:: REAL_2 semantic presentation
Lm1:
( 1 / 1 = 1 & 1 " = 1 & 1 / (- 1) = - 1 & (- 1) " = - 1 & (- 1) * (- 1) = 1 )
;
theorem :: REAL_2:1
canceled;
theorem :: REAL_2:2
canceled;
theorem :: REAL_2:3
canceled;
theorem :: REAL_2:4
canceled;
theorem :: REAL_2:5
canceled;
theorem :: REAL_2:6
canceled;
theorem :: REAL_2:7
canceled;
theorem :: REAL_2:8
canceled;
theorem :: REAL_2:9
canceled;
theorem :: REAL_2:10
canceled;
theorem :: REAL_2:11
canceled;
theorem :: REAL_2:12
canceled;
theorem :: REAL_2:13
canceled;
theorem :: REAL_2:14
canceled;
theorem :: REAL_2:15
canceled;
theorem :: REAL_2:16
canceled;
theorem :: REAL_2:17
canceled;
theorem :: REAL_2:18
canceled;
theorem :: REAL_2:19
canceled;
theorem :: REAL_2:20
canceled;
theorem :: REAL_2:21
canceled;
theorem :: REAL_2:22
canceled;
theorem :: REAL_2:23
canceled;
theorem :: REAL_2:24
canceled;
theorem :: REAL_2:25
canceled;
theorem :: REAL_2:26
canceled;
theorem :: REAL_2:27
canceled;
theorem :: REAL_2:28
canceled;
theorem :: REAL_2:29
canceled;
theorem :: REAL_2:30
canceled;
theorem :: REAL_2:31
canceled;
theorem :: REAL_2:32
canceled;
theorem :: REAL_2:33
canceled;
theorem :: REAL_2:34
canceled;
theorem :: REAL_2:35
canceled;
theorem :: REAL_2:36
canceled;
theorem :: REAL_2:37
canceled;
theorem :: REAL_2:38
canceled;
theorem :: REAL_2:39
canceled;
theorem :: REAL_2:40
canceled;
theorem :: REAL_2:41
canceled;
theorem :: REAL_2:42
canceled;
theorem :: REAL_2:43
canceled;
theorem :: REAL_2:44
canceled;
theorem :: REAL_2:45
canceled;
theorem :: REAL_2:46
canceled;
theorem :: REAL_2:47
canceled;
theorem :: REAL_2:48
canceled;
theorem :: REAL_2:49
canceled;
theorem :: REAL_2:50
canceled;
theorem :: REAL_2:51
canceled;
theorem :: REAL_2:52
canceled;
theorem :: REAL_2:53
canceled;
theorem :: REAL_2:54
canceled;
theorem :: REAL_2:55
canceled;
theorem :: REAL_2:56
canceled;
theorem :: REAL_2:57
canceled;
theorem :: REAL_2:58
canceled;
theorem :: REAL_2:59
canceled;
theorem :: REAL_2:60
canceled;
theorem :: REAL_2:61
canceled;
theorem :: REAL_2:62
canceled;
theorem :: REAL_2:63
theorem :: REAL_2:64
canceled;
theorem :: REAL_2:65
canceled;
theorem :: REAL_2:66
canceled;
theorem :: REAL_2:67
canceled;
theorem :: REAL_2:68
canceled;
theorem :: REAL_2:69
canceled;
theorem :: REAL_2:70
canceled;
theorem :: REAL_2:71
canceled;
theorem :: REAL_2:72
canceled;
theorem :: REAL_2:73
canceled;
theorem :: REAL_2:74
canceled;
theorem :: REAL_2:75
canceled;
theorem :: REAL_2:76
canceled;
theorem :: REAL_2:77
canceled;
theorem :: REAL_2:78
canceled;
theorem :: REAL_2:79
canceled;
theorem :: REAL_2:80
canceled;
theorem :: REAL_2:81
canceled;
theorem :: REAL_2:82
canceled;
theorem :: REAL_2:83
canceled;
theorem :: REAL_2:84
canceled;
theorem :: REAL_2:85
canceled;
theorem :: REAL_2:86
canceled;
theorem :: REAL_2:87
canceled;
theorem :: REAL_2:88
canceled;
theorem :: REAL_2:89
canceled;
theorem :: REAL_2:90
canceled;
theorem :: REAL_2:91
canceled;
theorem :: REAL_2:92
canceled;
theorem :: REAL_2:93
canceled;
theorem :: REAL_2:94
canceled;
theorem :: REAL_2:95
canceled;
theorem :: REAL_2:96
canceled;
theorem :: REAL_2:97
canceled;
theorem :: REAL_2:98
canceled;
theorem :: REAL_2:99
canceled;
theorem :: REAL_2:100
canceled;
theorem :: REAL_2:101
canceled;
theorem :: REAL_2:102
canceled;
theorem :: REAL_2:103
canceled;
theorem :: REAL_2:104
canceled;
theorem :: REAL_2:105
theorem :: REAL_2:106
for
a,
b,
e being
real number st (
a + (- b) < 0 or
b - a > 0 or
(- a) + b > 0 or
a - e < b + (- e) or
a + (- e) < b - e or
e - a > e - b ) holds
a < b
theorem :: REAL_2:107
canceled;
theorem :: REAL_2:108
canceled;
theorem :: REAL_2:109
theorem :: REAL_2:110
theorem :: REAL_2:111
canceled;
theorem :: REAL_2:112
canceled;
theorem :: REAL_2:113
canceled;
theorem :: REAL_2:114
canceled;
theorem :: REAL_2:115
canceled;
theorem :: REAL_2:116
canceled;
theorem :: REAL_2:117
theorem :: REAL_2:118
theorem :: REAL_2:119
theorem :: REAL_2:120
theorem :: REAL_2:121
theorem :: REAL_2:122
theorem :: REAL_2:123
canceled;
theorem :: REAL_2:124
canceled;
theorem :: REAL_2:125
theorem :: REAL_2:126
theorem :: REAL_2:127
theorem :: REAL_2:128
theorem :: REAL_2:129
theorem :: REAL_2:130
canceled;
theorem :: REAL_2:131
canceled;
theorem :: REAL_2:132
canceled;
theorem :: REAL_2:133
theorem :: REAL_2:134
theorem :: REAL_2:135
canceled;
theorem :: REAL_2:136
canceled;
theorem :: REAL_2:137
theorem :: REAL_2:138
theorem :: REAL_2:139
theorem :: REAL_2:140
theorem :: REAL_2:141
canceled;
theorem :: REAL_2:142
theorem :: REAL_2:143
theorem :: REAL_2:144
theorem :: REAL_2:145
theorem :: REAL_2:146
theorem :: REAL_2:147
theorem :: REAL_2:148
canceled;
theorem Th149: :: REAL_2:149
theorem :: REAL_2:150
for
a being
real number holds
( ( 1
/ a < 0 implies
a < 0 ) & ( 1
/ a > 0 implies
a > 0 ) )
theorem Th151: :: REAL_2:151
theorem Th152: :: REAL_2:152
theorem Th153: :: REAL_2:153
theorem :: REAL_2:154
theorem :: REAL_2:155
theorem :: REAL_2:156
theorem :: REAL_2:157
theorem :: REAL_2:158
theorem :: REAL_2:159
canceled;
theorem :: REAL_2:160
canceled;
theorem :: REAL_2:161
canceled;
theorem :: REAL_2:162
canceled;
theorem :: REAL_2:163
canceled;
theorem :: REAL_2:164
theorem :: REAL_2:165
theorem :: REAL_2:166
canceled;
theorem :: REAL_2:167
canceled;
theorem :: REAL_2:168
canceled;
theorem :: REAL_2:169
theorem :: REAL_2:170
theorem :: REAL_2:171
theorem :: REAL_2:172
canceled;
theorem :: REAL_2:173
theorem :: REAL_2:174
theorem :: REAL_2:175
canceled;
theorem :: REAL_2:176
canceled;
theorem :: REAL_2:177
theorem :: REAL_2:178
theorem :: REAL_2:179
canceled;
theorem :: REAL_2:180
canceled;
theorem :: REAL_2:181
theorem :: REAL_2:182
theorem :: REAL_2:183
theorem :: REAL_2:184
theorem :: REAL_2:185
theorem :: REAL_2:186
theorem :: REAL_2:187
theorem :: REAL_2:188
theorem :: REAL_2:189
canceled;
theorem :: REAL_2:190
canceled;
theorem :: REAL_2:191
canceled;
theorem :: REAL_2:192
canceled;
theorem :: REAL_2:193
theorem :: REAL_2:194
theorem :: REAL_2:195
canceled;
theorem :: REAL_2:196
canceled;
theorem :: REAL_2:197
canceled;
theorem :: REAL_2:198
canceled;
theorem :: REAL_2:199
theorem :: REAL_2:200
theorem :: REAL_2:201
theorem :: REAL_2:202
theorem :: REAL_2:203
theorem :: REAL_2:204