matita/matita/contribs/lambda_delta/Basic_2/computation/cprs_lcprs.ma

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  14
  15 include "Basic_2/computation/cprs_cprs.ma".
  16 include "Basic_2/computation/lcprs_lcprs.ma".
  17
  18 (* CONTEXT-SENSITIVE PARALLEL COMPUTATION ON TERMS **************************)
  19
  20 (* Properties exploiting context-senstive computation on local environments *)
  21
  22 (* Basic_1: was just: pr3_pr3_pr3_t *)
  23 lemma lcprs_cprs_trans: ∀L1,L2. L1 ⊢ ➡* L2 →
  24                         ∀T1,T2. L2 ⊢ T1 ➡* T2 → L1 ⊢ T1 ➡* T2.
  25 #L1 #L2 #HL12 @(lcprs_ind … HL12) -L2 // /3 width=3/
  26 qed.
  27
  28 (* Advanced inversion lemmas ************************************************)
  29
  30 (* Basic_1: was pr3_gen_abbr *)
  31 lemma cprs_inv_abbr1: ∀L,V1,T1,U2. L ⊢ ⓓV1. T1 ➡* U2 →
  32                       (∃∃V2,T2. L ⊢ V1 ➡* V2 & L. ⓓV1 ⊢ T1 ➡* T2 &
  33                                 U2 = ⓓV2. T2
  34                       ) ∨
  35                       ∃∃U. ⇧[0, 1] U2 ≡ U & L. ⓓV1 ⊢ T1 ➡* U.
  36 #L #V1 #T1 #U2 #H @(cprs_ind … H) -U2 /3 width=5/
  37 #U0 #U2 #_ #HU02 * *
  38 [ #V0 #T0 #HV10 #HT10 #H destruct
  39   elim (cpr_inv_abbr1 … HU02) -HU02 *
  40   [ #V #V2 #T2 #HV0 #HV2 #HT02 #H destruct
  41     lapply (cpr_intro … HV0 … HV2) -HV2 #HV02
  42     lapply (ltpr_cpr_trans (L.ⓓV0) … HT02) /2 width=1/ -V #HT02
  43     lapply (lcprs_cprs_trans (L. ⓓV1) … HT02) -HT02 /2 width=1/ /4 width=5/
  44   | -V0 #T2 #HT20 #HTU2
  45     elim (lift_total U2 0 1) #U0 #HU20
  46     lapply (cpr_lift (L.ⓓV1) … HT20 … HU20 HTU2) -T2 /2 width=1/ /4 width=5/
  47   ]
  48 | #U1 #HU01 #HTU1
  49   elim (lift_total U2 0 1) #U #HU2
  50   lapply (cpr_lift (L.ⓓV1) … HU01 … HU2 HU02) -U0 /2 width=1/ /4 width=5/
  51 ]
  52 qed-.