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 "delayed_updating/substitution/lift_prototerm_eq.ma".
16 include "delayed_updating/syntax/prototerm_constructors.ma".
18 (* LIFT FOR PROTOTERM *******************************************************)
20 lemma lift_iref_after_sn (f) (t:prototerm) (n:pnat):
21 ā[fāš®āØnā©]t ā ā[f](šn.t).
22 #f #t #n #p * #q #Hq #H0 destruct
23 @(ex2_intro ā¦ (š±nāšŗāq))
24 /2 width=1 by in_comp_iref/
27 lemma lift_iref_after_dx (f) (t) (n:pnat):
28 ā[f](šn.t) ā ā[fāš®āØnā©]t.
29 #f #t #n #p * #q #Hq #H0 destruct
30 elim (in_comp_inv_iref ā¦ Hq) -Hq #p #Hp #Ht destruct
31 /2 width=1 by in_comp_lift_bi/
34 lemma lift_iref_after (f) (t) (n:pnat):
35 ā[fāš®āØnā©]t ā ā[f](šn.t).
36 /3 width=1 by conj, lift_iref_after_sn, lift_iref_after_dx/
39 lemma lift_iref (f) (t) (n:pnat):
40 ā[f]ā[š®āØnā©]t ā ā[f](šn.t).
41 /3 width=3 by lift_term_after, subset_eq_trans/