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
|
; 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 "trans1-eqtrace-bldr")
(set-verify-guards-eagerness 2)
(set-case-split-limitations nil)
(set-well-founded-relation ord<)
(set-measure-function rank)
(defund rw.trans3-eqtrace-bldr (x box proofs)
(declare (xargs :guard (and (rw.eqtracep x)
(rw.hypboxp box)
(rw.trans3-eqtrace-okp x)
(rw.eqtrace-okp x box)
(logic.appeal-listp proofs)
(equal (logic.strip-conclusions proofs) (rw.eqtrace-formula-list (rw.eqtrace->subtraces x) box)))
:verify-guards nil)
(ignore box))
(if (rw.eqtrace->iffp x)
(let ((proof1 (if (rw.eqtrace->iffp (first (rw.eqtrace->subtraces x)))
(first proofs)
(build.disjoined-iff-from-equal (first proofs))))
(proof2 (if (rw.eqtrace->iffp (second (rw.eqtrace->subtraces x)))
(second proofs)
(build.disjoined-iff-from-equal (second proofs)))))
(build.disjoined-transitivity-of-iff proof1 (build.disjoined-commute-iff proof2)))
(build.disjoined-transitivity-of-equal (first proofs)
(build.disjoined-commute-equal (second proofs)))))
(defobligations rw.trans3-eqtrace-bldr
(build.disjoined-iff-from-equal
build.disjoined-transitivity-of-equal
build.disjoined-transitivity-of-iff
build.disjoined-commute-equal
build.disjoined-commute-iff))
(encapsulate
()
(local (in-theory (enable rw.eqtrace-formula
rw.trans3-eqtrace-bldr
rw.trans3-eqtrace-okp
lemma-1-for-forcing-logic.appealp-of-rw.trans1-eqtrace-bldr
lemma-2-for-forcing-logic.appealp-of-rw.trans1-eqtrace-bldr
lemma-3-for-forcing-logic.appealp-of-rw.trans1-eqtrace-bldr
lemma-4-for-forcing-logic.appealp-of-rw.trans1-eqtrace-bldr)))
(defthm rw.trans3-eqtrace-bldr-under-iff
(iff (rw.trans3-eqtrace-bldr x box proofs)
t))
(defthm forcing-logic.appealp-of-rw.trans3-eqtrace-bldr
(implies (force (and (rw.eqtracep x)
(rw.hypboxp box)
(rw.trans3-eqtrace-okp x)
(rw.eqtrace-okp x box)
(logic.appeal-listp proofs)
(equal (logic.strip-conclusions proofs) (rw.eqtrace-formula-list (rw.eqtrace->subtraces x) box))))
(equal (logic.appealp (rw.trans3-eqtrace-bldr x box proofs))
t)))
(defthm forcing-logic.conclusion-of-rw.trans3-eqtrace-bldr
(implies (force (and (rw.eqtracep x)
(rw.hypboxp box)
(rw.trans3-eqtrace-okp x)
(rw.eqtrace-okp x box)
(logic.appeal-listp proofs)
(equal (logic.strip-conclusions proofs) (rw.eqtrace-formula-list (rw.eqtrace->subtraces x) box))))
(equal (logic.conclusion (rw.trans3-eqtrace-bldr x box proofs))
(rw.eqtrace-formula x box)))
:rule-classes ((:rewrite :backchain-limit-lst 0)))
(defthm@ forcing-logic.proofp-of-rw.trans3-eqtrace-bldr
(implies (force (and (rw.eqtracep x)
(rw.hypboxp box)
(rw.trans3-eqtrace-okp x)
(rw.eqtrace-okp x box)
(logic.appeal-listp proofs)
(equal (logic.strip-conclusions proofs) (rw.eqtrace-formula-list (rw.eqtrace->subtraces x) box))
;; ---
(logic.proof-listp proofs axioms thms atbl)
(equal (cdr (lookup 'iff atbl)) 2)
(@obligations rw.trans3-eqtrace-bldr)))
(equal (logic.proofp (rw.trans3-eqtrace-bldr x box proofs) axioms thms atbl)
t)))
(verify-guards rw.trans3-eqtrace-bldr))
|
