update in basic_2

[helm.git] / matita / matita / contribs / lambdadelta / basic_2 / substitution / lpss_cpss.ma

diff --git a/matita/matita/contribs/lambdadelta/basic_2/substitution/lpss_cpss.ma b/matita/matita/contribs/lambdadelta/basic_2/substitution/lpss_cpss.ma
index c9c17fa19d788f5b7db566e95d7386ab35af64be..71ab873af3d4bd97b2cfa7e35d689d5d8e6cbc87 100644 (file)
--- a/matita/matita/contribs/lambdadelta/basic_2/substitution/lpss_cpss.ma
+++ b/matita/matita/contribs/lambdadelta/basic_2/substitution/lpss_cpss.ma
@@ -13,6 +13,7 @@
 (**************************************************************************)
 
 include "basic_2/grammar/lpx_sn_lpx_sn.ma".
+include "basic_2/substitution/fsupp.ma".
 include "basic_2/substitution/lpss_ldrop.ma".
 
 (* SN PARALLEL SUBSTITUTION FOR LOCAL ENVIRONMENTS **************************)
@@ -20,8 +21,8 @@ include "basic_2/substitution/lpss_ldrop.ma".
 (* Main properties on context-sensitive parallel substitution for terms *****)
 
 theorem cpss_trans_lpss: lpx_sn_transitive cpss cpss.
-#L1 #T1 @(f2_ind … fw … L1 T1) -L1 -T1 #n #IH #L1 * [|*]
-[ #I #Hn #T #H1 #L2 #HL12 #T2 #HT2 destruct
+#L0 #T0 @(fsupp_wf_ind … L0 T0) -L0 -T0 #L0 #T0 #IH #L1 * [|*]
+[ #I #HL #HT #T #H1 #L2 #HL12 #T2 #HT2 destruct
   elim (cpss_inv_atom1 … H1) -H1
   [ #H destruct
     elim (cpss_inv_atom1 … HT2) -HT2
@@ -29,19 +30,19 @@ theorem cpss_trans_lpss: lpx_sn_transitive cpss cpss.
     | * #K2 #V #V2 #i #HLK2 #HV2 #HVT2 #H destruct
       elim (lpss_ldrop_trans_O1 … HL12 … HLK2) -L2 #X #HLK1 #H
       elim (lpss_inv_pair2 … H) -H #K1 #V1 #HK12 #HV1 #H destruct
-      lapply (ldrop_pair2_fwd_fw … HLK1 (#i)) /3 width=9/
+      lapply (fsupp_lref … HLK1) /3 width=9/
     ]
   | * #K1 #V1 #V #i #HLK1 #HV1 #HVT #H destruct
     elim (lpss_ldrop_conf … HLK1 … HL12) -HL12 #X #H #HLK2
     elim (lpss_inv_pair1 … H) -H #K2 #W2 #HK12 #_ #H destruct
     lapply (ldrop_fwd_ldrop2 … HLK2) -W2 #HLK2
     elim (cpss_inv_lift1 … HT2 … HLK2 … HVT) -L2 -T
-    lapply (ldrop_pair2_fwd_fw … HLK1 (#i)) /3 width=9/
+    lapply (fsupp_lref … HLK1) /3 width=9/
   ]
-| #a #I #V1 #T1 #Hn #X1 #H1 #L2 #HL12 #X2 #H2
+| #a #I #V1 #T1 #HL #HT #X1 #H1 #L2 #HL12 #X2 #H2
   elim (cpss_inv_bind1 … H1) -H1 #V #T #HV1 #HT1 #H destruct
   elim (cpss_inv_bind1 … H2) -H2 #V2 #T2 #HV2 #HT2 #H destruct /4 width=5/
-| #I #V1 #T1 #Hn #X1 #H1 #L2 #HL12 #X2 #H2
+| #I #V1 #T1 #HL #HT #X1 #H1 #L2 #HL12 #X2 #H2
   elim (cpss_inv_flat1 … H1) -H1 #V #T #HV1 #HT1 #H destruct
   elim (cpss_inv_flat1 … H2) -H2 #V2 #T2 #HV2 #HT2 #H destruct /3 width=5/
 ]