milestone in basic_2

[helm.git] / matita / matita / contribs / lambdadelta / basic_2 / unfold / lpqs_cpqs.ma

diff --git a/matita/matita/contribs/lambdadelta/basic_2/unfold/lpqs_cpqs.ma b/matita/matita/contribs/lambdadelta/basic_2/unfold/lpqs_cpqs.ma
index fb94a49de339af9ef7ad61e09d10de3ad781e93d..7b8f17b4a5b12a3b843f0d50d693fbccab0667d5 100644 (file)
--- a/matita/matita/contribs/lambdadelta/basic_2/unfold/lpqs_cpqs.ma
+++ b/matita/matita/contribs/lambdadelta/basic_2/unfold/lpqs_cpqs.ma
@@ -13,6 +13,7 @@
 (**************************************************************************)
 
 include "basic_2/grammar/lpx_sn_lpx_sn.ma".
+include "basic_2/substitution/fsupp.ma".
 include "basic_2/unfold/lpqs_ldrop.ma".
 
 (* SN RESTRICTED PARALLEL COMPUTATION FOR LOCAL ENVIRONMENTS ****************)
@@ -20,8 +21,8 @@ include "basic_2/unfold/lpqs_ldrop.ma".
 (* Main properties on context-sensitive rest parallel computation for terms *)
 
 theorem cpqs_trans_lpqs: lpx_sn_transitive cpqs cpqs.
-#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 (cpqs_inv_atom1 … H1) -H1
   [ #H destruct
     elim (cpqs_inv_atom1 … HT2) -HT2
@@ -29,16 +30,16 @@ theorem cpqs_trans_lpqs: lpx_sn_transitive cpqs cpqs.
     | * #K2 #V #V2 #i #HLK2 #HV2 #HVT2 #H destruct
       elim (lpqs_ldrop_trans_O1 … HL12 … HLK2) -L2 #X #HLK1 #H
       elim (lpqs_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 (lpqs_ldrop_conf … HLK1 … HL12) -HL12 #X #H #HLK2
     elim (lpqs_inv_pair1 … H) -H #K2 #W2 #HK12 #_ #H destruct
     lapply (ldrop_fwd_ldrop2 … HLK2) -W2 #HLK2
     elim (cpqs_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 (cpqs_inv_bind1 … H1) -H1 *
   [ #V #T #HV1 #HT1 #H destruct
     elim (cpqs_inv_bind1 … H2) -H2 *
@@ -49,7 +50,7 @@ theorem cpqs_trans_lpqs: lpx_sn_transitive cpqs cpqs.
     elim (lift_total X2 0 1) #Y2 #HXY2
     lapply (cpqs_lift … H2 (L2.ⓓV1) … HXY1 … HXY2) /2 width=1/ -X1 /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 (cpqs_inv_flat1 … H1) -H1 *
   [ #V #T #HV1 #HT1 #H destruct
     elim (cpqs_inv_flat1 … H2) -H2 *