update in lambdadelta

[helm.git] / matita / matita / contribs / lambdadelta / basic_2A / dynamic / lsubsv_snv.ma

diff --git a/matita/matita/contribs/lambdadelta/basic_2A/dynamic/lsubsv_snv.ma b/matita/matita/contribs/lambdadelta/basic_2A/dynamic/lsubsv_snv.ma
new file mode 100644 (file)
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+++ b/matita/matita/contribs/lambdadelta/basic_2A/dynamic/lsubsv_snv.ma
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+(**************************************************************************)
+(*       ___                                                              *)
+(*      ||M||                                                             *)
+(*      ||A||       A project by Andrea Asperti                           *)
+(*      ||T||                                                             *)
+(*      ||I||       Developers:                                           *)
+(*      ||T||         The HELM team.                                      *)
+(*      ||A||         http://helm.cs.unibo.it                             *)
+(*      \   /                                                             *)
+(*       \ /        This file is distributed under the terms of the       *)
+(*        v         GNU General Public License Version 2                  *)
+(*                                                                        *)
+(**************************************************************************)
+
+include "basic_2A/dynamic/lsubsv_scpds.ma".
+
+(* LOCAL ENVIRONMENT REFINEMENT FOR STRATIFIED NATIVE VALIDITY **************)
+
+(* Properties concerning stratified native validity *************************)
+
+lemma lsubsv_snv_trans: ∀h,g,G,L2,T. ⦃G, L2⦄ ⊢ T ¡[h, g] →
+                        ∀L1. G ⊢ L1 ⫃¡[h, g] L2 → ⦃G, L1⦄ ⊢ T ¡[h, g].
+#h #g #G #L2 #T #H elim H -G -L2 -T //
+[ #I #G #L2 #K2 #V #i #HLK2 #_ #IHV #L1 #HL12
+  elim (lsubsv_drop_O1_trans … HL12 … HLK2) -L2 #X #H #HLK1
+  elim (lsubsv_inv_pair2 … H) -H * #K1
+  [ #HK12 #H destruct /3 width=5 by snv_lref/
+  | #W #d #HVW #_ #_ #_ #_ #H1 #H2 destruct -IHV
+    /3 width=6 by shnv_inv_snv, snv_lref/
+  ]
+| #a #I #G #L2 #V #T #_ #_ #IHV #IHT #L1 #HL12 destruct
+  /4 width=1 by snv_bind, lsubsv_pair/
+| #a #G #L2 #V #W0 #T #U0 #d #_ #_ #HVW0 #HTU0 #IHV #IHT #L1 #HL12
+  elim (lsubsv_scpds_trans … HVW0 … HL12) -HVW0 #V0 #HV0 #HWV0
+  elim (lsubsv_scpds_trans … HTU0 … HL12) -HTU0 #X #HT0 #H
+  elim (cprs_inv_abst1 … H) -H #W #T0 #HW0 #_ #H destruct
+  elim (cprs_conf … HWV0 … HW0) -W0
+  /4 width=10 by snv_appl, scpds_cprs_trans, cprs_bind/
+| #G #L2 #U #T #U0 #_ #_ #HU0 #HTU0 #IHU #IHT #L1 #HL12
+  elim (lsubsv_scpds_trans … HTU0 … HL12) -HTU0 #X0 #HTX0 #H1
+  elim (lsubsv_scpds_trans … HU0 … HL12) -HU0 #X #HUX #H2
+  elim (cprs_conf … H1 … H2) -U0 /3 width=5 by snv_cast, scpds_cprs_trans/
+]
+qed-.