- the theory of parallel substitution of local environments (ltps) is ready

[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 205eab2bfdb84c861c903edd77703be23f845c12..f9c99457db747c0e0c0b1983e4873c2aa52235fe 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
@@ -12,12 +12,13 @@
 (*                                                                        *)
 (**************************************************************************)
 
-include "lambda-delta/substitution/lift.ma".
+include "Basic-2/substitution/lift.ma".
 
 (* 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.
 #d #e #T1 #U #H elim H -H d e T1 U
 [ #k #d #e #X #HX
@@ -33,6 +34,7 @@ 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: ∀d1,e1,T1,T. ↑[d1, e1] T1 ≡ T →
                      ∀d2,e2,T2. ↑[d2 + e1, e2] T2 ≡ T →
                      d1 ≤ d2 →
@@ -78,6 +80,7 @@ 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: ∀d1,e1,T1,T. ↑[d1, e1] T1 ≡ T →
                        ∀d2,e2,T2. ↑[d2, e2] T ≡ T2 →
                        d1 ≤ d2 → d2 ≤ d1 + e1 → ↑[d1, e1 + e2] T1 ≡ T2.
@@ -103,6 +106,7 @@ 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: ∀d1,e1,T1,T. ↑[d1, e1] T1 ≡ T →
                        ∀d2,e2,T2. ↑[d2, e2] T ≡ T2 → d2 ≤ d1 →
                        ∃∃T0. ↑[d2, e2] T1 ≡ T0 & ↑[d1 + e2, e1] T0 ≡ T2.
@@ -127,6 +131,7 @@ 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: ∀d1,e1,T1,T. ↑[d1, e1] T1 ≡ T →
                        ∀d2,e2,T2. ↑[d2, e2] T ≡ T2 → d1 + e1 ≤ d2 →
                        ∃∃T0. ↑[d2 - e1, e2] T1 ≡ T0 & ↑[d1, e1] T0 ≡ T2.