matita/matita/contribs/lambdadelta/basic_2/dynamic/lsubv_lsuba.ma

   1 (**************************************************************************)
   2 (*       ___                                                              *)
   3 (*      ||M||                                                             *)
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  10 (*       \ /        This file is distributed under the terms of the       *)
  11 (*        v         GNU General Public License Version 2                  *)
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  14
  15 include "basic_2/dynamic/cnv_aaa.ma".
  16 include "basic_2/dynamic/lsubv.ma".
  17
  18 (* LOCAL ENVIRONMENT REFINEMENT FOR NATIVE VALIDITY *************************)
  19
  20 (* Forward lemmas with lenv refinement for atomic arity assignment **********)
  21
  22 (* Basic_2A1: uses: lsubsv_fwd_lsuba *)
  23 lemma lsubsv_fwd_lsuba (a) (h) (G): ∀L1,L2. G ⊢ L1 ⫃![a,h] L2 → G ⊢ L1 ⫃⁝ L2.
  24 #a #h #G #L1 #L2 #H elim H -L1 -L2 /2 width=1 by lsuba_bind/
  25 #L1 #L2 #W #V #H #_ #IH
  26 elim (cnv_inv_cast … H) -H #W0 #HW #HV #HW0 #HVW0
  27 elim (cnv_fwd_aaa … HW) -HW #B #HW
  28 elim (cnv_fwd_aaa … HV) -HV #A #HV
  29 lapply (cpms_aaa_conf … HW … HW0) -HW0 #H
  30 lapply (cpms_aaa_conf … HV … HVW0) -HVW0 #HW0
  31 lapply (aaa_mono … H … HW0) -W0 #H destruct
  32 /4 width=5 by lsuba_aaa_conf, lsuba_beta, aaa_cast/
  33 qed-.