X-Git-Url: http://matita.cs.unibo.it/gitweb/?a=blobdiff_plain;f=matita%2Fmatita%2Fcontribs%2Flambda_delta%2FBasic_2%2Fsubstitution%2Fltps_ldrop.ma;h=f777d1cd77c1111797a04a7e4db84915e725d19f;hb=9aa9a54946719d3fdb4cadb7c7d33fd13956c083;hp=32501c8e6d5b70d69cddba32c9049d8b91eb5c0b;hpb=035e3f52f8da3cb3cdb493aa20568ad673cc2cf5;p=helm.git

diff --git a/matita/matita/contribs/lambda_delta/Basic_2/substitution/ltps_ldrop.ma b/matita/matita/contribs/lambda_delta/Basic_2/substitution/ltps_ldrop.ma
index 32501c8e6..f777d1cd7 100644
--- a/matita/matita/contribs/lambda_delta/Basic_2/substitution/ltps_ldrop.ma
+++ b/matita/matita/contribs/lambda_delta/Basic_2/substitution/ltps_ldrop.ma
@@ -17,115 +17,115 @@ include "Basic_2/substitution/ltps.ma".
 (* PARALLEL SUBSTITUTION ON LOCAL ENVIRONMENTS ******************************)
 
 lemma ltps_ldrop_conf_ge: ∀L0,L1,d1,e1. L0 [d1, e1] ≫ L1 →
-                         ∀L2,e2. ↓[0, e2] L0 ≡ L2 →
-                         d1 + e1 ≤ e2 → ↓[0, e2] L1 ≡ L2.
-#L0 #L1 #d1 #e1 #H elim H -H L0 L1 d1 e1
+                          ∀L2,e2. ↓[0, e2] L0 ≡ L2 →
+                          d1 + e1 ≤ e2 → ↓[0, e2] L1 ≡ L2.
+#L0 #L1 #d1 #e1 #H elim H -L0 -L1 -d1 -e1
 [ #d1 #e1 #L2 #e2 #H >(ldrop_inv_atom1 … H) -H //
 | //
 | normalize #K0 #K1 #I #V0 #V1 #e1 #_ #_ #IHK01 #L2 #e2 #H #He12
-  lapply (plus_le_weak … He12) #He2
+  elim (le_inv_plus_l … He12) #_ #He2
   lapply (ldrop_inv_ldrop1 … H ?) -H // #HK0L2
-  lapply (IHK01 … HK0L2 ?) -IHK01 HK0L2 /2/
+  lapply (IHK01 … HK0L2 ?) -K0 /2 width=1/
 | #K0 #K1 #I #V0 #V1 #d1 #e1 >plus_plus_comm_23 #_ #_ #IHK01 #L2 #e2 #H #Hd1e2
-  lapply (plus_le_weak … Hd1e2) #He2
+  elim (le_inv_plus_l … Hd1e2) #_ #He2
   lapply (ldrop_inv_ldrop1 … H ?) -H // #HK0L2
-  lapply (IHK01 … HK0L2 ?) -IHK01 HK0L2 /2/
+  lapply (IHK01 … HK0L2 ?) -K0 /2 width=1/
 ]
 qed.
 
 lemma ltps_ldrop_trans_ge: ∀L1,L0,d1,e1. L1 [d1, e1] ≫ L0 →
-                          ∀L2,e2. ↓[0, e2] L0 ≡ L2 →
-                          d1 + e1 ≤ e2 → ↓[0, e2] L1 ≡ L2.
-#L1 #L0 #d1 #e1 #H elim H -H L1 L0 d1 e1
+                           ∀L2,e2. ↓[0, e2] L0 ≡ L2 →
+                           d1 + e1 ≤ e2 → ↓[0, e2] L1 ≡ L2.
+#L1 #L0 #d1 #e1 #H elim H -L1 -L0 -d1 -e1
 [ #d1 #e1 #L2 #e2 #H >(ldrop_inv_atom1 … H) -H //
 | //
 | normalize #K1 #K0 #I #V1 #V0 #e1 #_ #_ #IHK10 #L2 #e2 #H #He12
-  lapply (plus_le_weak … He12) #He2
+  elim (le_inv_plus_l … He12) #_ #He2
   lapply (ldrop_inv_ldrop1 … H ?) -H // #HK0L2
-  lapply (IHK10 … HK0L2 ?) -IHK10 HK0L2 /2/
+  lapply (IHK10 … HK0L2 ?) -K0 /2 width=1/
 | #K0 #K1 #I #V1 #V0 #d1 #e1 >plus_plus_comm_23 #_ #_ #IHK10 #L2 #e2 #H #Hd1e2
-  lapply (plus_le_weak … Hd1e2) #He2
+  elim (le_inv_plus_l … Hd1e2) #_ #He2
   lapply (ldrop_inv_ldrop1 … H ?) -H // #HK0L2
-  lapply (IHK10 … HK0L2 ?) -IHK10 HK0L2 /2/
+  lapply (IHK10 … HK0L2 ?) -IHK10 -HK0L2 /2 width=1/
 ]
 qed.
 
 lemma ltps_ldrop_conf_be: ∀L0,L1,d1,e1. L0 [d1, e1] ≫ L1 →
-                         ∀L2,e2. ↓[0, e2] L0 ≡ L2 → d1 ≤ e2 → e2 ≤ d1 + e1 →
-                         ∃∃L. L2 [0, d1 + e1 - e2] ≫ L & ↓[0, e2] L1 ≡ L.
-#L0 #L1 #d1 #e1 #H elim H -H L0 L1 d1 e1
-[ #d1 #e1 #L2 #e2 #H >(ldrop_inv_atom1 … H) -H /2/
+                          ∀L2,e2. ↓[0, e2] L0 ≡ L2 → d1 ≤ e2 → e2 ≤ d1 + e1 →
+                          ∃∃L. L2 [0, d1 + e1 - e2] ≫ L & ↓[0, e2] L1 ≡ L.
+#L0 #L1 #d1 #e1 #H elim H -L0 -L1 -d1 -e1
+[ #d1 #e1 #L2 #e2 #H >(ldrop_inv_atom1 … H) -H /2 width=3/
 | normalize #L #I #V #L2 #e2 #HL2 #_ #He2
-  lapply (le_n_O_to_eq … He2) -He2 #H destruct -e2;
-  lapply (ldrop_inv_refl … HL2) -HL2 #H destruct -L2 /2/
+  lapply (le_n_O_to_eq … He2) -He2 #H destruct
+  lapply (ldrop_inv_refl … HL2) -HL2 #H destruct /2 width=3/
 | normalize #K0 #K1 #I #V0 #V1 #e1 #HK01 #HV01 #IHK01 #L2 #e2 #H #_ #He21
   lapply (ldrop_inv_O1 … H) -H * * #He2 #HK0L2
-  [ destruct -IHK01 He21 e2 L2 <minus_n_O /3/
-  | -HK01 HV01 <minus_le_minus_minus_comm //
-    elim (IHK01 … HK0L2 ? ?) -IHK01 HK0L2 /3/
+  [ -IHK01 -He21 destruct <minus_n_O /3 width=3/
+  | -HK01 -HV01 <minus_le_minus_minus_comm //
+    elim (IHK01 … HK0L2 ? ?) -K0 // /2 width=1/ /3 width=3/
   ]
 | #K0 #K1 #I #V0 #V1 #d1 #e1 >plus_plus_comm_23 #_ #_ #IHK01 #L2 #e2 #H #Hd1e2 #He2de1
-  lapply (plus_le_weak … Hd1e2) #He2
+  elim (le_inv_plus_l … Hd1e2) #_ #He2
   <minus_le_minus_minus_comm //
   lapply (ldrop_inv_ldrop1 … H ?) -H // #HK0L2
-  elim (IHK01 … HK0L2 ? ?) -IHK01 HK0L2 /3/
+  elim (IHK01 … HK0L2 ? ?) -K0 /2 width=1/ /3 width=3/
 ]
 qed.
 
 lemma ltps_ldrop_trans_be: ∀L1,L0,d1,e1. L1 [d1, e1] ≫ L0 →
-                          ∀L2,e2. ↓[0, e2] L0 ≡ L2 → d1 ≤ e2 → e2 ≤ d1 + e1 →
-                          ∃∃L. L [0, d1 + e1 - e2] ≫ L2 & ↓[0, e2] L1 ≡ L.
-#L1 #L0 #d1 #e1 #H elim H -H L1 L0 d1 e1
-[ #d1 #e1 #L2 #e2 #H >(ldrop_inv_atom1 … H) -H /2/
+                           ∀L2,e2. ↓[0, e2] L0 ≡ L2 → d1 ≤ e2 → e2 ≤ d1 + e1 →
+                           ∃∃L. L [0, d1 + e1 - e2] ≫ L2 & ↓[0, e2] L1 ≡ L.
+#L1 #L0 #d1 #e1 #H elim H -L1 -L0 -d1 -e1
+[ #d1 #e1 #L2 #e2 #H >(ldrop_inv_atom1 … H) -H /2 width=3/
 | normalize #L #I #V #L2 #e2 #HL2 #_ #He2
-  lapply (le_n_O_to_eq … He2) -He2 #H destruct -e2;
-  lapply (ldrop_inv_refl … HL2) -HL2 #H destruct -L2 /2/
+  lapply (le_n_O_to_eq … He2) -He2 #H destruct
+  lapply (ldrop_inv_refl … HL2) -HL2 #H destruct /2 width=3/
 | normalize #K1 #K0 #I #V1 #V0 #e1 #HK10 #HV10 #IHK10 #L2 #e2 #H #_ #He21
   lapply (ldrop_inv_O1 … H) -H * * #He2 #HK0L2
-  [ destruct -IHK10 He21 e2 L2 <minus_n_O /3/
-  | -HK10 HV10 <minus_le_minus_minus_comm //
-    elim (IHK10 … HK0L2 ? ?) -IHK10 HK0L2 /3/
+  [ -IHK10 -He21 destruct <minus_n_O /3 width=3/
+  | -HK10 -HV10 <minus_le_minus_minus_comm //
+    elim (IHK10 … HK0L2 ? ?) -K0 // /2 width=1/ /3 width=3/
   ]
 | #K1 #K0 #I #V1 #V0 #d1 #e1 >plus_plus_comm_23 #_ #_ #IHK10 #L2 #e2 #H #Hd1e2 #He2de1
-  lapply (plus_le_weak … Hd1e2) #He2
+  elim (le_inv_plus_l … Hd1e2) #_ #He2
   <minus_le_minus_minus_comm //
   lapply (ldrop_inv_ldrop1 … H ?) -H // #HK0L2
-  elim (IHK10 … HK0L2 ? ?) -IHK10 HK0L2 /3/
+  elim (IHK10 … HK0L2 ? ?) -K0 /2 width=1/ /3 width=3/
 ]
 qed.
 
 lemma ltps_ldrop_conf_le: ∀L0,L1,d1,e1. L0 [d1, e1] ≫ L1 →
-                         ∀L2,e2. ↓[0, e2] L0 ≡ L2 → e2 ≤ d1 →
-                         ∃∃L. L2 [d1 - e2, e1] ≫ L & ↓[0, e2] L1 ≡ L.
-#L0 #L1 #d1 #e1 #H elim H -H L0 L1 d1 e1
-[ #d1 #e1 #L2 #e2 #H >(ldrop_inv_atom1 … H) -H /2/
-| /2/
+                          ∀L2,e2. ↓[0, e2] L0 ≡ L2 → e2 ≤ d1 →
+                          ∃∃L. L2 [d1 - e2, e1] ≫ L & ↓[0, e2] L1 ≡ L.
+#L0 #L1 #d1 #e1 #H elim H -L0 -L1 -d1 -e1
+[ #d1 #e1 #L2 #e2 #H >(ldrop_inv_atom1 … H) -H /2 width=3/
+| /2 width=3/
 | normalize #K0 #K1 #I #V0 #V1 #e1 #HK01 #HV01 #_ #L2 #e2 #H #He2
-  lapply (le_n_O_to_eq … He2) -He2 #He2 destruct -e2;
-  lapply (ldrop_inv_refl … H) -H #H destruct -L2 /3/
+  lapply (le_n_O_to_eq … He2) -He2 #He2 destruct
+  lapply (ldrop_inv_refl … H) -H #H destruct /3 width=3/
 | #K0 #K1 #I #V0 #V1 #d1 #e1 #HK01 #HV01 #IHK01 #L2 #e2 #H #He2d1
   lapply (ldrop_inv_O1 … H) -H * * #He2 #HK0L2
-  [ destruct -IHK01 He2d1 e2 L2 <minus_n_O /3/
-  | -HK01 HV01 <minus_le_minus_minus_comm //
-    elim (IHK01 … HK0L2 ?) -IHK01 HK0L2 /3/
+  [ -IHK01 -He2d1 destruct <minus_n_O /3 width=3/
+  | -HK01 -HV01 <minus_le_minus_minus_comm //
+    elim (IHK01 … HK0L2 ?) -K0 /2 width=1/ /3 width=3/
   ]
 ]
 qed.
 
 lemma ltps_ldrop_trans_le: ∀L1,L0,d1,e1. L1 [d1, e1] ≫ L0 →
-                          ∀L2,e2. ↓[0, e2] L0 ≡ L2 → e2 ≤ d1 →
-                          ∃∃L. L [d1 - e2, e1] ≫ L2 & ↓[0, e2] L1 ≡ L.
-#L1 #L0 #d1 #e1 #H elim H -H L1 L0 d1 e1
-[ #d1 #e1 #L2 #e2 #H >(ldrop_inv_atom1 … H) -H /2/
-| /2/
+                           ∀L2,e2. ↓[0, e2] L0 ≡ L2 → e2 ≤ d1 →
+                           ∃∃L. L [d1 - e2, e1] ≫ L2 & ↓[0, e2] L1 ≡ L.
+#L1 #L0 #d1 #e1 #H elim H -L1 -L0 -d1 -e1
+[ #d1 #e1 #L2 #e2 #H >(ldrop_inv_atom1 … H) -H /2 width=3/
+| /2 width=3/
 | normalize #K1 #K0 #I #V1 #V0 #e1 #HK10 #HV10 #_ #L2 #e2 #H #He2
-  lapply (le_n_O_to_eq … He2) -He2 #He2 destruct -e2;
-  lapply (ldrop_inv_refl … H) -H #H destruct -L2 /3/
+  lapply (le_n_O_to_eq … He2) -He2 #He2 destruct
+  lapply (ldrop_inv_refl … H) -H #H destruct /3 width=3/
 | #K1 #K0 #I #V1 #V0 #d1 #e1 #HK10 #HV10 #IHK10 #L2 #e2 #H #He2d1
   lapply (ldrop_inv_O1 … H) -H * * #He2 #HK0L2
-  [ destruct -IHK10 He2d1 e2 L2 <minus_n_O /3/
-  | -HK10 HV10 <minus_le_minus_minus_comm //
-    elim (IHK10 … HK0L2 ?) -IHK10 HK0L2 /3/
+  [ -IHK10 -He2d1 destruct <minus_n_O /3 width=3/
+  | -HK10 -HV10 <minus_le_minus_minus_comm //
+    elim (IHK10 … HK0L2 ?) -K0 /2 width=1/ /3 width=3/
   ]
 ]
 qed.