- lambdadelta: third recursive part of preservation finally proved!

[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 f6ef16c40b028d2f445bacd96d46cb24692e3aed..94db2292b6336b85310675172967670aa364f2d3 100644 (file)
--- a/matita/matita/contribs/lambdadelta/basic_2/dynamic/lsubsv_ssta.ma
+++ b/matita/matita/contribs/lambdadelta/basic_2/dynamic/lsubsv_ssta.ma
@@ -12,39 +12,15 @@
 (*                                                                        *)
 (**************************************************************************)
 
-include "basic_2/equivalence/cpcs_cpcs.ma".
-include "basic_2/dynamic/lsubsv_ldrop.ma".
+include "basic_2/equivalence/lsubse_ssta.ma".
+include "basic_2/dynamic/lsubsv.ma".
 
 (* LOCAL ENVIRONMENT REFINEMENT FOR STRATIFIED NATIVE VALIDITY **************)
 
-(* Properties on stratified native type assignment **************************)
+(* Properties on stratified static type assignment **************************)
 
 lemma lsubsv_ssta_trans: ∀h,g,L2,T,U2,l. ⦃h, L2⦄ ⊢ T •[g,l] U2 →
                          ∀L1. h ⊢ L1 ⊩:⊑[g] L2 →
-                         ∃∃U1. L1 ⊢ U2 ⬌* U1 & ⦃h, L1⦄ ⊢ T •[g,l] U1.
-#h #g #L2 #T #U2 #l #H elim H -L2 -T -U2 -l
-[ #L2 #k #l #Hkl #L1 #_ /3 width=3/
-| #L2 #K2 #V2 #W2 #U2 #i #l #HLK2 #_ #HWU2 #IHVW2 #L1 #HL12
-  elim (lsubsv_ldrop_O1_trans … HL12 … HLK2) -L2 #X #H #HLK1
-  elim (lsubsv_inv_pair2 … H) -H *
-  [ #K1 #HK12 #H destruct
-    elim (IHVW2 … HK12) -K2 #W1 #HW21 #H
-    elim (lift_total W1 0 (i+1)) #U1 #HWU1
-    lapply (ldrop_fwd_ldrop2 … HLK1) /3 width=9/
-  | #K1 #V1 #W1 #l0 #_ #_ #_ #_ #_ #_ #H destruct
-  ]
-| #L2 #K2 #W2 #V2 #U2 #i #l #HLK2 #_ #HWU2 #IHWV2 #L1 #HL12
-  elim (lsubsv_ldrop_O1_trans … HL12 … HLK2) -L2 #X #H #HLK1
-  elim (lsubsv_inv_pair2 … H) -H *
-  [ #K1 #HK12 #H destruct
-    elim (IHWV2 … HK12) -K2 #V1 #_ #H -V2 /3 width=6/
-  | #K1 #W1 #V1 #l0 #HV1 #HVW1 #HW21 #HW2 #HK12 #H #_ destruct
-    elim (IHWV2 … HK12) -K2 #V #_ #H
-    elim (lift_total W1 0 (i+1)) #U1 #HWU1
-    lapply (ldrop_fwd_ldrop2 … HLK1) #HLK
-    @(ex2_intro … U1)
-    [ @(cpcs_lift … HLK … HWU2 … HWU1 HW21)
-    | @(ssta_ldef … HLK1 … HWU1) 
-  (*  
-    /3 width=9/
-  *)
\ No newline at end of file
+                         ∃∃U1. ⦃h, L1⦄ ⊢ T •[g,l] U1 & L1 ⊢ U1 ⬌* U2.
+/3 width=3 by lsubsv_fwd_lsubse, lsubse_ssta_trans/
+qed-.