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
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
|
; 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 "tuple-listp")
(include-book "list-list-fix")
(set-verify-guards-eagerness 2)
(set-case-split-limitations nil)
(set-well-founded-relation ord<)
(set-measure-function rank)
(defund remove-all-from-ranges (a x)
(declare (xargs :guard (mapp x)))
(if (consp x)
(cons (cons (car (car x))
(remove-all a (cdr (car x))))
(remove-all-from-ranges a (cdr x)))
nil))
(defthm remove-all-from-ranges-when-not-consp
(implies (not (consp x))
(equal (remove-all-from-ranges a x)
nil))
:hints(("Goal" :in-theory (enable remove-all-from-ranges))))
(defthm remove-all-from-ranges-of-cons
(equal (remove-all-from-ranges a (cons b x))
(cons (cons (car b) (remove-all a (cdr b)))
(remove-all-from-ranges a x)))
:hints(("Goal" :in-theory (enable remove-all-from-ranges))))
(defthm true-listp-of-remove-all-from-ranges
(equal (true-listp (remove-all-from-ranges a x))
t)
:hints(("Goal" :induct (cdr-induction x))))
(defthm true-list-listp-of-remove-all-from-ranges
(equal (true-list-listp (remove-all-from-ranges a x))
t)
:hints(("Goal" :induct (cdr-induction x))))
(defthm mapp-of-remove-all-from-ranges
(equal (mapp (remove-all-from-ranges a x))
t)
:hints(("Goal" :induct (cdr-induction x))))
(defthm remove-all-from-ranges-of-list-fix
(equal (remove-all-from-ranges a (list-fix x))
(remove-all-from-ranges a x))
:hints(("Goal" :induct (cdr-induction x))))
(defthm remove-all-from-ranges-of-list-list-fix
(equal (remove-all-from-ranges a (list-list-fix x))
(remove-all-from-ranges a x))
:hints(("Goal" :induct (cdr-induction x))))
(defthm remove-all-from-ranges-of-app
(equal (remove-all-from-ranges a (app x y))
(app (remove-all-from-ranges a x)
(remove-all-from-ranges a y)))
:hints(("Goal" :induct (cdr-induction x))))
(defthm remove-all-from-ranges-of-rev
(equal (remove-all-from-ranges a (rev x))
(rev (remove-all-from-ranges a x)))
:hints(("Goal" :induct (cdr-induction x))))
(defthm len-of-remove-all-from-ranges
(equal (len (remove-all-from-ranges a x))
(len x))
:hints(("Goal" :induct (cdr-induction x))))
|
