matita/matita/contribs/lambdadelta/static_2/static/aaa_rdeq.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 "static_2/static/rdeq.ma".
  16 include "static_2/static/aaa.ma".
  17
  18 (* ATONIC ARITY ASSIGNMENT ON TERMS *****************************************)
  19
  20 (* Properties with sort-irrelevant equivalence on referred entries **********)
  21
  22 lemma aaa_tdeq_conf_rdeq: ∀G,L1,T1,A. ⦃G, L1⦄ ⊢ T1 ⁝ A → ∀T2. T1 ≛ T2 →
  23                           ∀L2. L1 ≛[T1] L2 → ⦃G, L2⦄ ⊢ T2 ⁝ A.
  24 #G #L1 #T1 #A #H elim H -G -L1 -T1 -A
  25 [ #G #L1 #s1 #X #H1 elim (tdeq_inv_sort1 … H1) -H1 //
  26 | #I #G #L1 #V1 #B #_ #IH #X #H1 >(tdeq_inv_lref1 … H1) -H1
  27   #Y #H2 elim (rdeq_inv_zero_pair_sn … H2) -H2
  28   #L2 #V2 #HL12 #HV12 #H destruct /3 width=1 by aaa_zero/
  29 | #I #G #L1 #A #i #_ #IH #X #H1 >(tdeq_inv_lref1 … H1) -H1
  30   #Y #H2 elim (rdeq_inv_lref_bind_sn … H2) -H2
  31   #J #L2 #HL12 #H destruct /3 width=1 by aaa_lref/
  32 | #p #G #L1 #V1 #T1 #B #A #_ #_ #IHV #IHT #X #H1 elim (tdeq_inv_pair1 … H1) -H1
  33   #V2 #T2 #HV12 #HT12 #H #L2 #H2 elim (rdeq_inv_bind … H2) -H2 destruct
  34   /5 width=2 by aaa_abbr, rdeq_bind_repl_dx, ext2_pair/
  35 | #p #G #L1 #V1 #T1 #B #A #_ #_ #IHV #IHT #X #H1 elim (tdeq_inv_pair1 … H1) -H1
  36   #V2 #T2 #HV12 #HT12 #H #L2 #H2 elim (rdeq_inv_bind … H2) -H2 destruct
  37   /5 width=2 by aaa_abst, rdeq_bind_repl_dx, ext2_pair/
  38 | #G #L1 #V1 #T1 #B #A #_ #_ #IHV #IHT #X #H1 elim (tdeq_inv_pair1 … H1) -H1
  39   #V2 #T2 #HV12 #HT12 #H #L2 #H2 elim (rdeq_inv_flat … H2) -H2 destruct
  40   /3 width=3 by aaa_appl/
  41 | #G #L1 #V1 #T1 #A #_ #_ #IHV #IHT #X #H1 elim (tdeq_inv_pair1 … H1) -H1
  42   #V2 #T2 #HV12 #HT12 #H #L2 #H2 elim (rdeq_inv_flat … H2) -H2 destruct
  43   /3 width=1 by aaa_cast/
  44 ]
  45 qed-.