(* *)
(**************************************************************************)
-include "basic_2/relocation/lift.ma".
+include "basic_2/substitution/lift.ma".
include "apps_2/functional/notation.ma".
(* FUNCTIONAL RELOCATION ****************************************************)
(* Main properties **********************************************************)
-theorem flift_lift: â\88\80T,d,e. â\87§[d, e] T ≡ ↑[d, e] T.
+theorem flift_lift: â\88\80T,d,e. â¬\86[d, e] T ≡ ↑[d, e] T.
#T elim T -T
[ * #i #d #e //
elim (lt_or_eq_or_gt i d) #Hid normalize
(* Main inversion properties ************************************************)
-theorem flift_inv_lift: â\88\80d,e,T1,T2. â\87§[d, e] T1 ≡ T2 → ↑[d, e] T1 = T2.
+theorem flift_inv_lift: â\88\80d,e,T1,T2. â¬\86[d, e] T1 ≡ T2 → ↑[d, e] T1 = T2.
#d #e #T1 #T2 #H elim H -d -e -T1 -T2 normalize //
[ #i #d #e #Hid >(tri_lt ?????? Hid) //
| #i #d #e #Hid
(* Derived properties *******************************************************)
-lemma flift_join: â\88\80e1,e2,T. â\87§[e1, e2] ↑[0, e1] T ≡ ↑[0, e1 + e2] T.
+lemma flift_join: â\88\80e1,e2,T. â¬\86[e1, e2] ↑[0, e1] T ≡ ↑[0, e1 + e2] T.
#e1 #e2 #T
lapply (flift_lift T 0 (e1+e2)) #H
-elim (lift_split … H e1 e1 ? ? ?) -H // #U #H
+elim (lift_split … H e1 e1) -H // #U #H
>(flift_inv_lift … H) -H //
qed.