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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 *)
10 (* \ / This file is distributed under the terms of the *)
11 (* v GNU General Public License Version 2 *)
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15 include "delayed_updating/substitution/lift_prototerm_id.ma".
16 include "delayed_updating/substitution/lift_path_uni.ma".
17 include "delayed_updating/syntax/prototerm_constructors_eq.ma".
18 include "ground/relocation/nap.ma".
20 (* LIFT FOR PROTOTERM *******************************************************)
22 lemma lift_term_iref_pap_sn (f) (t:prototerm) (k:pnat):
23 (๐f๏ผ โงฃโจkโฉ.โ[โ*[k]f]t) โ โ[f](๐k.t).
24 #f #t #k #p * #q * #r #Hr #H1 #H2 destruct
25 @(ex2_intro โฆ (๐ฑkโ๐บโr))
26 /2 width=1 by in_comp_iref/
29 lemma lift_term_iref_pap_dx (f) (t) (k:pnat):
30 โ[f](๐k.t) โ ๐f๏ผ โงฃโจkโฉ.โ[โ*[k]f]t.
31 #f #t #k #p * #q #Hq #H0 destruct
32 elim (in_comp_inv_iref โฆ Hq) -Hq #p #H0 #Hp destruct
33 <lift_path_d_sn <lift_path_m_sn
34 /3 width=1 by in_comp_iref, in_comp_lift_path_term/
37 lemma lift_term_iref_pap (f) (t) (k:pnat):
38 (๐f๏ผ โงฃโจkโฉ.โ[โ*[k]f]t) โ โ[f](๐k.t).
39 /3 width=1 by conj, lift_term_iref_pap_sn, lift_term_iref_pap_dx/
42 lemma lift_term_iref_nap (f) (t) (n):
43 (๐โ(f๏ผ ยงโจnโฉ).โ[โ*[โn]f]t) โ โ[f](๐โn.t).
48 lemma lift_term_iref_uni (t) (n) (k):
49 (๐(k+n).t) โ โ[๐ฎโจnโฉ](๐k.t).
51 @(subset_eq_trans โฆ (lift_term_iref_pap โฆ))
52 <tr_uni_pap >nsucc_pnpred <tr_tls_succ_uni
53 /3 width=1 by iref_eq_repl, lift_term_id/