- update in Basic_2

[helm.git] / matita / matita / contribs / lambda_delta / Basic_2 / substitution / ldrop_ldrop.ma

diff --git a/matita/matita/contribs/lambda_delta/Basic_2/substitution/ldrop_ldrop.ma b/matita/matita/contribs/lambda_delta/Basic_2/substitution/ldrop_ldrop.ma
index a495bbdcb4b9766bf854b76c1bb181a541eb6276..90f724ad36f93a19d2570ccbc88d62eae1bae8e0 100644 (file)
--- a/matita/matita/contribs/lambda_delta/Basic_2/substitution/ldrop_ldrop.ma
+++ b/matita/matita/contribs/lambda_delta/Basic_2/substitution/ldrop_ldrop.ma
@@ -19,49 +19,49 @@ include "Basic_2/substitution/ldrop.ma".
 
 (* Main properties **********************************************************)
 
-(* Basic_1: was: ldrop_mono *)
-theorem ldrop_mono: â\88\80d,e,L,L1. â\86\93[d, e] L ≡ L1 →
-                    â\88\80L2. â\86\93[d, e] L ≡ L2 → L1 = L2.
-#d #e #L #L1 #H elim H -H d e L L1
+(* Basic_1: was: drop_mono *)
+theorem ldrop_mono: â\88\80d,e,L,L1. â\87©[d, e] L ≡ L1 →
+                    â\88\80L2. â\87©[d, e] L ≡ L2 → L1 = L2.
+#d #e #L #L1 #H elim H -d -e -L -L1
 [ #d #e #L2 #H
-  >(ldrop_inv_atom1 … H) -H L2 //
+  >(ldrop_inv_atom1 … H) -L2 //
 | #K #I #V #L2 #HL12
-   <(ldrop_inv_refl … HL12) -HL12 L2 //
+   <(ldrop_inv_refl … HL12) -L2 //
 | #L #K #I #V #e #_ #IHLK #L2 #H
-  lapply (ldrop_inv_ldrop1 … H ?) -H /2/
+  lapply (ldrop_inv_ldrop1 … H ?) -H // /2 width=1/
 | #L #K1 #I #T #V1 #d #e #_ #HVT1 #IHLK1 #X #H
-  elim (ldrop_inv_skip1 … H ?) -H // <minus_plus_m_m #K2 #V2 #HLK2 #HVT2 #H destruct -X
-  >(lift_inj … HVT1 … HVT2) -HVT1 HVT2
-  >(IHLK1 … HLK2) -IHLK1 HLK2 // 
+  elim (ldrop_inv_skip1 … H ?) -H // <minus_plus_m_m #K2 #V2 #HLK2 #HVT2 #H destruct
+  >(lift_inj … HVT1 … HVT2) -HVT1 -HVT2
+  >(IHLK1 … HLK2) -IHLK1 -HLK2 //
 ]
 qed-.
 
-(* Basic_1: was: ldrop_conf_ge *)
-theorem ldrop_conf_ge: â\88\80d1,e1,L,L1. â\86\93[d1, e1] L ≡ L1 →
-                       â\88\80e2,L2. â\86\93[0, e2] L ≡ L2 → d1 + e1 ≤ e2 →
-                       â\86\93[0, e2 - e1] L1 ≡ L2.
-#d1 #e1 #L #L1 #H elim H -H d1 e1 L L1
+(* Basic_1: was: drop_conf_ge *)
+theorem ldrop_conf_ge: â\88\80d1,e1,L,L1. â\87©[d1, e1] L ≡ L1 →
+                       â\88\80e2,L2. â\87©[0, e2] L ≡ L2 → d1 + e1 ≤ e2 →
+                       â\87©[0, e2 - e1] L1 ≡ L2.
+#d1 #e1 #L #L1 #H elim H -d1 -e1 -L -L1
 [ #d #e #e2 #L2 #H
-  >(ldrop_inv_atom1 … H) -H L2 //
+  >(ldrop_inv_atom1 … H) -L2 //
 | //
 | #L #K #I #V #e #_ #IHLK #e2 #L2 #H #He2
-  lapply (ldrop_inv_ldrop1 … H ?) -H /2/ #HL2
-  <minus_plus_comm /3/
+  lapply (ldrop_inv_ldrop1 … H ?) -H /2 width=2/ #HL2
+  <minus_plus >minus_minus_comm /3 width=1/
 | #L #K #I #V1 #V2 #d #e #_ #_ #IHLK #e2 #L2 #H #Hdee2
   lapply (transitive_le 1 … Hdee2) // #He2
   lapply (ldrop_inv_ldrop1 … H ?) -H // -He2 #HL2
   lapply (transitive_le (1 + e) … Hdee2) // #Hee2
-  @ldrop_ldrop_lt >minus_minus_comm /3/ (**) (* explicit constructor *)
+  @ldrop_ldrop_lt >minus_minus_comm /3 width=1/ (**) (* explicit constructor *)
 ]
 qed.
 
-(* Basic_1: was: ldrop_conf_lt *)
-theorem ldrop_conf_lt: â\88\80d1,e1,L,L1. â\86\93[d1, e1] L ≡ L1 →
-                       â\88\80e2,K2,I,V2. â\86\93[0, e2] L â\89¡ K2. ð\9d\95\93{I} V2 →
+(* Basic_1: was: drop_conf_lt *)
+theorem ldrop_conf_lt: â\88\80d1,e1,L,L1. â\87©[d1, e1] L ≡ L1 →
+                       â\88\80e2,K2,I,V2. â\87©[0, e2] L â\89¡ K2. â\93\91{I} V2 →
                        e2 < d1 → let d ≝ d1 - e2 - 1 in
-                       â\88\83â\88\83K1,V1. â\86\93[0, e2] L1 â\89¡ K1. ð\9d\95\93{I} V1 &
-                                â\86\93[d, e1] K2 â\89¡ K1 & â\86\91[d, e1] V1 ≡ V2.
-#d1 #e1 #L #L1 #H elim H -H d1 e1 L L1
+                       â\88\83â\88\83K1,V1. â\87©[0, e2] L1 â\89¡ K1. â\93\91{I} V1 &
+                                â\87©[d, e1] K2 â\89¡ K1 & â\87§[d, e1] V1 ≡ V2.
+#d1 #e1 #L #L1 #H elim H -d1 -e1 -L -L1
 [ #d #e #e2 #K2 #I #V2 #H
   lapply (ldrop_inv_atom1 … H) -H #H destruct
 | #L #I #V #e2 #K2 #J #V2 #_ #H
@@ -70,58 +70,57 @@ theorem ldrop_conf_lt: ∀d1,e1,L,L1. ↓[d1, e1] L ≡ L1 →
   elim (lt_zero_false … H)
 | #L1 #L2 #I #V1 #V2 #d #e #HL12 #HV12 #IHL12 #e2 #K2 #J #V #H #He2d
   elim (ldrop_inv_O1 … H) -H *
-  [ -IHL12 He2d #H1 #H2 destruct -e2 K2 J V /2 width=5/
+  [ -IHL12 -He2d #H1 #H2 destruct /2 width=5/
   | -HL12 -HV12 #He #HLK
-    elim (IHL12 … HLK ?) -IHL12 HLK [ <minus_minus /3 width=5/ | /2/ ] (**) (* a bit slow *)
+    elim (IHL12 … HLK ?) -IHL12 -HLK [ <minus_minus /3 width=5/ | /2 width=1/ ] (**) (* a bit slow *)
   ]
 ]
 qed.
 
-(* Basic_1: was: ldrop_trans_le *)
-theorem ldrop_trans_le: â\88\80d1,e1,L1,L. â\86\93[d1, e1] L1 ≡ L →
-                        â\88\80e2,L2. â\86\93[0, e2] L ≡ L2 → e2 ≤ d1 →
-                        â\88\83â\88\83L0. â\86\93[0, e2] L1 â\89¡ L0 & â\86\93[d1 - e2, e1] L0 ≡ L2.
-#d1 #e1 #L1 #L #H elim H -H d1 e1 L1 L
+(* Basic_1: was: drop_trans_le *)
+theorem ldrop_trans_le: â\88\80d1,e1,L1,L. â\87©[d1, e1] L1 ≡ L →
+                        â\88\80e2,L2. â\87©[0, e2] L ≡ L2 → e2 ≤ d1 →
+                        â\88\83â\88\83L0. â\87©[0, e2] L1 â\89¡ L0 & â\87©[d1 - e2, e1] L0 ≡ L2.
+#d1 #e1 #L1 #L #H elim H -d1 -e1 -L1 -L
 [ #d #e #e2 #L2 #H
-  >(ldrop_inv_atom1 … H) -H L2 /2/
+  >(ldrop_inv_atom1 … H) -L2 /2 width=3/
 | #K #I #V #e2 #L2 #HL2 #H
-  lapply (le_O_to_eq_O … H) -H #H destruct -e2 /2/
+  lapply (le_n_O_to_eq … H) -H #H destruct /2 width=3/
 | #L1 #L2 #I #V #e #_ #IHL12 #e2 #L #HL2 #H
-  lapply (le_O_to_eq_O … H) -H #H destruct -e2;
-  elim (IHL12 … HL2 ?) -IHL12 HL2 // #L0 #H #HL0
-  lapply (ldrop_inv_refl … H) -H #H destruct -L1 /3 width=5/
+  lapply (le_n_O_to_eq … H) -H #H destruct
+  elim (IHL12 … HL2 ?) -IHL12 -HL2 // #L0 #H #HL0
+  lapply (ldrop_inv_refl … H) -H #H destruct /3 width=5/
 | #L1 #L2 #I #V1 #V2 #d #e #HL12 #HV12 #IHL12 #e2 #L #H #He2d
   elim (ldrop_inv_O1 … H) -H *
-  [ -He2d IHL12 #H1 #H2 destruct -e2 L /3 width=5/
-  | -HL12 HV12 #He2 #HL2
-    elim (IHL12 … HL2 ?) -IHL12 HL2 L2
-    [ >minus_le_minus_minus_comm // /3/ | /2/ ]
+  [ -He2d -IHL12 #H1 #H2 destruct /3 width=5/
+  | -HL12 -HV12 #He2 #HL2
+    elim (IHL12 … HL2 ?) -L2 [ >minus_le_minus_minus_comm // /3 width=3/ | /2 width=1/ ]
   ]
 ]
 qed.
 
-(* Basic_1: was: ldrop_trans_ge *)
-theorem ldrop_trans_ge: â\88\80d1,e1,L1,L. â\86\93[d1, e1] L1 ≡ L →
-                        â\88\80e2,L2. â\86\93[0, e2] L â\89¡ L2 â\86\92 d1 â\89¤ e2 â\86\92 â\86\93[0, e1 + e2] L1 ≡ L2.
-#d1 #e1 #L1 #L #H elim H -H d1 e1 L1 L
+(* Basic_1: was: drop_trans_ge *)
+theorem ldrop_trans_ge: â\88\80d1,e1,L1,L. â\87©[d1, e1] L1 ≡ L →
+                        â\88\80e2,L2. â\87©[0, e2] L â\89¡ L2 â\86\92 d1 â\89¤ e2 â\86\92 â\87©[0, e1 + e2] L1 ≡ L2.
+#d1 #e1 #L1 #L #H elim H -d1 -e1 -L1 -L
 [ #d #e #e2 #L2 #H
-  >(ldrop_inv_atom1 … H) -H L2 //
+  >(ldrop_inv_atom1 … H) -H -L2 //
 | //
-| /3/
+| /3 width=1/
 | #L1 #L2 #I #V1 #V2 #d #e #H_ #_ #IHL12 #e2 #L #H #Hde2
   lapply (lt_to_le_to_lt 0 … Hde2) // #He2
   lapply (lt_to_le_to_lt … (e + e2) He2 ?) // #Hee2
   lapply (ldrop_inv_ldrop1 … H ?) -H // #HL2
-  @ldrop_ldrop_lt // >le_plus_minus // @IHL12 /2/ (**) (* explicit constructor *)
+  @ldrop_ldrop_lt // >le_plus_minus // @IHL12 /2 width=1/ (**) (* explicit constructor *)
 ]
 qed.
 
 theorem ldrop_trans_ge_comm: ∀d1,e1,e2,L1,L2,L.
-                             â\86\93[d1, e1] L1 â\89¡ L â\86\92 â\86\93[0, e2] L ≡ L2 → d1 ≤ e2 →
-                             â\86\93[0, e2 + e1] L1 ≡ L2.
+                             â\87©[d1, e1] L1 â\89¡ L â\86\92 â\87©[0, e2] L ≡ L2 → d1 ≤ e2 →
+                             â\87©[0, e2 + e1] L1 ≡ L2.
 #e1 #e1 #e2 >commutative_plus /2 width=5/
 qed.
 
-(* Basic_1: was: ldrop_conf_rev *)
-axiom ldrop_div: â\88\80e1,L1,L. â\86\93[0, e1] L1 â\89¡ L â\86\92 â\88\80e2,L2. â\86\93[0, e2] L2 ≡ L →
-                 â\88\83â\88\83L0. â\86\93[0, e1] L0 â\89¡ L2 & â\86\93[e1, e2] L0 ≡ L1.
+(* Basic_1: was: drop_conf_rev *)
+axiom ldrop_div: â\88\80e1,L1,L. â\87©[0, e1] L1 â\89¡ L â\86\92 â\88\80e2,L2. â\87©[0, e2] L2 ≡ L →
+                 â\88\83â\88\83L0. â\87©[0, e1] L0 â\89¡ L2 & â\87©[e1, e2] L0 ≡ L1.