closure property S4 added to abstract candidates of reducibility ...

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

diff --git a/matita/matita/contribs/lambda_delta/Basic_2/substitution/lift_lift.ma b/matita/matita/contribs/lambda_delta/Basic_2/substitution/lift_lift.ma
index 3666799d455ddbe7ffa3a4fff82ad67ba3df51f1..30bf8886e2485351bba39599feb160468e373219 100644 (file)
--- a/matita/matita/contribs/lambda_delta/Basic_2/substitution/lift_lift.ma
+++ b/matita/matita/contribs/lambda_delta/Basic_2/substitution/lift_lift.ma
@@ -14,12 +14,12 @@
 
 include "Basic_2/substitution/lift.ma".
 
-(* RELOCATION ***************************************************************)
+(* BASIC TERM RELOCATION ****************************************************)
 
 (* Main properies ***********************************************************)
 
 (* Basic_1: was: lift_inj *)
-theorem lift_inj:  ∀d,e,T1,U. ↑[d,e] T1 ≡ U → ∀T2. ↑[d,e] T2 ≡ U → T1 = T2.
+theorem lift_inj: ∀d,e,T1,U. ⇧[d,e] T1 ≡ U → ∀T2. ⇧[d,e] T2 ≡ U → T1 = T2.
 #d #e #T1 #U #H elim H -d -e -T1 -U
 [ #k #d #e #X #HX
   lapply (lift_inv_sort2 … HX) -HX //
@@ -37,10 +37,10 @@ theorem lift_inj:  ∀d,e,T1,U. ↑[d,e] T1 ≡ U → ∀T2. ↑[d,e] T2 ≡ U 
 qed-.
 
 (* Basic_1: was: lift_gen_lift *)
-theorem lift_div_le: â\88\80d1,e1,T1,T. â\86\91[d1, e1] T1 ≡ T →
-                     â\88\80d2,e2,T2. â\86\91[d2 + e1, e2] T2 ≡ T →
+theorem lift_div_le: â\88\80d1,e1,T1,T. â\87§[d1, e1] T1 ≡ T →
+                     â\88\80d2,e2,T2. â\87§[d2 + e1, e2] T2 ≡ T →
                      d1 ≤ d2 →
-                     â\88\83â\88\83T0. â\86\91[d1, e1] T0 â\89¡ T2 & â\86\91[d2, e2] T0 ≡ T1.
+                     â\88\83â\88\83T0. â\87§[d1, e1] T0 â\89¡ T2 & â\87§[d2, e2] T0 ≡ T1.
 #d1 #e1 #T1 #T #H elim H -d1 -e1 -T1 -T
 [ #k #d1 #e1 #d2 #e2 #T2 #Hk #Hd12
   lapply (lift_inv_sort2 … Hk) -Hk #Hk destruct /3 width=3/
@@ -70,10 +70,10 @@ theorem lift_div_le: ∀d1,e1,T1,T. ↑[d1, e1] T1 ≡ T →
 qed.
 
 (* Note: apparently this was missing in Basic_1 *)
-theorem lift_div_be: â\88\80d1,e1,T1,T. â\86\91[d1, e1] T1 ≡ T →
-                     â\88\80e,e2,T2. â\86\91[d1 + e, e2] T2 ≡ T →
+theorem lift_div_be: â\88\80d1,e1,T1,T. â\87§[d1, e1] T1 ≡ T →
+                     â\88\80e,e2,T2. â\87§[d1 + e, e2] T2 ≡ T →
                      e ≤ e1 → e1 ≤ e + e2 →
-                     â\88\83â\88\83T0. â\86\91[d1, e] T0 â\89¡ T2 & â\86\91[d1, e + e2 - e1] T0 ≡ T1.
+                     â\88\83â\88\83T0. â\87§[d1, e] T0 â\89¡ T2 & â\87§[d1, e + e2 - e1] T0 ≡ T1.
 #d1 #e1 #T1 #T #H elim H -d1 -e1 -T1 -T
 [ #k #d1 #e1 #e #e2 #T2 #H >(lift_inv_sort2 … H) -H /2 width=3/
 | #i #d1 #e1 #Hid1 #e #e2 #T2 #H #He1 #He1e2
@@ -99,7 +99,7 @@ theorem lift_div_be: ∀d1,e1,T1,T. ↑[d1, e1] T1 ≡ T →
 ]
 qed.
 
-theorem lift_mono: â\88\80d,e,T,U1. â\86\91[d,e] T â\89¡ U1 â\86\92 â\88\80U2. â\86\91[d,e] T ≡ U2 → U1 = U2.
+theorem lift_mono: â\88\80d,e,T,U1. â\87§[d,e] T â\89¡ U1 â\86\92 â\88\80U2. â\87§[d,e] T ≡ U2 → U1 = U2.
 #d #e #T #U1 #H elim H -d -e -T -U1
 [ #k #d #e #X #HX
   lapply (lift_inv_sort1 … HX) -HX //
@@ -117,9 +117,9 @@ theorem lift_mono: ∀d,e,T,U1. ↑[d,e] T ≡ U1 → ∀U2. ↑[d,e] T ≡ U2 
 qed-.
 
 (* Basic_1: was: lift_free (left to right) *)
-theorem lift_trans_be: â\88\80d1,e1,T1,T. â\86\91[d1, e1] T1 ≡ T →
-                       â\88\80d2,e2,T2. â\86\91[d2, e2] T ≡ T2 →
-                       d1 â\89¤ d2 â\86\92 d2 â\89¤ d1 + e1 â\86\92 â\86\91[d1, e1 + e2] T1 ≡ T2.
+theorem lift_trans_be: â\88\80d1,e1,T1,T. â\87§[d1, e1] T1 ≡ T →
+                       â\88\80d2,e2,T2. â\87§[d2, e2] T ≡ T2 →
+                       d1 â\89¤ d2 â\86\92 d2 â\89¤ d1 + e1 â\86\92 â\87§[d1, e1 + e2] T1 ≡ T2.
 #d1 #e1 #T1 #T #H elim H -d1 -e1 -T1 -T
 [ #k #d1 #e1 #d2 #e2 #T2 #HT2 #_ #_
   >(lift_inv_sort1 … HT2) -HT2 //
@@ -145,9 +145,9 @@ theorem lift_trans_be: ∀d1,e1,T1,T. ↑[d1, e1] T1 ≡ T →
 qed.
 
 (* Basic_1: was: lift_d (right to left) *)
-theorem lift_trans_le: â\88\80d1,e1,T1,T. â\86\91[d1, e1] T1 ≡ T →
-                       â\88\80d2,e2,T2. â\86\91[d2, e2] T ≡ T2 → d2 ≤ d1 →
-                       â\88\83â\88\83T0. â\86\91[d2, e2] T1 â\89¡ T0 & â\86\91[d1 + e2, e1] T0 ≡ T2.
+theorem lift_trans_le: â\88\80d1,e1,T1,T. â\87§[d1, e1] T1 ≡ T →
+                       â\88\80d2,e2,T2. â\87§[d2, e2] T ≡ T2 → d2 ≤ d1 →
+                       â\88\83â\88\83T0. â\87§[d2, e2] T1 â\89¡ T0 & â\87§[d1 + e2, e1] T0 ≡ T2.
 #d1 #e1 #T1 #T #H elim H -d1 -e1 -T1 -T
 [ #k #d1 #e1 #d2 #e2 #X #HX #_
   >(lift_inv_sort1 … HX) -HX /2 width=3/
@@ -172,9 +172,9 @@ theorem lift_trans_le: ∀d1,e1,T1,T. ↑[d1, e1] T1 ≡ T →
 qed.
 
 (* Basic_1: was: lift_d (left to right) *)
-theorem lift_trans_ge: â\88\80d1,e1,T1,T. â\86\91[d1, e1] T1 ≡ T →
-                       â\88\80d2,e2,T2. â\86\91[d2, e2] T ≡ T2 → d1 + e1 ≤ d2 →
-                       â\88\83â\88\83T0. â\86\91[d2 - e1, e2] T1 â\89¡ T0 & â\86\91[d1, e1] T0 ≡ T2.
+theorem lift_trans_ge: â\88\80d1,e1,T1,T. â\87§[d1, e1] T1 ≡ T →
+                       â\88\80d2,e2,T2. â\87§[d2, e2] T ≡ T2 → d1 + e1 ≤ d2 →
+                       â\88\83â\88\83T0. â\87§[d2 - e1, e2] T1 â\89¡ T0 & â\87§[d1, e1] T0 ≡ T2.
 #d1 #e1 #T1 #T #H elim H -d1 -e1 -T1 -T
 [ #k #d1 #e1 #d2 #e2 #X #HX #_
   >(lift_inv_sort1 … HX) -HX /2 width=3/