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_path_eq.ma".
16 include "delayed_updating/substitution/lift_path_prelift.ma".
18 (* UNWIND FOR PATH **********************************************************)
20 (* Constructions with lift_path *********************************************)
22 lemma lift_unwind2_path_after (p) (f1) (f2):
23 ↑[f2]▼[f1]p = ▼[f2∘f1]p.
24 #p @(path_ind_unwind … p) -p // [ #n | #p ] #IH #f1 #f2
25 [ <unwind2_path_d_empty <unwind2_path_d_empty
26 <lift_path_d_sn <lift_path_empty //
27 | <unwind2_path_L_sn <unwind2_path_L_sn <lift_path_L_sn
28 >tr_compose_push_bi //
32 lemma unwind2_path_after_lift (p) (f1) (f2):
33 ▼[f2]↑[f1]p = ▼[f2∘f1]p.
34 #p @(path_ind_unwind … p) -p // [ #n #l ] #p #IH #f1 #f2
35 [ <lift_path_d_sn <unwind2_path_d_lcons
36 <lift_path_lcons_prelift <unwind2_path_d_lcons >lift_path_lcons_prelift
38 >(unwind2_path_eq_repl … (tr_compose_assoc …))
39 >(unwind2_path_eq_repl … (tr_compose_assoc …))
40 <unwind2_path_after <unwind2_path_after in ⊢ (???%);
41 /3 width=1 by unwind2_path_eq_repl, eq_f/
42 | <lift_path_m_sn <unwind2_path_m_sn <unwind2_path_m_sn //
43 | <lift_path_L_sn <unwind2_path_L_sn <unwind2_path_L_sn
44 >tr_compose_push_bi //