- 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 f4b20bcb594ab4fbf93f5a2cc4d0bc9dc650289e..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
@@ -19,9 +19,9 @@ 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.
+(* 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) -L2 //
@@ -36,17 +36,17 @@ theorem ldrop_mono: ∀d,e,L,L1. ↓[d, e] L ≡ L1 →
 ]
 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.
+(* 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) -L2 //
 | //
 | #L #K #I #V #e #_ #IHLK #e2 #L2 #H #He2
   lapply (ldrop_inv_ldrop1 … H ?) -H /2 width=2/ #HL2
-  <minus_plus_comm /3 width=1/
+  <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
@@ -55,12 +55,12 @@ theorem ldrop_conf_ge: ∀d1,e1,L,L1. ↓[d1, e1] L ≡ L1 →
 ]
 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.
+                       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
@@ -77,17 +77,17 @@ theorem ldrop_conf_lt: ∀d1,e1,L,L1. ↓[d1, e1] L ≡ L1 →
 ]
 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.
+(* 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) -L2 /2 width=3/
 | #K #I #V #e2 #L2 #HL2 #H
-  lapply (le_O_to_eq_O … H) -H #H destruct /2 width=3/
+  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
+  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
@@ -99,9 +99,9 @@ theorem ldrop_trans_le: ∀d1,e1,L1,L. ↓[d1, e1] L1 ≡ L →
 ]
 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.
+(* 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 //
@@ -116,11 +116,11 @@ theorem ldrop_trans_ge: ∀d1,e1,L1,L. ↓[d1, e1] L1 ≡ L →
 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.