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

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  14
  15 include "basic_2/reducibility/cpr_delift.ma".
  16 include "basic_2/reducibility/cpr_cpr.ma".
  17 include "basic_2/computation/cprs.ma".
  18
  19 (* CONTEXT-SENSITIVE PARALLEL COMPUTATION ON TERMS **************************)
  20
  21 (* Properties on inverse basic term relocation ******************************)
  22
  23 (* Note: this should be stated with tprs *)
  24 lemma cprs_zeta_delift: ∀L,V,T1,T2. L.ⓓV ⊢ ▼*[O, 1] T1 ≡ T2 → L ⊢ +ⓓV.T1 ➡* T2.
  25 #L #V #T1 #T2 * #T #HT1 #HT2
  26 @(cprs_strap2 … (+ⓓV.T)) [ /3 width=3/ | @inj /3 width=3/ ] (**) (* explicit constructor, /5 width=3/ is too slow *)
  27 qed.
  28
  29 (* Basic_1: was only: pr3_gen_cabbr *)
  30 lemma thin_cprs_delift_conf: ∀L,U1,U2. L ⊢ U1 ➡* U2 →
  31                              ∀K,d,e. ▼*[d, e] L ≡ K → ∀T1. L ⊢ ▼*[d, e] U1 ≡ T1 →
  32                              ∃∃T2. K ⊢ T1 ➡* T2 & L ⊢ ▼*[d, e] U2 ≡ T2.
  33 #L #U1 #U2 #H @(cprs_ind … H) -U2 /2 width=3/
  34 #U #U2 #_ #HU2 #IHU1 #K #d #e #HLK #T1 #HTU1
  35 elim (IHU1 … HLK … HTU1) -U1 #T #HT1 #HUT
  36 elim (thin_cpr_delift_conf … HU2 … HLK … HUT) -U -HLK /3 width=3/
  37 qed.