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
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
|
; 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-4")
(%interactive)
(%autoadmit mapp)
(%autoprove mapp-when-not-consp
(%restrict default mapp (equal x 'x)))
(%autoprove mapp-of-cons
(%restrict default mapp (equal x '(cons a x))))
(%autoprove booleanp-of-mapp
(%cdr-induction x))
(%autoprove mapp-of-list-fix
(%cdr-induction x))
(%autoprove mapp-of-app
(%cdr-induction x))
(%autoadmit cons-fix)
(%autoprove cons-fix-when-not-consp
(%restrict default cons-fix (equal x 'x)))
(%autoprove cons-fix-when-consp
(%restrict default cons-fix (equal x 'x)))
(%autoprove consp-of-cons-fix
(%car-cdr-elim x))
(%autoprove cons-fix-under-iff
(%car-cdr-elim x))
(%autoprove cons-fix-of-cons)
(%autoprove car-of-cons-fix)
(%autoprove cdr-of-cons-fix)
(%autoadmit lookup)
(%autoprove lookup-when-not-consp
(%restrict default lookup (equal x 'x)))
(%autoprove lookup-of-cons
(%restrict default lookup (equal x '(cons b x))))
(%autoprove lookup-of-list-fix
(%cdr-induction x))
(%autoprove lookup-of-app
(%cdr-induction x))
(%autoprove car-of-lookup-when-found
(%cdr-induction map))
(%autoprove consp-of-lookup-under-iff
(%cdr-induction x))
(%autoadmit update)
(%autoprove car-of-update
(%enable default update))
(%autoprove cdr-of-update
(%enable default update))
(%autoprove consp-of-update
(%enable default update))
(%autoprove update-of-list-fix
(%enable default update))
(%autoprove mapp-of-update-when-mapp
;; BOZO I think this should be forced
(%enable default update))
(%autoprove lookup-of-update
(%enable default update))
(%autoadmit domain)
(%autoprove domain-when-not-consp
(%restrict default domain (equal x 'x)))
(%autoprove domain-of-cons
(%restrict default domain (equal x '(cons a x))))
(%autoprove domain-of-list-fix
(%cdr-induction x))
(%autoprove consp-of-domain)
(%autoprove true-listp-of-domain
(%cdr-induction x))
(%autoprove domain-of-app
(%cdr-induction x))
(%autoprove domain-of-update
(%enable default update))
(%autoprove memberp-of-domain-when-memberp
(%cdr-induction x))
(%autoprove memberp-of-domain-when-memberp-of-subset-domain
(%cdr-induction x))
(%autoprove subsetp-of-domains
(%use (%instance (%thm subsetp-badguy-membership-property)
(x (domain x))
(y (domain y)))))
(%autoprove uniquep-when-uniquep-of-domain
(%cdr-induction x))
(%autoprove memberp-of-domain-under-iff
(%cdr-induction x))
(%autoprove rev-of-domain
(%cdr-induction x))
(%autoprove domain-of-rev)
(%autoadmit fast-domain$)
(%autoprove fast-domain$-when-not-consp
(%restrict default fast-domain$ (equal x 'x)))
(%autoprove fast-domain$-of-cons
(%restrict default fast-domain$ (equal x '(cons a x))))
(%autoprove forcing-fast-domain$-removal
(%autoinduct fast-domain$)
(%enable default fast-domain$-when-not-consp fast-domain$-of-cons))
(%autoadmit range)
(%autoprove range-when-not-consp
(%restrict default range (equal x 'x)))
(%autoprove range-of-cons
(%restrict default range (equal x '(cons a x))))
(%autoprove range-of-list-fix
(%cdr-induction x))
(%autoprove true-listp-of-range
(%cdr-induction x))
(%autoprove len-of-range
(%cdr-induction x))
(%autoprove range-of-app
(%cdr-induction x))
(%autoadmit fast-range$)
(%autoprove fast-range$-when-not-consp
(%restrict default fast-range$ (equal x 'x)))
(%autoprove fast-range$-of-cons
(%restrict default fast-range$ (equal x '(cons a x))))
(%autoprove forcing-fast-range$-removal
(%autoinduct fast-range$)
(%enable default fast-range$-when-not-consp fast-range$-of-cons))
|
