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
|
; 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 "contradictionp")
(include-book "eqtrace-compiler")
(%interactive)
(%deftheorem theorem-inequality-of-not-x-and-x)
(%deftheorem theorem-not-x-and-x-under-iff)
(%deftheorem rw.eqtrace-contradiction-lemma1)
(defsection rw.eqtrace-contradiction-lemma2
(%autoadmit rw.eqtrace-contradiction-lemma2)
(local (%enable default
rw.eqtrace-contradiction-lemma2
theorem-not-x-and-x-under-iff
theorem-symmetry-of-iff))
(%autoprove rw.eqtrace-contradiction-lemma2-under-iff)
(%autoprove forcing-logic.appealp-of-rw.eqtrace-contradiction-lemma2)
(%autoprove forcing-logic.conclusion-of-rw.eqtrace-contradiction-lemma2)
(%autoprove forcing-logic.proofp-of-rw.eqtrace-contradiction-lemma2))
(%defderiv rw.eqtrace-contradiction-bldr-lemma3a :omit-okp t)
(%defderiv rw.eqtrace-contradiction-bldr-lemma3 :omit-okp t)
(defsection rw.eqtrace-contradiction-bldr
(%autoadmit rw.eqtrace-contradiction-bldr)
(local (%enable default
rw.eqtrace-contradictionp
rw.eqtrace-contradiction-bldr
rw.eqtrace-formula
rw.eqtrace-contradiction-lemma1
theorem-inequality-of-not-x-and-x))
(%autoprove rw.eqtrace-contradiction-bldr-under-iff)
(%autoprove forcing-logic.appealp-of-rw.eqtrace-contradiction-bldr)
(%autoprove forcing-logic.conclusion-of-rw.eqtrace-contradiction-bldr)
(%autoprove forcing-logic.proofp-of-rw.eqtrace-contradiction-bldr))
(%autoadmit rw.eqtrace-contradiction-bldr-okp)
(%autoadmit rw.eqtrace-contradiction-bldr-high)
(defsection rw.eqtrace-contradiction-bldr-okp
(local (%enable default rw.eqtrace-contradiction-bldr-okp))
(%autoprove booleanp-of-rw.eqtrace-contradiction-bldr-okp)
(%autoprove rw.eqtrace-contradiction-bldr-okp-of-logic.appeal-identity)
(local (%enable default backtracking-logic.formula-atblp-rules))
(local (%disable default
forcing-logic.formula-atblp-rules
forcing-lookup-of-logic.function-name-free
forcing-logic.term-list-atblp-of-logic.function-args))
(%autoprove lemma-1-for-soundness-of-rw.eqtrace-contradiction-bldr-okp)
(%autoprove lemma-2-for-soundness-of-rw.eqtrace-contradiction-bldr-okp)
(%autoprove forcing-soundness-of-rw.eqtrace-contradiction-bldr-okp
(%enable default
lemma-1-for-soundness-of-rw.eqtrace-contradiction-bldr-okp
lemma-2-for-soundness-of-rw.eqtrace-contradiction-bldr-okp)
(%use (%instance (%thm forcing-logic.provablep-when-logic.proofp)
(x (rw.eqtrace-contradiction-bldr (first (logic.extras x))
(second (logic.extras x))))))))
|
