update in basic_2 and ground_2

[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 979eebb8f76a83dce473c0e4508486584c2da607..fa1b25fea1402486f3130047f20cf158e130c2b5 100644 (file)
--- a/matita/matita/contribs/lambdadelta/basic_2/dynamic/lsubsv_lstas.ma
+++ b/matita/matita/contribs/lambdadelta/basic_2/dynamic/lsubsv_lstas.ma
@@ -19,32 +19,32 @@ include "basic_2/dynamic/lsubsv.ma".
 
 (* Properties on nat-iterated static type assignment ************************)
 
-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 elim H -G -L2 -T -U -l2
+lemma lsubsv_lstas_trans: ∀h,o,G,L2,T,U2,d2. ⦃G, L2⦄ ⊢ T •*[h, d2] U2 →
+                          ∀d1. d2 ≤ d1 → ⦃G, L2⦄ ⊢ T ▪[h, o] d1 →
+                          ∀L1. G ⊢ L1 ⫃¡[h, o] L2 →
+                          ∃∃U1. ⦃G, L1⦄ ⊢ T •*[h, d2] U1 & ⦃G, L1⦄ ⊢ U1 ⬌* U2.
+#h #o #G #L2 #T #U #d2 #H elim H -G -L2 -T -U -d2
 [ /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
+| #G #L2 #K2 #V #W #U #i #d2 #HLK2 #_ #HWU #IHVW #d1 #Hd21 #Hd1 #L1 #HL12
+  elim (da_inv_lref … Hd1) -Hd1 * #K0 #V0 [| #d0 ] #HK0 #HV0
   lapply (drop_mono … HK0 … HLK2) -HK0 #H destruct
   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 (IHVW … Hl21 HV0 … HK12) -K2 -l1 #T #HVT #HTW
+    elim (IHVW … Hd21 HV0 … HK12) -K2 -d1 #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/
-  | #V0 #l0 #_ #_ #_ #_ #_ #H destruct
+  | #V0 #d0 #_ #_ #_ #_ #_ #H destruct
   ]
-| #G #L2 #K2 #V #W #i #HLK2 #_ #IHVW #l1 #_ #Hl1 #L1 #HL12
-  elim (da_inv_lref … Hl1) -Hl1 * #K0 #V0 [| #l0 ] #HK0 #HV0 [| #H1 ]
+| #G #L2 #K2 #V #W #i #HLK2 #_ #IHVW #d1 #_ #Hd1 #L1 #HL12
+  elim (da_inv_lref … Hd1) -Hd1 * #K0 #V0 [| #d0 ] #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
+  | #V1 #d1 #_ #_ #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
@@ -53,46 +53,46 @@ lemma lsubsv_lstas_trans: ∀h,g,G,L2,T,U2,l2. ⦃G, L2⦄ ⊢ T •*[h, l2] U2
     @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 ]
+| #G #L2 #K2 #V #W #U #i #d2 #HLK2 #_ #HWU #IHVW #d1 #Hd21 #Hd1 #L1 #HL12
+  elim (da_inv_lref … Hd1) -Hd1 * #K0 #V0 [| #d0 ] #HK0 #HV0 [| #H1 ]
   lapply (drop_mono … HK0 … HLK2) -HK0 #H2 destruct
-  lapply (le_plus_to_le_r … Hl21) -Hl21 #Hl21
+  lapply (le_plus_to_le_c … Hd21) -Hd21 #Hd21
   elim (lsubsv_drop_O1_trans … HL12 … HLK2) -L2 #Y #H #HLK1
   elim (lsubsv_inv_pair2 … H) -H * #K1
   [ #HK12 #H destruct
-    elim (IHVW … Hl21 HV0 … HK12) -K2 -Hl21 #X
+    elim (IHVW … Hd21 HV0 … HK12) -K2 -Hd21 #X
     lapply (drop_fwd_drop2 … HLK1)
     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
+  | #V1 #d1 #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 (H … Hd21) -H #HVV1
+    elim (IHVW … Hd21 HV0 … HK12) -K2 -Hd21 #X #HVX #HXW
+    elim (da_lstas … HV1 (d2+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/
   ]
-| #a #I #G #L2 #V2 #T2 #U2 #l1 #_ #IHTU2 #l2 #Hl12 #Hl2 #L1 #HL12
-  lapply (da_inv_bind … Hl2) -Hl2 #Hl2
-  elim (IHTU2 … Hl2 (L1.ⓑ{I}V2) …)
+| #a #I #G #L2 #V2 #T2 #U2 #d1 #_ #IHTU2 #d2 #Hd12 #Hd2 #L1 #HL12
+  lapply (da_inv_bind … Hd2) -Hd2 #Hd2
+  elim (IHTU2 … Hd2 (L1.ⓑ{I}V2) …)
   /3 width=3 by lsubsv_pair, lstas_bind, cpcs_bind_dx, ex2_intro/
-| #G #L2 #V2 #T2 #U2 #l1 #_ #IHTU2 #l2 #Hl12 #Hl2 #L1 #HL12
-  lapply (da_inv_flat … Hl2) -Hl2 #Hl2
-  elim (IHTU2 … Hl2 … HL12) -L2
+| #G #L2 #V2 #T2 #U2 #d1 #_ #IHTU2 #d2 #Hd12 #Hd2 #L1 #HL12
+  lapply (da_inv_flat … Hd2) -Hd2 #Hd2
+  elim (IHTU2 … Hd2 … HL12) -L2
   /3 width=5 by lstas_appl, cpcs_flat, ex2_intro/
-| #G #L2 #W2 #T2 #U2 #l1 #_ #IHTU2 #l2 #Hl12 #Hl2 #L1 #HL12
-  lapply (da_inv_flat … Hl2) -Hl2 #Hl2
-  elim (IHTU2 … Hl2 … HL12) -L2
+| #G #L2 #W2 #T2 #U2 #d1 #_ #IHTU2 #d2 #Hd12 #Hd2 #L1 #HL12
+  lapply (da_inv_flat … Hd2) -Hd2 #Hd2
+  elim (IHTU2 … Hd2 … HL12) -L2
   /3 width=3 by lstas_cast, ex2_intro/
 ]
 qed-.
 
-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 →
+lemma lsubsv_sta_trans: ∀h,o,G,L2,T,U2. ⦃G, L2⦄ ⊢ T •*[h, 1] U2 →
+                        ∀d. ⦃G, L2⦄ ⊢ T ▪[h, o] d+1 →
+                        ∀L1. G ⊢ L1 ⫃¡[h, o] L2 →
                         ∃∃U1. ⦃G, L1⦄ ⊢ T •*[h, 1] U1 & ⦃G, L1⦄ ⊢ U1 ⬌* U2.
 /2 width=7 by lsubsv_lstas_trans/ qed-.