matita/matita/contribs/lambdadelta/basic_2/dynamic/lsubsv_lsuba.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/dynamic/snv_aaa.ma".
  16 include "basic_2/dynamic/lsubsv.ma".
  17
  18 (* LOCAL ENVIRONMENT REFINEMENT FOR STRATIFIED NATIVE VALIDITY **************)
  19
  20 (* Properties on local environment refinement for atomic arity assignment ***)
  21
  22 lemma lsubsv_fwd_lsuba: ∀h,g,L1,L2. h ⊢ L1 ¡⊑[g] L2 → L1 ⁝⊑ L2.
  23 #h #g #L1 #L2 #H elim H -L1 -L2 // /2 width=1/
  24 #L1 #L2 #V1 #V2 #W1 #W2 #l #HV1 #HVW1 #HW12 #HW2 #_ #_ #HL12
  25 elim (snv_fwd_aaa … HV1) -HV1 #A #HV1
  26 elim (snv_fwd_aaa … HW2) -HW2 #B #HW2
  27 lapply (ssta_aaa … HV1 … HVW1) -HVW1 #H1
  28 lapply (lsuba_aaa_trans … HW2 … HL12) #H2
  29 lapply (aaa_cpcs_mono … HW12 … H1 … H2) -W1 -H2 #H destruct /2 width=3/
  30 qed-.