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 *)
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15 include "basic_2/relocation/lifts_lifts.ma".
16 include "basic_2/relocation/lifts_vector.ma".
18 (* GENERIC RELOCATION FOR TERM VECTORS *************************************)
20 (* Main properties **********************************************************)
22 (* Basic_1: includes: lifts_inj *)
23 theorem liftsv_inj: ∀f,T1s,Us. ⬆*[f] T1s ≘ Us →
24 ∀T2s. ⬆*[f] T2s ≘ Us → T1s = T2s.
25 #f #T1s #Us #H elim H -T1s -Us
26 [ #T2s #H >(liftsv_inv_nil2 … H) -H //
27 | #T1s #Us #T1 #U #HT1U #_ #IHT1Us #X #H destruct
28 elim (liftsv_inv_cons2 … H) -H #T2 #T2s #HT2U #HT2Us #H destruct
29 >(lifts_inj … HT1U … HT2U) -U /3 width=1 by eq_f/
33 (* Basic_2A1: includes: liftv_mono *)
34 theorem liftsv_mono: ∀f,Ts,U1s. ⬆*[f] Ts ≘ U1s →
35 ∀U2s. ⬆*[f] Ts ≘ U2s → U1s = U2s.
36 #f #Ts #U1s #H elim H -Ts -U1s
37 [ #U2s #H >(liftsv_inv_nil1 … H) -H //
38 | #Ts #U1s #T #U1 #HTU1 #_ #IHTU1s #X #H destruct
39 elim (liftsv_inv_cons1 … H) -H #U2 #U2s #HTU2 #HTU2s #H destruct
40 >(lifts_mono … HTU1 … HTU2) -T /3 width=1 by eq_f/
44 (* Basic_1: includes: lifts1_xhg (right to left) *)
45 (* Basic_2A1: includes: liftsv_liftv_trans_le *)
46 theorem liftsv_trans: ∀f1,T1s,Ts. ⬆*[f1] T1s ≘ Ts → ∀T2s,f2. ⬆*[f2] Ts ≘ T2s →
47 ∀f. f2 ⊚ f1 ≘ f → ⬆*[f] T1s ≘ T2s.
48 #f1 #T1s #Ts #H elim H -T1s -Ts
49 [ #T2s #f2 #H >(liftsv_inv_nil1 … H) -T2s /2 width=3 by liftsv_nil/
50 | #T1s #Ts #T1 #T #HT1 #_ #IHT1s #X #f2 #H elim (liftsv_inv_cons1 … H) -H
51 #T2 #T2s #HT2 #HT2s #H destruct /3 width=6 by lifts_trans, liftsv_cons/