matita/matita/contribs/lambdadelta/basic_2/etc_2A1/lpc/lfpcs_aaa.etc

   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                  *)
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  13 (**************************************************************************)
  14
  15 include "basic_2/computation/lfprs_aaa.ma".
  16 include "basic_2/equivalence/lfpcs_lfpcs.ma".
  17
  18 (* FOCALIZED PARALLEL EQUIVALENCE ON LOCAL ENVIRONMENTS *********************)
  19
  20 (* Main properties about atomic arity assignment on terms *******************)
  21
  22 theorem aaa_lfpcs_mono: ∀L1,L2. ⦃L1⦄ ⬌* ⦃L2⦄ →
  23                         ∀T,A1. L1 ⊢ T ⁝ A1 → ∀A2. L2 ⊢ T ⁝ A2 →
  24                         A1 = A2.
  25 #L1 #L2 #HL12 #T #A1 #HT1 #A2 #HT2
  26 elim (lfpcs_inv_lfprs … HL12) -HL12 #L #HL1 #HL2
  27 lapply (aaa_lfprs_conf … HT1 … HL1) -L1 #HT1
  28 lapply (aaa_lfprs_conf … HT2 … HL2) -L2 #HT2
  29 lapply (aaa_mono … HT1 … HT2) -L -T //
  30 qed-.