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/unwind/unwind2_prototerm_eq.ma".
16 include "delayed_updating/unwind/unwind2_path_append.ma".
17 include "delayed_updating/syntax/prototerm_constructors.ma".
19 (* TAILED UNWIND FOR PROTOTERM **********************************************)
21 (* Constructions with constructors for prototerm ****************************)
23 lemma unwind2_term_iref_sn (f) (t) (k:pnat):
24 ▼[f∘𝐮❨k❩]t ⊆ ▼[f](𝛕k.t).
25 #f #t #k #p * #q #Hq #H0 destruct
26 @(ex2_intro … (𝗱k◗𝗺◗q))
27 /2 width=1 by in_comp_iref_hd/
30 lemma unwind2_term_iref_dx (f) (t) (k:pnat):
31 ▼[f](𝛕k.t) ⊆ ▼[f∘𝐮❨k❩]t.
32 #f #t #k #p * #q #Hq #H0 destruct
33 elim (in_comp_inv_iref … Hq) -Hq #p #Hp #Ht destruct
34 /2 width=1 by in_comp_unwind2_path_term/
37 lemma unwind2_term_iref (f) (t) (k:pnat):
38 ▼[f∘𝐮❨k❩]t ⇔ ▼[f](𝛕k.t).
39 /3 width=2 by conj, unwind2_term_iref_sn, unwind2_term_iref_dx/