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

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  14
  15 include "basic_2/dynamic/lsubsv_scpds.ma".
  16
  17 (* LOCAL ENVIRONMENT REFINEMENT FOR STRATIFIED NATIVE VALIDITY **************)
  18
  19 (* Properties concerning stratified native validity *************************)
  20
  21 lemma lsubsv_snv_trans: ∀h,o,G,L2,T. ⦃G, L2⦄ ⊢ T ¡[h, o] →
  22                         ∀L1. G ⊢ L1 ⫃¡[h, o] L2 → ⦃G, L1⦄ ⊢ T ¡[h, o].
  23 #h #o #G #L2 #T #H elim H -G -L2 -T //
  24 [ #I #G #L2 #K2 #V #i #HLK2 #_ #IHV #L1 #HL12
  25   elim (lsubsv_drop_O1_trans … HL12 … HLK2) -L2 #X #H #HLK1
  26   elim (lsubsv_inv_pair2 … H) -H * #K1
  27   [ #HK12 #H destruct /3 width=5 by snv_lref/
  28   | #W #d #HVW #_ #_ #_ #_ #H1 #H2 destruct -IHV
  29     /3 width=6 by shnv_inv_snv, snv_lref/
  30   ]
  31 | #a #I #G #L2 #V #T #_ #_ #IHV #IHT #L1 #HL12 destruct
  32   /4 width=1 by snv_bind, lsubsv_pair/
  33 | #a #G #L2 #V #W0 #T #U0 #d #_ #_ #HVW0 #HTU0 #IHV #IHT #L1 #HL12
  34   elim (lsubsv_scpds_trans … HVW0 … HL12) -HVW0 #V0 #HV0 #HWV0
  35   elim (lsubsv_scpds_trans … HTU0 … HL12) -HTU0 #X #HT0 #H
  36   elim (cprs_inv_abst1 … H) -H #W #T0 #HW0 #_ #H destruct
  37   elim (cprs_conf … HWV0 … HW0) -W0
  38   /4 width=10 by snv_appl, scpds_cprs_trans, cprs_bind/
  39 | #G #L2 #U #T #U0 #_ #_ #HU0 #HTU0 #IHU #IHT #L1 #HL12
  40   elim (lsubsv_scpds_trans … HTU0 … HL12) -HTU0 #X0 #HTX0 #H1
  41   elim (lsubsv_scpds_trans … HU0 … HL12) -HU0 #X #HUX #H2
  42   elim (cprs_conf … H1 … H2) -U0 /3 width=5 by snv_cast, scpds_cprs_trans/
  43 ]
  44 qed-.