1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
|
; Milawa - A Reflective Theorem Prover
; Copyright (C) 2005-2009 Kookamara LLC
;
; Contact:
;
; Kookamara LLC
; 11410 Windermere Meadows
; Austin, TX 78759, USA
; http://www.kookamara.com/
;
; License: (An MIT/X11-style license)
;
; Permission is hereby granted, free of charge, to any person obtaining a
; copy of this software and associated documentation files (the "Software"),
; to deal in the Software without restriction, including without limitation
; the rights to use, copy, modify, merge, publish, distribute, sublicense,
; and/or sell copies of the Software, and to permit persons to whom the
; Software is furnished to do so, subject to the following conditions:
;
; The above copyright notice and this permission notice shall be included in
; all copies or substantial portions of the Software.
;
; THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
; IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
; FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
; AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
; LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING
; FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER
; DEALINGS IN THE SOFTWARE.
;
; Original author: Jared Davis <jared@kookamara.com>
(in-package "MILAWA")
(include-book "utilities-5-prefixp")
(include-book "utilities-5-firstn")
(include-book "utilities-5-restn")
(include-book "utilities-5-first-index")
(include-book "utilities-5-mapp")
(%interactive)
(%autoprove nth-of-first-index-of-domain-and-range
(%cdr-induction x)
(%restrict default firstn (equal n 'n)))
(%autoprove prefixp-of-firstn
(%autoinduct firstn)
(%restrict default firstn (equal n 'n)))
(%autoprove prefixp-of-firstn-unusual
(%autoinduct firstn)
(%restrict default firstn (equal n 'n)))
(%autoprove app-of-firstn-and-restn
(%autoinduct restn)
(%restrict default firstn (equal n 'n))
(%restrict default restn (equal n 'n)))
(%autoprove lemma-for-equal-of-app-with-firstn-and-restn)
(%autoprove lemma-2-for-equal-of-app-with-firstn-and-restn)
(%autoprove lemma-3-for-equal-of-app-with-firstn-and-restn)
(%autoprove lemma-4-for-equal-of-app-with-firstn-and-restn
(%enable default lemma-3-for-equal-of-app-with-firstn-and-restn)
(%use (%instance (%thm lemma-for-equal-of-app-with-firstn-and-restn)
(n (len y))
(x x)))
(%use (%instance (%thm lemma-2-for-equal-of-app-with-firstn-and-restn)
(n (len y))
(y (list-fix y))))
(%auto :strategy (cleanup split crewrite)))
(%autoprove equal-of-app-with-firstn-and-restn
(%enable default lemma-4-for-equal-of-app-with-firstn-and-restn)
(%use (%instance (%thm lemma-for-equal-of-app-with-firstn-and-restn))))
|
