lambdadelta

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

diff --git a/matita/matita/contribs/lambdadelta/basic_2/dynamic/lsubsv_ssta.ma b/matita/matita/contribs/lambdadelta/basic_2/dynamic/lsubsv_ssta.ma
index 594c72662507e83af8f5efa25158f4d495ef1090..b372dca9c5e81c18ebe4b4516c363e959a9e8d53 100644 (file)
--- a/matita/matita/contribs/lambdadelta/basic_2/dynamic/lsubsv_ssta.ma
+++ b/matita/matita/contribs/lambdadelta/basic_2/dynamic/lsubsv_ssta.ma
@@ -12,8 +12,9 @@
 (*                                                                        *)
 (**************************************************************************)
 
-include "basic_2/equivalence/lsubss_ssta.ma".
-include "basic_2/dynamic/lsubsv.ma".
+include "basic_2/static/ssta_ssta.ma".
+include "basic_2/equivalence/cpcs_cpcs.ma".
+include "basic_2/dynamic/lsubsv_ldrop.ma".
 
 (* LOCAL ENVIRONMENT REFINEMENT FOR STRATIFIED NATIVE VALIDITY **************)
 
@@ -22,5 +23,35 @@ include "basic_2/dynamic/lsubsv.ma".
 lemma lsubsv_ssta_trans: ∀h,g,L2,T,U2,l. ⦃h, L2⦄ ⊢ T •[g] ⦃l, U2⦄ →
                          ∀L1. h ⊢ L1 ¡⊑[g] L2 →
                          ∃∃U1. ⦃h, L1⦄ ⊢ T •[g] ⦃l, U1⦄ & L1 ⊢ U1 ⬌* U2.
-/3 width=3 by lsubsv_fwd_lsubss, lsubss_ssta_trans/
+#h #g #L2 #T #U #l #H elim H -L2 -T -U -l
+[ /3 width=3/
+| #L2 #K2 #X #Y #U #i #l #HLK2 #_ #HYU #IHXY #L1 #HL12
+  elim (lsubsv_ldrop_O1_trans … HL12 … HLK2) -L2 #X #H #HLK1
+  elim (lsubsv_inv_pair2 … H) -H * #K1 [ | -HYU -IHXY -HLK1 ]
+  [ #HK12 #H destruct
+    elim (IHXY … HK12) -K2 #T #HXT #HTY
+    lapply (ldrop_fwd_ldrop2 … HLK1) #H
+    elim (lift_total T 0 (i+1)) /3 width=11/
+  | #V #W1 #V2 #l0 #_ #_ #_ #_ #_ #H destruct
+  ]
+| #L2 #K2 #Y #X #U #i #l #HLK2 #HYX #HYU #IHYX #L1 #HL12
+  elim (lsubsv_ldrop_O1_trans … HL12 … HLK2) -L2 #X #H #HLK1
+  elim (lsubsv_inv_pair2 … H) -H * #K1 [ -HYX | -IHYX ]
+  [ #HK12 #H destruct
+    elim (IHYX … HK12) -K2 /3 width=6/
+  | #V #W1 #V2 #l0 #HYV #_ #HV #HY #_ #_ #H destruct
+    elim (snv_inv_cast … HYV) -HYV #W #l1 #_ #_ #HVW #HWY
+    elim (ssta_mono … HVW … HV) -HV #Hl10 #_
+    elim (ssta_mono … HYX … HY) -HYX -HY #H #_ destruct
+    lapply (ldrop_fwd_ldrop2 … HLK1) #H
+    elim (lift_total W 0 (i+1))
+    /4 width=11 by cpcs_lift, ex2_intro, ssta_ldef, ssta_cast/
+  ]
+| #a #I #L2 #V2 #T2 #U2 #l #_ #IHTU2 #L1 #HL12
+  elim (IHTU2 (L1.ⓑ{I}V2) …) [2: /2 width=1/ ] -L2 /3 width=3/
+| #L2 #V2 #T2 #U2 #l #_ #IHTU2 #L1 #HL12
+  elim (IHTU2 … HL12) -L2 /3 width=5/
+| #L2 #W2 #T2 #U2 #l #_ #IHTU2 #L1 #HL12
+  elim (IHTU2 … HL12) -L2 /3 width=3/
+]
 qed-.