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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/unwind_k/preunwind2_rmap.ma".
16 include "delayed_updating/syntax/path.ma".
18 (* TAILED UNWIND FOR RELOCATION MAP *****************************************)
20 rec definition unwind2_rmap (f) (p) on p: tr_map ≝
23 | list_lcons l q ⇒ ▶[unwind2_rmap f q]l
27 "tailed unwind (relocation map)"
28 'BlackRightTriangle f p = (unwind2_rmap f p).
30 (* Basic constructions ******************************************************)
32 lemma unwind2_rmap_empty (f):
36 lemma unwind2_rmap_rcons (f) (p) (l):
37 ▶[▶[f]p]l = ▶[f](p◖l).
40 lemma unwind2_rmap_d_dx (f) (p) (k:pnat):
41 ▶[f]p∘𝐮❨k❩ = ▶[f](p◖𝗱k).
44 lemma unwind2_rmap_m_dx (f) (p):
48 lemma unwind2_rmap_L_dx (f) (p):
52 lemma unwind2_rmap_A_dx (f) (p):
56 lemma unwind2_rmap_S_dx (f) (p):
60 (* Constructions with path_append *******************************************)
62 lemma unwind2_rmap_append (f) (p) (q):
63 ▶[▶[f]p]q = ▶[f](p●q).
64 #f #p #q elim q -q // #l #q #IH
65 <unwind2_rmap_rcons <unwind2_rmap_rcons //
68 (* Constructions with path_lcons ********************************************)
70 lemma unwind2_rmap_lcons (f) (p) (l):
71 ▶[▶[f]l]p = ▶[f](l◗p).
74 lemma unwind2_rmap_d_sn (f) (p) (k:pnat):
75 ▶[f∘𝐮❨k❩]p = ▶[f](𝗱k◗p).
78 lemma unwind2_rmap_m_sn (f) (p):
82 lemma unwind2_rmap_L_sn (f) (p):
86 lemma unwind2_rmap_A_sn (f) (p):
90 lemma unwind2_rmap_S_sn (f) (p):