matita/matita/contribs/lambdadelta/basic_2/etc/lsubsv/lsubsv_lsuba.etc

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  14
  15 include "basic_2/equivalence/scpes_aaa.ma".
  16 include "basic_2/dynamic/snv_aaa.ma".
  17 include "basic_2/dynamic/lsubsv.ma".
  18
  19 (* LOCAL ENVIRONMENT REFINEMENT FOR STRATIFIED NATIVE VALIDITY **************)
  20
  21 (* Forward lemmas on lenv refinement for atomic arity assignment ************)
  22
  23 lemma lsubsv_fwd_lsuba: ∀h,o,G,L1,L2. G ⊢ L1 ⫃¡[h, o] L2 → G ⊢ L1 ⫃⁝ L2.
  24 #h #o #G #L1 #L2 #H elim H -L1 -L2 /2 width=1 by lsuba_pair/
  25 #L1 #L2 #W #V #d1 #H #_ #_ #_ #_ #IHL12
  26 elim (shnv_inv_cast … H) -H #HW #HV #H
  27 lapply (H 0 ?) // -d1 #HWV
  28 elim (snv_fwd_aaa … HW) -HW #B #HW
  29 elim (snv_fwd_aaa … HV) -HV #A #HV
  30 lapply (scpes_aaa_mono … HWV … HW … HV) #H destruct
  31 /4 width=5 by lsuba_aaa_conf, lsuba_beta, aaa_cast/
  32 qed-.