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/computation/csn_aaa.ma".
  16 include "basic_2/computation/dxprs_aaa.ma".
  17 include "basic_2/equivalence/cpcs_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,L,T. ⦃h, L⦄ ⊢ T ¡[g] → ∃A. L ⊢ T ⁝ A.
  25 #h #g #L #T #H elim H -L -T
  26 [ /2 width=2/
  27 | #I #L #K #V #i #HLK #_ * /3 width=6/
  28 | #a * #L #V #T #_ #_ * #B #HV * #A #HA /3 width=2/
  29 | #a #L #V #W #W0 #T #U #l #_ #_ #HVW #HW0 #HTU * #B #HV * #X #HT
  30   lapply (dxprs_aaa h g … HV W0 ?) [ -HTU /3 width=4/ ] -W #HW0 (**) (* auto fail without -HTU *)
  31   lapply (dxprs_aaa … HT … HTU) -HTU #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/
  34 | #L #W #T #U #l #_ #_ #HTU #HUW * #B #HW * #A #HT
  35   lapply (aaa_cpcs_mono … HUW A … HW) -HUW /2 width=7/ -HTU #H destruct /3 width=3/
  36 ]
  37 qed-.
  38
  39 lemma snv_fwd_csn: ∀h,g,L,T. ⦃h, L⦄ ⊢ T ¡[g] → L ⊢ ⬊* T.
  40 #h #g #L #T #H elim (snv_fwd_aaa … H) -H /2 width=2/
  41 qed-.