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
|
\begin{theindex}
\item {\ptt add}, theory, 5
\item {\ptt ADD\_DIV\_ADD\_DIV}, 6, 22
\item {\ptt ADD\_DIV\_SUC\_DIV}, 22
\item {\ptt ADD\_EQ\_IMP\_SUB\_EQ}, 19
\item {\ptt ADD\_EQ\_LESS\_EQ}, 18
\item {\ptt ADD\_EQ\_LESS\_IMP\_LESS}, 18
\item {\ptt ADD\_GREATER\_EQ}, 18
\item {\ptt ADD\_LESS\_EQ\_SUB}, 19
\item {\ptt ADD\_MONO\_LESS}, 18
\item {\ptt ADD\_SUB\_SYM}, 5, 19
\item {\ptt ADD\_SUC\_0}, 18
\item {\ptt ADD\_SYM\_ASSOC}, 5, 18
\item {\ptt ADDL\_GREATER}, 5, 17
\item {\ptt ADDL\_GREATER\_EQ}, 17
\item {\ptt ADDR\_GREATER}, 17
\item {\ptt ADDR\_GREATER\_EQ}, 18
\indexspace
\item {\ptt DIV}, 6
\item {\ptt DIV\_DIV\_DIV\_MULT}, 22
\item {\ptt DIV\_ONE}, 22
\item {\ptt div\_mod}, theory, 6
\indexspace
\item {\ptt EQ\_LESS\_EQ}, 4
\item {\ptt EVEN}, 7
\item {\ptt EVEN\_IMPL\_MULT}, 7
\item {\ptt EVEN\_MULT}, 24
\item {\ptt EVEN\_ODD\_0}, 7, 24
\item {\ptt EVEN\_ODD\_PLUS\_CASES}, 24
\item {\ptt EVEN\_ODD\_SUC}, 7, 24
\item {\ptt EXP1}, 22
\indexspace
\item {\ptt GEN\_INDUCT\_RULE}, 11
\item {\ptt GEN\_INDUCT\_TAC}, 12
\item {\ptt GEN\_INDUCTION}, 15
\item {\ptt GREATER\_EQ\_ANTISYM}, 15
\item {\ptt GREATER\_EQ\_SPLIT}, 18
\item {\ptt GREATER\_EQ\_SUB\_LESS\_TO\_ADD}, 19
\item {\ptt GREATER\_NOT\_ZERO}, 4, 15
\indexspace
\item {\ptt ineq}, theory, 4
\indexspace
\item {\ptt LEFT\_SUB\_DISTRIB}, 6
\item {\ptt LESS1EQ0}, 4, 16
\item {\ptt LESS\_ADD1}, 5, 18
\item {\ptt LESS\_ADD\_ASSOC}, 18
\item {\ptt LESS\_DIV\_EQ\_ZERO}, 22
\item {\ptt LESS\_EQ\_0\_EQ}, 4, 16
\item {\ptt LESS\_EQ\_ADD1}, 5, 18
\item {\ptt LESS\_EQ\_ADD\_SUB1}, 19
\item {\ptt LESS\_EQ\_LESS\_EQ\_EQ}, 4, 15
\item {\ptt LESS\_EQ\_LESS\_SUC}, 16
\item {\ptt LESS\_EQ\_MONO\_ADD\_EQ0}, 18
\item {\ptt LESS\_EQ\_MONO\_ADD\_EQ1}, 18
\item {\ptt LESS\_EQ\_MONO\_DIV}, 22
\item {\ptt LESS\_EQ\_SPLIT}, 5, 18
\item {\ptt LESS\_EQ\_SUB\_1}, 19
\item {\ptt LESS\_EQ\_SUB\_ADD}, 20
\item {\ptt LESS\_IMP\_LESS\_EQ\_PRE}, 17
\item {\ptt LESS\_IS\_NOT\_LESS\_OR\_EQ}, 15
\item {\ptt LESS\_LESS\_EQ}, 18
\item {\ptt LESS\_LESS\_EQ\_MONO}, 19
\item {\ptt LESS\_LESS\_MONO}, 19
\item {\ptt LESS\_MONO\_MULT1}, 6, 22
\item {\ptt LESS\_MULT\_PLUS\_DIFF}, 6, 22
\item {\ptt LESS\_PRE}, 20
\item {\ptt LESS\_SUB\_IMP\_INV}, 20
\item {\ptt LESS\_SUB\_IMP\_SUM\_LESS}, 20
\item {\ptt LESS\_SUB\_TO\_ADDL\_LESS}, 20
\item {\ptt LESS\_SUB\_TO\_ADDR\_LESS}, 20
\item {\ptt LESS\_TRANS\_ADD}, 19
\item {\ptt LESS\_TWICE\_IMP\_LESS\_SUB}, 20
\item {\ptt load\_more\_arithmetic}, 9
\indexspace
\item {\ptt M\_LESS\_0\_LESS}, 4, 16
\item {\ptt MAX}, 6
\item {\ptt MAX\_0}, 7, 23
\item {\ptt MAX\_DEF}, 6, 23
\item {\ptt MAX\_REFL}, 7, 23
\item {\ptt MAX\_SUC}, 23
\item {\ptt MAX\_SYM}, 7, 23
\item {\ptt MIN}, 6
\item {\ptt MIN\_0}, 7, 23
\item {\ptt MIN\_DEF}, 6, 23
\item {\ptt min\_max}, theory, 6
\item {\ptt MIN\_REFL}, 7, 23
\item {\ptt MIN\_SUC}, 24
\item {\ptt MIN\_SYM}, 7, 24
\item {\ptt MOD}, 6
\item {\ptt MOD\_MULT\_MOD}, 6, 23
\item {\ptt more\_arithmetic}, theory, 3
\item {\ptt mult}, theory, 6
\item {\ptt MULT\_DIV}, 23
\item {\ptt MULT\_EVEN}, 24
\item {\ptt MULT\_ODD}, 24
\indexspace
\item {\ptt NOT\_0\_AND\_MORE}, 4, 16
\item {\ptt NOT\_0\_GREATER\_EQ\_SUC}, 16
\item {\ptt NOT\_0\_SUB}, 5, 20
\item {\ptt NOT\_1\_TWICE}, 19
\item {\ptt NOT\_ADD\_LESS}, 19
\item {\ptt NOT\_EQ\_0}, 4, 16
\item {\ptt NOT\_EQ\_LESS\_EQ}, 4, 15
\item {\ptt NOT\_EVEN\_ODD\_SUC\_EVEN\_ODD}, 24
\item {\ptt NOT\_FORALL\_SUC\_LESS\_EQ}, 16
\item {\ptt NOT\_LESS\_AND\_GREATER}, 15
\item {\ptt NOT\_LESS\_IMP\_LESS\_EQ\_ADD1}, 19
\item {\ptt NOT\_LESS\_SUB}, 20
\item {\ptt NOT\_MULT\_LESS\_0}, 22
\item {\ptt NOT\_SUB\_0}, 20
\item {\ptt NOT\_SUC\_LESS\_EQ\_0}, 4
\item {\ptt NOT\_SUC\_LESS\_EQ\_SELF}, 4, 16
\item {\ptt NUM\_EQ\_PLUS\_CONV}, 12
\item {\ptt NUM\_LESS\_EQ\_PLUS\_CONV}, 13
\item {\ptt NUM\_LESS\_PLUS\_CONV}, 13
\indexspace
\item {\ptt ODD}, 7
\item {\ptt ODD\_MULT}, 24
\item {\ptt odd\_even}, theory, 7
\item {\ptt ONE\_LESS\_EQ\_TWO\_EXP}, 22
\item {\ptt ONE\_LESS\_TWO\_EXP\_SUC}, 6, 22
\indexspace
\item {\ptt pre}, theory, 5
\item {\ptt PRE\_ADD}, 5, 17
\item {\ptt PRE\_K\_K}, 5, 17
\item {\ptt PRE\_LESS}, 17
\item {\ptt PRE\_LESS\_EQ}, 5, 17
\item {\ptt PRE\_LESS\_LESS\_SUC}, 20
\item {\ptt PRE\_MONO}, 5, 17
\item {\ptt PRE\_MONO\_LESS\_EQ}, 17
\item {\ptt PRE\_SUB\_SUC}, 20
\indexspace
\item {\ptt SMALLER\_SUM}, 20
\item {\ptt sub}, theory, 5
\item {\ptt SUB\_1\_LESS}, 20
\item {\ptt SUB\_1\_LESS\_EQ}, 20
\item {\ptt SUB\_ADD\_SELF}, 5, 20
\item {\ptt SUB\_BOTH\_SIDES}, 5, 21
\item {\ptt SUB\_EQ\_SUB\_ADD\_SUB}, 21
\item {\ptt SUB\_GREATER\_0}, 21
\item {\ptt SUB\_GREATER\_EQ\_ADD}, 21
\item {\ptt SUB\_LE\_ADD}, 5, 21
\item {\ptt SUB\_LESS\_BOTH\_SIDES}, 21
\item {\ptt SUB\_LESS\_EQ\_SUB1}, 21
\item {\ptt SUB\_LESS\_EQ\_SUB\_SUC}, 21
\item {\ptt SUB\_LESS\_TO\_LESS\_ADDL}, 21
\item {\ptt SUB\_LESS\_TO\_LESS\_ADDR}, 21
\item {\ptt SUB\_PRE\_SUB\_1}, 21
\item {\ptt SUB\_SUB\_ID}, 21
\item {\ptt SUB\_SUC}, 21
\item {\ptt SUB\_SUC\_PRE\_SUB}, 21
\item {\ptt suc}, theory, 4
\item {\ptt SUC\_0}, 16
\item {\ptt SUC\_DIV\_CASES}, 23
\item {\ptt SUC\_DIV\_SELF}, 6, 23
\item {\ptt SUC\_GREATER\_EQ\_SUC}, 4, 16
\item {\ptt SUC\_LESS\_EQ}, 16
\item {\ptt SUC\_LESS\_EQ\_PRE}, 17
\item {\ptt SUC\_LESS\_N\_LESS}, 19
\item {\ptt SUC\_LESS\_PRE}, 17
\item {\ptt SUC\_MAX}, 24
\item {\ptt SUC\_MIN}, 24
\item {\ptt SUC\_MOD}, 23
\item {\ptt SUC\_MOD\_SELF}, 6, 23
\item {\ptt SUC\_NOT\_0}, 4, 16
\item {\ptt SUC\_PRE}, 5, 17
\item {\ptt SUC\_SUB}, 21
\item {\ptt SUM\_LESS}, 19
\indexspace
\item {\ptt zero\_ineq}, theory, 4
\item {\ptt ZERO\_LESS\_TWO\_EXP}, 22
\end{theindex}
|
