matita/matita/contribs/lambda_delta/basic_2/equivalence/cpcs_delift.ma

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