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

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   2 (*       ___                                                              *)
   3 (*      ||M||                                                             *)
   4 (*      ||A||       A project by Andrea Asperti                           *)
   5 (*      ||T||                                                             *)
   6 (*      ||I||       Developers:                                           *)
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  10 (*       \ /        This file is distributed under the terms of the       *)
  11 (*        v         GNU General Public License Version 2                  *)
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  14
  15 include "basic_2/computation/lcprs_aaa.ma".
  16 include "basic_2/equivalence/cpcs_cpcs.ma".
  17 include "basic_2/equivalence/lcpcs_lcpcs.ma".
  18
  19 (* CONTEXT-SENSITIVE PARALLEL EQUIVALENCE ON LOCAL EBVIRONMENTS *************)
  20
  21 (* Main properties about atomic arity assignment on terms *******************)
  22
  23 theorem aaa_lcpcs_mono: ∀L1,L2. L1 ⊢ ⬌* L2 →
  24                         ∀T,A1. L1 ⊢ T ⁝ A1 → ∀A2. L2 ⊢ T ⁝ A2 →
  25                         A1 = A2.
  26 #L1 #L2 #HL12 #T #A1 #HT1 #A2 #HT2
  27 elim (lcpcs_inv_lcprs … HL12) -HL12 #L #HL1 #HL2
  28 lapply (aaa_lcprs_conf … HT1 … HL1) -L1 #HT1
  29 lapply (aaa_lcprs_conf … HT2 … HL2) -L2 #HT2
  30 lapply (aaa_mono … HT1 … HT2) -L -T //
  31 qed-.
  32
  33 theorem aaa_cpcs_mono: ∀L,T1,T2. L ⊢ T1 ⬌* T2 →
  34                        ∀A1. L ⊢ T1 ⁝ A1 → ∀A2. L ⊢ T2 ⁝ A2 →
  35                        A1 = A2.
  36 #L #T1 #T2 #HT12 #A1 #HA1 #A2 #HA2
  37 elim (cpcs_inv_cprs … HT12) -HT12 #T #HT1 #HT2
  38 lapply (aaa_cprs_conf … HA1 … HT1) -T1 #HA1
  39 lapply (aaa_cprs_conf … HA2 … HT2) -T2 #HA2
  40 lapply (aaa_mono … HA1 … HA2) -L -T //
  41 qed-.