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
|
; 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 "substitute-term")
(set-verify-guards-eagerness 2)
(set-case-split-limitations nil)
(set-well-founded-relation ord<)
(set-measure-function rank)
(defund logic.negate-term (x)
(declare (xargs :guard (logic.termp x)))
(logic.function 'not (list x)))
(defthm forcing-logic.termp-of-logic.negate-term
(implies (force (logic.termp x))
(equal (logic.termp (logic.negate-term x))
t))
:hints(("Goal" :in-theory (enable logic.negate-term))))
(defthm forcing-logic.term-atblp-of-logic.negate-term
(implies (force (and (logic.term-atblp x atbl)
(equal (cdr (lookup 'not atbl)) 1)))
(equal (logic.term-atblp (logic.negate-term x) atbl)
t))
:hints(("Goal" :in-theory (enable logic.negate-term))))
(defprojection :list (logic.negate-term-list x)
:element (logic.negate-term x)
:guard (logic.term-listp x))
(defthm forcing-logic.term-listp-of-logic.negate-term-list
(implies (force (logic.term-listp x))
(equal (logic.term-listp (logic.negate-term-list x))
t))
:hints(("Goal" :in-theory (enable logic.negate-term-list))))
(defthm forcing-logic.term-list-atblp-of-logic.negate-term-list
(implies (force (and (logic.term-list-atblp x atbl)
(equal (cdr (lookup 'not atbl)) 1)))
(equal (logic.term-list-atblp (logic.negate-term-list x) atbl)
t))
:hints(("Goal" :in-theory (enable logic.negate-term-list))))
(defthm logic.substitute-of-logic.negate-term
(equal (logic.substitute (logic.negate-term x) sigma)
(logic.negate-term (logic.substitute x sigma)))
:hints(("Goal" :in-theory (enable logic.negate-term))))
(defthm logic.substitute-list-of-logic.negate-term-list
(equal (logic.substitute-list (logic.negate-term-list x) sigma)
(logic.negate-term-list (logic.substitute-list x sigma)))
:hints(("Goal" :induct (cdr-induction x))))
|
