matita/matita/contribs/lambdadelta/basic_2/dynamic/snv_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_2/static/da_aaa.ma".
  16 include "basic_2/computation/csx_aaa.ma".
  17 include "basic_2/computation/scpds_aaa.ma".
  18 include "basic_2/dynamic/snv.ma".
  19
  20 (* STRATIFIED NATIVE VALIDITY FOR TERMS *************************************)
  21
  22 (* Forward lemmas on atomic arity assignment for terms **********************)
  23
  24 lemma snv_fwd_aaa: ∀h,g,G,L,T. ⦃G, L⦄ ⊢ T ¡[h, g] → ∃A. ⦃G, L⦄ ⊢ T ⁝ A.
  25 #h #g #G #L #T #H elim H -G -L -T
  26 [ /2 width=2 by aaa_sort, ex_intro/
  27 | #I #G #L #K #V #i #HLK #_ * /3 width=6 by aaa_lref, ex_intro/
  28 | #a * #G #L #V #T #_ #_ * #B #HV * #A #HA /3 width=2 by aaa_abbr, aaa_abst, ex_intro/
  29 | #a #G #L #V #W0 #T #U0 #l #_ #_ #HVW0 #HTU0 * #B #HV * #X #HT
  30   lapply (scpds_aaa_conf … HV … HVW0) -HVW0 #HW0
  31   lapply (scpds_aaa_conf … HT … HTU0) -HTU0 #H
  32   elim (aaa_inv_abst … H) -H #B0 #A #H1 #HU #H2 destruct
  33   lapply (aaa_mono … H1 … HW0) -W0 #H destruct /3 width=4 by aaa_appl, ex_intro/
  34 | #G #L #U #T #U0 #_ #_ #HU0 #HTU0 * #B #HU * #A #HT
  35   lapply (scpds_aaa_conf … HU … HU0) -HU0 #HU0
  36   lapply (scpds_aaa_conf … HT … HTU0) -HTU0 #H
  37   lapply (aaa_mono … H … HU0) -U0 #H destruct /3 width=3 by aaa_cast, ex_intro/
  38 ]
  39 qed-.
  40
  41 lemma snv_fwd_csx: ∀h,g,G,L,T. ⦃G, L⦄ ⊢ T ¡[h, g] → ⦃G, L⦄ ⊢ ⬊*[h, g] T.
  42 #h #g #G #L #T #H elim (snv_fwd_aaa … H) -H /2 width=2 by aaa_csx/
  43 qed-.
  44
  45 (* Advanced forward lemmas **************************************************)
  46
  47 lemma snv_fwd_da: ∀h,g,G,L,T. ⦃G, L⦄ ⊢ T ¡[h, g] → ∃l. ⦃G, L⦄ ⊢ T ▪[h, g] l.
  48 #h #g #G #L #T #H elim (snv_fwd_aaa … H) -H /2 width=2 by aaa_da/
  49 qed-.
  50
  51 lemma snv_fwd_lstas: ∀h,g,G,L,T. ⦃G, L⦄ ⊢ T ¡[h, g] →
  52                      ∀l. ∃U. ⦃G, L⦄ ⊢ T •*[h, l] U.
  53 #h #g #G #L #T #H #l elim (snv_fwd_aaa … H) -H
  54 #A #HT elim (aaa_lstas h … HT l) -HT /2 width=2 by ex_intro/
  55 qed-.