commit completed! the new iterated static type assignment is up!

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

diff --git a/matita/matita/contribs/lambdadelta/basic_2/dynamic/lsubsv_lstas.ma b/matita/matita/contribs/lambdadelta/basic_2/dynamic/lsubsv_lstas.ma
index 5600eeabafcd763c50214e861505a22698a01bf9..979eebb8f76a83dce473c0e4508486584c2da607 100644 (file)
--- a/matita/matita/contribs/lambdadelta/basic_2/dynamic/lsubsv_lstas.ma
+++ b/matita/matita/contribs/lambdadelta/basic_2/dynamic/lsubsv_lstas.ma
@@ -12,10 +12,8 @@
 (*                                                                        *)
 (**************************************************************************)
 
-include "basic_2/static/lsubd_da.ma".
-include "basic_2/unfold/lstas_alt.ma".
 include "basic_2/equivalence/scpes_cpcs.ma".
-include "basic_2/dynamic/lsubsv_lsubd.ma".
+include "basic_2/dynamic/lsubsv.ma".
 
 (* LOCAL ENVIRONMENT REFINEMENT FOR STRATIFIED NATIVE VALIDITY **************)
 
@@ -25,44 +23,56 @@ lemma lsubsv_lstas_trans: ∀h,g,G,L2,T,U2,l2. ⦃G, L2⦄ ⊢ T •*[h, l2] U2
                           ∀l1. l2 ≤ l1 → ⦃G, L2⦄ ⊢ T ▪[h, g] l1 →
                           ∀L1. G ⊢ L1 ⫃¡[h, g] L2 →
                           ∃∃U1. ⦃G, L1⦄ ⊢ T •*[h, l2] U1 & ⦃G, L1⦄ ⊢ U1 ⬌* U2.
-#h #g #G #L2 #T #U #l2 #H @(lstas_ind_alt … H) -G -L2 -T -U -l2
-[1,2: /2 width=3 by ex2_intro/
-| #G #L2 #K2 #X #Y #U #i #l2 #HLK2 #_ #HYU #IHXY #l1 #Hl21 #Hl1 #L1 #HL12
+#h #g #G #L2 #T #U #l2 #H elim H -G -L2 -T -U -l2
+[ /2 width=3 by ex2_intro/
+| #G #L2 #K2 #V #W #U #i #l2 #HLK2 #_ #HWU #IHVW #l1 #Hl21 #Hl1 #L1 #HL12
   elim (da_inv_lref … Hl1) -Hl1 * #K0 #V0 [| #l0 ] #HK0 #HV0
   lapply (drop_mono … HK0 … HLK2) -HK0 #H destruct
-  elim (lsubsv_drop_O1_trans … HL12 … HLK2) -L2 #X #H #HLK1
-  elim (lsubsv_inv_pair2 … H) -H * #K1 [ | -HYU -IHXY -HLK1 ]
+  elim (lsubsv_drop_O1_trans … HL12 … HLK2) -L2 #Y #H #HLK1
+  elim (lsubsv_inv_pair2 … H) -H * #K1 [ | -HWU -IHVW -HLK1 ]
   [ #HK12 #H destruct
-    elim (IHXY … Hl21 HV0 … HK12) -K2 -l1 #T #HXT #HTY
+    elim (IHVW … Hl21 HV0 … HK12) -K2 -l1 #T #HVT #HTW
     lapply (drop_fwd_drop2 … HLK1) #H
     elim (lift_total T 0 (i+1))
     /3 width=12 by lstas_ldef, cpcs_lift, ex2_intro/
-  | #V #l0 #_ #_ #_ #_ #_ #H destruct
+  | #V0 #l0 #_ #_ #_ #_ #_ #H destruct
   ]
-| #G #L2 #K2 #X #Y #Y0 #U #i #l2 #HLK2 #HXY0 #_ #HYU #IHXY #l1 #Hl21 #Hl1 #L1 #HL12
+| #G #L2 #K2 #V #W #i #HLK2 #_ #IHVW #l1 #_ #Hl1 #L1 #HL12
+  elim (da_inv_lref … Hl1) -Hl1 * #K0 #V0 [| #l0 ] #HK0 #HV0 [| #H1 ]
+  lapply (drop_mono … HK0 … HLK2) -HK0 #H2 destruct
+  elim (lsubsv_drop_O1_trans … HL12 … HLK2) -L2 #Y #H #HLK1
+  elim (lsubsv_inv_pair2 … H) -H * #K1
+  [ #HK12 #H destruct
+    elim (IHVW … HV0 … HK12) -K2 /3 width=5 by lstas_zero, ex2_intro/
+  | #V1 #l1 #_ #_ #HV1 #HV #HK12 #_ #H destruct
+    lapply (da_mono … HV0 … HV) -HV #H destruct
+    elim (da_lstas … HV1 0) -HV1 #W1 #HVW1 #_
+    elim (lift_total W1 0 (i+1)) #U1 #HWU1
+    elim (IHVW … HV0 … HK12) -K2 // #X #HVX #_ -W
+    @(ex2_intro … U1) /3 width=6 by lstas_cast, lstas_ldef/ (**) (* full auto too slow *)
+    @cpcs_cprs_sn @(cprs_delta … HLK1 … HWU1)
+    /4 width=2 by cprs_strap1, cpr_cprs, lstas_cpr, cpr_eps/
+  ]
+| #G #L2 #K2 #V #W #U #i #l2 #HLK2 #_ #HWU #IHVW #l1 #Hl21 #Hl1 #L1 #HL12
   elim (da_inv_lref … Hl1) -Hl1 * #K0 #V0 [| #l0 ] #HK0 #HV0 [| #H1 ]
   lapply (drop_mono … HK0 … HLK2) -HK0 #H2 destruct
   lapply (le_plus_to_le_r … Hl21) -Hl21 #Hl21
-  elim (lsubsv_drop_O1_trans … HL12 … HLK2) -L2 #X #H #HLK1
+  elim (lsubsv_drop_O1_trans … HL12 … HLK2) -L2 #Y #H #HLK1
   elim (lsubsv_inv_pair2 … H) -H * #K1
   [ #HK12 #H destruct
-    lapply (lsubsv_fwd_lsubd … HK12) #H
-    lapply (lsubd_da_trans … HV0 … H) -H #H
-    elim (da_inv_sta … H) -H
-    elim (IHXY … Hl21 HV0 … HK12) -K2 -Hl21 #Y1
+    elim (IHVW … Hl21 HV0 … HK12) -K2 -Hl21 #X
     lapply (drop_fwd_drop2 … HLK1)
-    elim (lift_total Y1 0 (i+1))
-    /3 width=12 by lstas_ldec, cpcs_lift, ex2_intro/
-  | #V #l1 #HXV #_ #HV #HX #HK12 #_ #H destruct
-    lapply (da_mono … HV0 … HX) -HX #H destruct
-    elim (shnv_inv_cast … HXV) -HXV #_ #_ #H
-    lapply (H … Hl21) -H #HXV
-    elim (IHXY … Hl21 HV0 … HK12) -K2 -Hl21 #Y0 #HXY0 #HY0
-    elim (da_inv_sta … HV) -HV #W #HVW
-    elim (lstas_total … HVW (l2+1)) -W #W #HVW
-    lapply (scpes_inv_lstas_eq … HXV … HXY0 … HVW) -HXV -HXY0 #HY0W
-    lapply (cpcs_canc_sn … HY0W … HY0) -Y0 #HYW
-    elim (lift_total W 0 (i+1))
+    elim (lift_total X 0 (i+1))
+    /3 width=12 by lstas_succ, cpcs_lift, ex2_intro/
+  | #V1 #l1 #H0 #_ #HV1 #HV #HK12 #_ #H destruct
+    lapply (da_mono … HV0 … HV) -HV #H destruct
+    elim (shnv_inv_cast … H0) -H0 #_ #_ #H
+    lapply (H … Hl21) -H #HVV1
+    elim (IHVW … Hl21 HV0 … HK12) -K2 -Hl21 #X #HVX #HXW
+    elim (da_lstas … HV1 (l2+1)) -HV1 #X1 #HVX1 #_
+    lapply (scpes_inv_lstas_eq … HVV1 … HVX … HVX1) -HVV1 -HVX #HXX1
+    lapply (cpcs_canc_sn … HXX1 … HXW) -X
+    elim (lift_total X1 0 (i+1))
     lapply (drop_fwd_drop2 … HLK1)
     /4 width=12 by cpcs_lift, lstas_cast, lstas_ldef, ex2_intro/
   ]
@@ -81,11 +91,8 @@ lemma lsubsv_lstas_trans: ∀h,g,G,L2,T,U2,l2. ⦃G, L2⦄ ⊢ T •*[h, l2] U2
 ]
 qed-.
 
-lemma lsubsv_sta_trans: ∀h,g,G,L2,T,U2. ⦃G, L2⦄ ⊢ T •[h] U2 →
+lemma lsubsv_sta_trans: ∀h,g,G,L2,T,U2. ⦃G, L2⦄ ⊢ T •*[h, 1] U2 →
                         ∀l. ⦃G, L2⦄ ⊢ T ▪[h, g] l+1 →
                         ∀L1. G ⊢ L1 ⫃¡[h, g] L2 →
-                        ∃∃U1. ⦃G, L1⦄ ⊢ T •[h] U1 & ⦃G, L1⦄ ⊢ U1 ⬌* U2.
-#h #g #G #L2 #T #U2 #H #l #HTl #L1 #HL12
-elim (lsubsv_lstas_trans … U2 1 … HTl … HL12)
-/3 width=3 by lstas_inv_SO, sta_lstas, ex2_intro/
-qed-.
+                        ∃∃U1. ⦃G, L1⦄ ⊢ T •*[h, 1] U1 & ⦃G, L1⦄ ⊢ U1 ⬌* U2.
+/2 width=7 by lsubsv_lstas_trans/ qed-.