matita/matita/contribs/lambdadelta/basic_2A/equivalence/cpcs_aaa.ma

   1 (**************************************************************************)
   2 (*       ___                                                              *)
   3 (*      ||M||                                                             *)
   4 (*      ||A||       A project by Andrea Asperti                           *)
   5 (*      ||T||                                                             *)
   6 (*      ||I||       Developers:                                           *)
   7 (*      ||T||         The HELM team.                                      *)
   8 (*      ||A||         http://helm.cs.unibo.it                             *)
   9 (*      \   /                                                             *)
  10 (*       \ /        This file is distributed under the terms of the       *)
  11 (*        v         GNU General Public License Version 2                  *)
  12 (*                                                                        *)
  13 (**************************************************************************)
  14
  15 include "basic_2A/computation/cpxs_aaa.ma".
  16 include "basic_2A/equivalence/cpcs_cpcs.ma".
  17
  18 (* CONTEXT-SENSITIVE PARALLEL EQUIVALENCE ON TERMS **************************)
  19
  20 (* Main inversion lemmas about atomic arity assignment on terms *************)
  21
  22 theorem cpcs_aaa_mono: ∀G,L,T1,T2. ⦃G, L⦄ ⊢ T1 ⬌* T2 →
  23                        ∀A1. ⦃G, L⦄ ⊢ T1 ⁝ A1 → ∀A2. ⦃G, L⦄ ⊢ T2 ⁝ A2 →
  24                        A1 = A2.
  25 #G #L #T1 #T2 #HT12 #A1 #HA1 #A2 #HA2
  26 elim (cpcs_inv_cprs … HT12) -HT12 #T #HT1 #HT2
  27 lapply (cprs_aaa_conf … HA1 … HT1) -T1 #HA1
  28 lapply (cprs_aaa_conf … HA2 … HT2) -T2 #HA2
  29 lapply (aaa_mono … HA1 … HA2) -L -T //
  30 qed-.