift_lift.ma".
  16 include "basic_2/unfold/delift_delift.ma".
  17 include "basic_2/computation/cprs_delift.ma".
  18 include "basic_2/equivalence/cpcs_cpcs.ma".
  19
  20 (* CONTEXT-SENSITIVE PARALLEL EQUIVALENCE ON TERMS **************************)
  21
  22 (* Properties on inverse basic term relocation ******************************)
  23
  24 lemma cpcs_zeta_delift_comm: ∀L,V,T1,T2. L.ⓓV ⊢ ▼*[O, 1] T1 ≡ T2 →
  25                              L ⊢ T2 ⬌* +ⓓV.T1.
  26 /3 width=1/ qed.
  27
  28 (* Basic_1: was only: pc3_gen_cabbr *)
  29 lemma thin_cpcs_delift_mono: ∀L,U1,U2. L ⊢ U1 ⬌* U2 →
  30                              ∀K,d,e. ▼*[d, e] L ≡ K → ∀T1. L ⊢ ▼*[d, e] U1 ≡ T1 →
  31                              ∀T2. L ⊢ ▼*[d, e] U2 ≡ T2 → K ⊢ T1 ⬌* T2.
  32 #L #U1 #U2 #H #K #d #e #HLK #T1 #HTU1 #T2 #HTU2
  33 elim (cpcs_inv_cprs … H) -H #U #HU1 #HU2
  34 elim (thin_cprs_delift_conf … HU1 … HLK … HTU1) -U1 #T #HT1 #HUT
  35 elim (thin_cprs_delift_conf … HU2 … HLK … HTU2) -U2 -HLK #X #HT2 #H
  36 lapply (delift_mono … H … HUT) -L #H destruct /2 width=3/
  37 qed.