(* 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 →
∀T1,T0. ⬆*[cs0] T1 ≡ T0 →