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4 (* ||A|| A project by Andrea Asperti *)
6 (* ||I|| Developers: *)
7 (* ||T|| The HELM team. *)
8 (* ||A|| http://helm.cs.unibo.it *)
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15 include "basic_2/substitution/lift_lift_vector.ma".
16 include "basic_2/unfold/lifts_lift.ma".
17 include "basic_2/unfold/lifts_vector.ma".
19 (* GENERIC RELOCATION *******************************************************)
21 (* Main properties **********************************************************)
23 (* Basic_1: was: lifts1_xhg (right to left) *)
24 lemma liftsv_liftv_trans_le: ∀T1s,Ts,des. ⇧*[des] T1s ≡ Ts →
25 ∀T2s:list term. ⇧[0, 1] Ts ≡ T2s →
26 ∃∃T0s. ⇧[0, 1] T1s ≡ T0s & ⇧*[des + 1] T0s ≡ T2s.
27 #T1s #Ts #des #H elim H -T1s -Ts
29 >(liftv_inv_nil1 … H) -T1s /2 width=3/
30 | #T1s #Ts #T1 #T #HT1 #_ #IHT1s #X #H
31 elim (liftv_inv_cons1 … H) -H #T2 #T2s #HT2 #HT2s #H destruct
32 elim (IHT1s … HT2s) -Ts #Ts #HT1s #HT2s
33 elim (lifts_lift_trans_le … HT1 … HT2) -T /3 width=5/