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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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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: ∀T1c,Us,f. ⬆*[f] T1c ≡ Us →
24 ∀T2c. ⬆*[f] T2c ≡ Us → T1c = T2c.
25 #T1c #Us #f #H elim H -T1c -Us
26 [ #T2c #H >(liftsv_inv_nil2 … H) -H //
27 | #T1c #Us #T1 #U #HT1U #_ #IHT1Us #X #H destruct
28 elim (liftsv_inv_cons2 … H) -H #T2 #T2c #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: ∀Ts,U1c,f. ⬆*[f] Ts ≡ U1c →
35 ∀U2c. ⬆*[f] Ts ≡ U2c → U1c = U2c.
36 #Ts #U1c #f #H elim H -Ts -U1c
37 [ #U2c #H >(liftsv_inv_nil1 … H) -H //
38 | #Ts #U1c #T #U1 #HTU1 #_ #IHTU1c #X #H destruct
39 elim (liftsv_inv_cons1 … H) -H #U2 #U2c #HTU2 #HTU2c #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: ∀T1c,Ts,f1. ⬆*[f1] T1c ≡ Ts → ∀T2c,f2. ⬆*[f2] Ts ≡ T2c →
47 ∀f. f2 ⊚ f1 ≡ f → ⬆*[f] T1c ≡ T2c.
48 #T1c #Ts #f1 #H elim H -T1c -Ts
49 [ #T2c #f2 #H >(liftsv_inv_nil1 … H) -T2c /2 width=3 by liftsv_nil/
50 | #T1c #Ts #T1 #T #HT1 #_ #IHT1c #X #f2 #H elim (liftsv_inv_cons1 … H) -H
51 #T2 #T2c #HT2 #HT2c #H destruct /3 width=6 by lifts_trans, liftsv_cons/