1 (**************************************************************************)
4 (* ||A|| A project by Andrea Asperti *)
6 (* ||I|| Developers: *)
7 (* ||T|| The HELM team. *)
8 (* ||A|| http://helm.cs.unibo.it *)
10 (* \ / This file is distributed under the terms of the *)
11 (* v GNU General Public License Version 2 *)
13 (**************************************************************************)
15 include "Basic_2/substitution/lift_lift.ma".
16 include "Basic_2/unfold/lifts.ma".
18 (* GENERIC RELOCATION *******************************************************)
20 (* Main properties **********************************************************)
22 (* Basic_1: was: lift1_xhg *)
23 lemma lifts_lift_trans_le: ∀T1,T,des. ⇧*[des] T1 ≡ T → ∀T2. ⇧[0, 1] T ≡ T2 →
24 ∃∃T0. ⇧[0, 1] T1 ≡ T0 & ⇧*[ss des] T0 ≡ T2.
25 #T1 #T #des #H elim H -T1 -T -des
27 | #T1 #T3 #T #des #d #e #HT13 #_ #IHT13 #T2 #HT2
28 elim (IHT13 … HT2) -T #T #HT3 #HT2
29 elim (lift_trans_le … HT13 … HT3 ?) -T3 // /3 width=5/
33 (* Basic_1: was: lift1_lift1 *)
34 theorem lifts_trans: ∀T1,T,des1. ⇧*[des1] T1 ≡ T → ∀T2:term. ∀des2. ⇧*[des2] T ≡ T2 →
35 ⇧*[des1 @ des2] T1 ≡ T2.
36 #T1 #T #des1 #H elim H -T1 -T -des1 // /3 width=3/