matita/matita/contribs/lambdadelta/basic_2/computation/cprs_lfprs.ma

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  14
  15 include "basic_2/computation/cprs_cprs.ma".
  16 include "basic_2/computation/lfprs_lfprs.ma".
  17
  18 (* CONTEXT-SENSITIVE PARALLEL COMPUTATION ON TERMS **************************)
  19
  20 (* Properties on focalized computation for local environments ***************)
  21
  22 (* Basic_1: was just: pr3_pr3_pr3_t *)
  23 lemma lfprs_cprs_trans: ∀L1,L2. ⦃L1⦄ ➡* ⦃L2⦄ →
  24                         ∀T1,T2. L2 ⊢ T1 ➡* T2 → L1 ⊢ T1 ➡* T2.
  25 #L1 #L2 #HL12 @(lfprs_ind … HL12) -L2 // /3 width=3/
  26 qed.
  27
  28 lemma lfprs_cpr_trans: ∀L1,L2. ⦃L1⦄ ➡* ⦃L2⦄ →
  29                        ∀T1,T2. L2 ⊢ T1 ➡ T2 → L1 ⊢ T1 ➡* T2.
  30 /3 width=3 by lfprs_cprs_trans, inj/ qed.
  31
  32 (* Advanced inversion lemmas ************************************************)
  33
  34 (* Basic_1: was pr3_gen_abbr *)
  35 lemma cprs_inv_abbr1: ∀a,L,V1,T1,U2. L ⊢ ⓓ{a}V1. T1 ➡* U2 →
  36                       (∃∃V2,T2. L ⊢ V1 ➡* V2 & L. ⓓV1 ⊢ T1 ➡* T2 &
  37                                 U2 = ⓓ{a}V2. T2
  38                       ) ∨
  39                       ∃∃T2. L. ⓓV1 ⊢ T1 ➡* T2 & ⇧[0, 1] U2 ≡ T2 & a = true.
  40 #a #L #V1 #T1 #U2 #H @(cprs_ind … H) -U2 /3 width=5/
  41 #U0 #U2 #_ #HU02 * *
  42 [ #V0 #T0 #HV10 #HT10 #H destruct
  43   elim (cpr_inv_abbr1 … HU02) -HU02 *
  44   [ #V #V2 #T2 #HV0 #HV2 #HT02 #H destruct
  45     lapply (cpr_intro … HV0 … HV2) -HV2 #HV02
  46     lapply (ltpr_cpr_trans (L.ⓓV0) … HT02) /2 width=1/ -V #HT02
  47     lapply (lfprs_cprs_trans (L. ⓓV1) … HT02) -HT02 /2 width=1/ /4 width=5/
  48   | #T2 #HT02 #HUT2
  49     lapply (lfprs_cpr_trans (L.ⓓV1) … HT02) -HT02 /2 width=1/ -V0 #HT02
  50     lapply (cprs_trans … HT10 … HT02) -T0 /3 width=3/
  51   ]
  52 | #U1 #HTU1 #HU01
  53   elim (lift_total U2 0 1) #U #HU2
  54   lapply (cpr_lift (L.ⓓV1) … HU01 … HU2 HU02) -U0 /2 width=1/ /4 width=3/
  55 ]
  56 qed-.