matita/matita/contribs/lambdadelta/static_2/static/aaa_reqg.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/reqg_fqup.ma".
  16 include "static_2/static/aaa.ma".
  17
  18 (* ATONIC ARITY ASSIGNMENT ON TERMS *****************************************)
  19
  20 (* Properties with generic equivalence on referred entries ******************)
  21
  22 lemma aaa_teqg_conf_reqg (S) (G):
  23       reflexive … S →
  24       ∀L1,T1,A. ❨G,L1❩ ⊢ T1 ⁝ A → ∀T2. T1 ≛[S] T2 →
  25       ∀L2. L1 ≛[S,T1] L2 → ❨G,L2❩ ⊢ T2 ⁝ A.
  26 #S #G #HS #L1 #T1 #A #H elim H -G -L1 -T1 -A
  27 [ #G #L1 #s1 #X #H1 elim (teqg_inv_sort1 … H1) -H1 //
  28 | #I #G #L1 #V1 #B #_ #IH #X #H1 >(teqg_inv_lref1 … H1) -H1
  29   #Y #H2 elim (reqg_inv_zero_pair_sn … H2) -H2
  30   #L2 #V2 #HL12 #HV12 #H destruct /3 width=1 by aaa_zero/
  31 | #I #G #L1 #A #i #_ #IH #X #H1 >(teqg_inv_lref1 … H1) -H1
  32   #Y #H2 elim (reqg_inv_lref_bind_sn … H2) -H2
  33   #J #L2 #HL12 #H destruct /3 width=1 by aaa_lref/
  34 | #p #G #L1 #V1 #T1 #B #A #_ #_ #IHV #IHT #X #H1 elim (teqg_inv_pair1 … H1) -H1
  35   #V2 #T2 #HV12 #HT12 #H #L2 #H2 elim (reqg_inv_bind_refl … H2) -H2 destruct
  36   /5 width=2 by aaa_abbr, reqg_bind_repl_dx, ext2_pair/
  37 | #p #G #L1 #V1 #T1 #B #A #_ #_ #IHV #IHT #X #H1 elim (teqg_inv_pair1 … H1) -H1
  38   #V2 #T2 #HV12 #HT12 #H #L2 #H2 elim (reqg_inv_bind_refl … H2) -H2 destruct
  39   /5 width=2 by aaa_abst, reqg_bind_repl_dx, ext2_pair/
  40 | #G #L1 #V1 #T1 #B #A #_ #_ #IHV #IHT #X #H1 elim (teqg_inv_pair1 … H1) -H1
  41   #V2 #T2 #HV12 #HT12 #H #L2 #H2 elim (reqg_inv_flat … H2) -H2 destruct
  42   /3 width=3 by aaa_appl/
  43 | #G #L1 #V1 #T1 #A #_ #_ #IHV #IHT #X #H1 elim (teqg_inv_pair1 … H1) -H1
  44   #V2 #T2 #HV12 #HT12 #H #L2 #H2 elim (reqg_inv_flat … H2) -H2 destruct
  45   /3 width=1 by aaa_cast/
  46 ]
  47 qed-.
  48
  49 lemma aaa_teqg_conf (S) (G) (L) (A):
  50       reflexive … S →
  51       ∀T1. ❨G,L❩ ⊢ T1 ⁝ A → ∀T2. T1 ≛[S] T2 → ❨G,L❩ ⊢ T2 ⁝ A.
  52 /3 width=7 by aaa_teqg_conf_reqg, reqg_refl/ qed-.
  53
  54 lemma aaa_reqg_conf (S) (G) (T) (A):
  55       reflexive … S →
  56       ∀L1. ❨G,L1❩ ⊢ T ⁝ A → ∀L2. L1 ≛[S,T] L2 → ❨G,L2❩ ⊢ T ⁝ A.
  57 /3 width=7 by aaa_teqg_conf_reqg, teqg_refl/ qed-.