Adds transformation of generic monotape machines into machines using a binary

[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..dc922ff5424eb152fb84d12390437d7acacc8763 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 +12,46 @@
 (*                                                                        *)
 (**************************************************************************)
 
+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 **************)
 
-(* 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
+lemma lsubsv_ssta_trans: ∀h,g,G,L2,T,U2,l. ⦃G, L2⦄ ⊢ T •[h, g] ⦃l, U2⦄ →
+                         ∀L1. G ⊢ L1 ¡⊑[h, g] L2 →
+                         ∃∃U1. ⦃G, L1⦄ ⊢ T •[h, g] ⦃l, U1⦄ & ⦃G, L1⦄ ⊢ U1 ⬌* U2.
+#h #g #G #L2 #T #U #l #H elim H -G -L2 -T -U -l
+[ /3 width=3/
+| #G #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 #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
+  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 #W2 #V2 #U2 #i #l #HLK2 #_ #HWU2 #IHWV2 #L1 #HL12
+| #G #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 #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
+  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 #G #L2 #V2 #T2 #U2 #l #_ #IHTU2 #L1 #HL12
+  elim (IHTU2 (L1.ⓑ{I}V2) …) [2: /2 width=1/ ] -L2 /3 width=3/
+| #G #L2 #V2 #T2 #U2 #l #_ #IHTU2 #L1 #HL12
+  elim (IHTU2 … HL12) -L2 /3 width=5/
+| #G #L2 #W2 #T2 #U2 #l #_ #IHTU2 #L1 #HL12
+  elim (IHTU2 … HL12) -L2 /3 width=3/
+]
+qed-.