- the relation for pointwise extensions now takes a binder as argument

[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 18ca504d493d935a64db5494174964fedb3661f8..e4596e7d4fb57e7becab9f5ac4c8a5c53845a079 100644 (file)
--- a/matita/matita/contribs/lambdadelta/basic_2/dynamic/lsubsv_snv.ma
+++ b/matita/matita/contribs/lambdadelta/basic_2/dynamic/lsubsv_snv.ma
@@ -12,45 +12,41 @@
 (*                                                                        *)
 (**************************************************************************)
 
-include "basic_2/dynamic/lsubsv_ldrop.ma".
+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_ssta.ma".
-*)
+
 (* LOCAL ENVIRONMENT REFINEMENT FOR STRATIFIED NATIVE VALIDITY **************)
 
 (* Properties concerning stratified native validity *************************)
-(*
-axiom lsubsv_xprs_trans: ∀h,g,L1,L2. h ⊢ L1 ⊩:⊑[g] L2 →
-                         ∀T1,T2. ⦃h, L2⦄ ⊢ T1 •➡*[g] T2 → ⦃h, L1⦄ ⊢ T1 •➡*[g] T2.
 
-/3 width=3 by lsubsv_fwd_lsubss, lsubss_xprs_trans/ qed-.
-*)
-lemma lsubsv_snv_trans: ∀h,g,L2,T. ⦃h, L2⦄ ⊩ T :[g] →
-                        ∀L1. h ⊢ L1 ⊩:⊑[g] L2 → ⦃h, L1⦄ ⊩ T :[g].
-#h #g #L2 #T #H elim H -L2 -T //
-[ #I2 #L2 #K2 #W2 #i #HLK2 #_ #IHW2 #L1 #HL12
+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_ldrop_O1_trans … HL12 … HLK2) -L2 #X #H #HLK1
-  elim (lsubsv_inv_pair2 … H) -H * #K1 [ | -IHW2 ]
-  [ #HK12 #H destruct /3 width=5/
-  | #W1 #V1 #l #HV1 #_ #_ #_ #_ #H #_ destruct /2 width=5/
+  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/
   ]
-| #a #I #L2 #V #T #_ #_ #IHV #IHT #L1 #HL12 /4 width=1/
-| #a #L2 #V #W #W0 #T #U #l #_ #_ #HVW #HW0 #HTU #IHV #IHT #L1 #HL12
-  lapply (IHV … HL12) -IHV #HV
-  lapply (IHT … HL12) -IHT #HT
+| #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
-(*
-  lapply (lsubsv_ssta_trans … HVW … HL12) -HVW #HVW
-  lapply (lsubsv_xprs_trans … HL12 … HTU) -HL12 -HTU /2 width=8/
-*)
-| #L2 #W #T #U #l #_ #_ #HTU #HUW #IHW #IHT #L1 #HL12
-  lapply (IHW … HL12) -IHW #HW
-  lapply (IHT … HL12) -IHT #HT
+  elim (lsubsv_ssta_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
-(*  
-  lapply (lsubsv_ssta_trans … HTU … HL12) -HTU #HTU
--HL12 -HWU /2 width=4/
+  elim (lsubsv_ssta_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/
 ]
 qed-.
-*)