matita/matita/contribs/lambdadelta/basic_2/static/aaa_lfeq.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_2/static/lfeq_lreq.ma".
  16 include "basic_2/static/aaa.ma".
  17
  18 (* ATONIC ARITY ASSIGNMENT ON TERMS *****************************************)
  19
  20 (* Properties with equivalence on referred entries **************************)
  21
  22 lemma lfeq_aaa_trans: ∀G,L2,T,A. ⦃G, L2⦄ ⊢ T ⁝ A →
  23                       ∀L1. L1 ≡[T] L2 → ⦃G, L1⦄ ⊢ T ⁝ A.
  24 #G #L2 #T #A #H elim H -G -L2 -T -A /2 width=1 by aaa_sort/
  25 [ #I #G #L2 #V2 #A #_ #IH #L1 #H
  26   elim (lfeq_inv_zero_pair_dx  … H) -H /3 width=1 by aaa_zero/
  27 | #I #G #L2 #V2 #A #i #_ #IH #L1 #H
  28   elim (lfeq_inv_lref_pair_dx  … H) -H /3 width=1 by aaa_lref/
  29 | #p #G #L2 #V #T #B #A #_ #_ #IHV #IHT #L1 #H
  30   elim (lfeq_inv_bind … H) -H /3 width=2 by aaa_abbr/
  31 | #p #G #L2 #V #T #B #A #_ #_ #IHV #IHT #L1 #H
  32   elim (lfeq_inv_bind … H) -H /3 width=1 by aaa_abst/
  33 | #G #L2 #V #T #B #A #_ #_ #IHV #IHT #L1 #H
  34   elim (lfeq_inv_flat … H) -H /3 width=3 by aaa_appl/
  35 | #G #L2 #V #T #A #_ #_ #IHV #IHT #L1 #H
  36   elim (lfeq_inv_flat … H) -H /3 width=1 by aaa_cast/
  37 ]
  38 qed-.
  39
  40 lemma aaa_lfeq_conf: ∀G,L2,T,A. ⦃G, L2⦄ ⊢ T ⁝ A →
  41                      ∀L1. L2 ≡[T] L1 → ⦃G, L1⦄ ⊢ T ⁝ A.
  42 /3 width=3 by lfeq_aaa_trans, lfeq_sym/ qed-.