(* *)
(**************************************************************************)
+include "ground/relocation/mr2_minus.ma".
include "basic_2A/substitution/lift_lift.ma".
-include "basic_2A/multiple/mr2_minus.ma".
include "basic_2A/multiple/lifts.ma".
(* GENERIC TERM RELOCATION **************************************************)
(* Properties concerning basic term relocation ******************************)
-(* Basic_1: was: lift1_xhg (right to left) *)
lemma lifts_lift_trans_le: ∀T1,T,cs. ⬆*[cs] T1 ≡ T → ∀T2. ⬆[0, 1] T ≡ T2 →
∃∃T0. ⬆[0, 1] T1 ≡ T0 & ⬆*[cs + 1] T0 ≡ T2.
#T1 #T #cs #H elim H -T1 -T -cs
]
qed-.
-(* Basic_1: was: lift1_free (right to left) *)
-lemma lifts_lift_trans: ∀cs,i,i0. @⦃i, cs⦄ ≡ i0 →
- ∀cs0. cs + 1 ▭ i + 1 ≡ cs0 + 1 →
+lemma lifts_lift_trans: ∀cs,i,i0. @❪i, cs❫ ≘ i0 →
+ ∀cs0. cs + 1 ▭ i + 1 ≘ cs0 + 1 →
∀T1,T0. ⬆*[cs0] T1 ≡ T0 →
∀T2. ⬆[O, i0 + 1] T0 ≡ T2 →
∃∃T. ⬆[0, i + 1] T1 ≡ T & ⬆*[cs] T ≡ T2.