update in basic_2 and ground_2

[helm.git] / matita / matita / contribs / lambdadelta / basic_2 / dynamic / lsubsv_snv.ma

diff --git a/matita/matita/contribs/lambdadelta/basic_2/dynamic/lsubsv_snv.ma b/matita/matita/contribs/lambdadelta/basic_2/dynamic/lsubsv_snv.ma
index 0777e36cd0083f144d464cf942a990ff6252d5dd..365849c366c86c8d2953b276652d934ed5dfce23 100644 (file)
--- a/matita/matita/contribs/lambdadelta/basic_2/dynamic/lsubsv_snv.ma
+++ b/matita/matita/contribs/lambdadelta/basic_2/dynamic/lsubsv_snv.ma
@@ -12,41 +12,33 @@
 (*                                                                        *)
 (**************************************************************************)
 
-include "basic_2/computation/cpds_cpds.ma".
-include "basic_2/dynamic/snv_aaa.ma".
-include "basic_2/dynamic/lsubsv_cpds.ma".
-include "basic_2/dynamic/lsubsv_cpcs.ma".
+include "basic_2/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 //
+lemma lsubsv_snv_trans: ∀h,o,G,L2,T. ⦃G, L2⦄ ⊢ T ¡[h, o] →
+                        ∀L1. G ⊢ L1 ⫃¡[h, o] L2 → ⦃G, L1⦄ ⊢ T ¡[h, o].
+#h #o #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 #l #H1V #H1W #HWV #_ #HWl #_ #_ #H1 #H2 destruct -IHV
-    /3 width=10 by snv_scast, 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 #W #W0 #T #U #l #_ #_ #HVl #HVW #HW0 #HTU #IHV #IHT #L1 #HL12
-  lapply (lsubsv_cprs_trans … HL12 … HW0) -HW0 #HW0
-  elim (lsubsv_sta_trans … HVW … HVl … HL12) -HVW #W1 #HVW1 #HW1
-  lapply (cpcs_cprs_strap1 … HW1 … HW0) -W #HW10
-  lapply (lsubd_da_trans … HVl L1 ?) -HVl /2 width=1 by lsubsv_fwd_lsubd/ #HVl
-  elim (lsubsv_cpds_trans … HTU … HL12) -HTU #X #HTU #H
-  elim (cprs_inv_abst1 … H) -H #W #U2 #HW0 #_ #H destruct
-  lapply (cpcs_cprs_strap1 … HW10 … HW0) -W0 #H
-  elim (cpcs_inv_cprs … H) -H #W0 #HW10 #HW0
-  /4 width=11 by snv_appl, cpds_cprs_trans, cprs_bind/
-| #G #L2 #W #T #U #l #_ #_ #HTl #HTU #HUW #IHW #IHT #L1 #HL12
-  lapply (lsubsv_cpcs_trans … HL12 … HUW) -HUW #HUW
-  elim (lsubsv_sta_trans … HTU … HTl … HL12) -HTU #U0 #HTU0 #HU0
-  lapply (lsubd_da_trans … HTl L1 ?) -HTl
-  /4 width=5 by lsubsv_fwd_lsubd, snv_cast, cpcs_trans/
+| #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-.