| step type | requirements | statement |
0 | deduction | 1 | ⊢ |
1 | instantiation | 424, 2, 3 | ⊢ |
| : , : , : |
2 | instantiation | 4, 622, 5, 6, 7, 8 | ⊢ |
| : , : , : |
3 | instantiation | 466, 9, 10, 11 | ⊢ |
| : , : , : , : |
4 | conjecture | | ⊢ |
| proveit.numbers.exponentiation.exp_pos_less |
5 | instantiation | 632, 538, 29 | ⊢ |
| : , : , : |
6 | instantiation | 632, 333, 12 | ⊢ |
| : , : , : |
7 | instantiation | 337, 13, 14 | ⊢ |
| : , : |
8 | instantiation | 572, 627 | ⊢ |
| : |
9 | instantiation | 280, 553, 15, 16, 17* | ⊢ |
| : , : |
10 | instantiation | 566 | ⊢ |
| : |
11 | instantiation | 409, 18 | ⊢ |
| : , : |
12 | instantiation | 19, 35 | ⊢ |
| : |
13 | instantiation | 20, 21 | ⊢ |
| : |
14 | instantiation | 424, 22, 23 | ⊢ |
| : , : , : |
15 | instantiation | 632, 621, 24 | ⊢ |
| : , : , : |
16 | instantiation | 25, 479, 612, 420 | ⊢ |
| : , : |
17 | instantiation | 62, 479, 622, 564, 420, 26* | ⊢ |
| : , : , : |
18 | instantiation | 573, 27, 28 | ⊢ |
| : , : , : |
19 | conjecture | | ⊢ |
| proveit.numbers.absolute_value.abs_complex_closure |
20 | conjecture | | ⊢ |
| proveit.numbers.number_sets.real_numbers.nonneg_if_in_real_nonneg |
21 | instantiation | 632, 379, 29 | ⊢ |
| : , : , : |
22 | instantiation | 404, 84, 30, 31, 32, 117, 33* | ⊢ |
| : , : , : |
23 | instantiation | 34, 35, 36, 37, 38* | ⊢ |
| : , : |
24 | instantiation | 39, 508, 634 | ⊢ |
| : , : |
25 | conjecture | | ⊢ |
| proveit.numbers.exponentiation.exp_not_eq_zero |
26 | instantiation | 40, 612, 541, 598* | ⊢ |
| : , : |
27 | instantiation | 582, 41 | ⊢ |
| : , : , : |
28 | instantiation | 42, 612, 417, 627, 43*, 44* | ⊢ |
| : , : , : |
29 | instantiation | 45, 299, 537, 420 | ⊢ |
| : , : |
30 | instantiation | 46, 245, 318, 190 | ⊢ |
| : , : |
31 | instantiation | 46, 183, 241, 182 | ⊢ |
| : , : |
32 | instantiation | 401, 47, 48 | ⊢ |
| : , : , : |
33 | instantiation | 573, 49, 50 | ⊢ |
| : , : , : |
34 | conjecture | | ⊢ |
| proveit.numbers.absolute_value.abs_eq |
35 | instantiation | 51, 52 | ⊢ |
| : |
36 | instantiation | 412, 56, 57 | ⊢ |
| : , : |
37 | instantiation | 463, 53, 54 | ⊢ |
| : , : , : |
38 | instantiation | 486, 627, 55, 56, 57, 58*, 59* | ⊢ |
| : , : |
39 | conjecture | | ⊢ |
| proveit.numbers.exponentiation.exp_real_closure_nat_power |
40 | conjecture | | ⊢ |
| proveit.numbers.multiplication.mult_neg_right |
41 | instantiation | 280, 612, 479, 420 | ⊢ |
| : , : |
42 | conjecture | | ⊢ |
| proveit.numbers.exponentiation.posnat_power_of_product |
43 | instantiation | 466, 60, 61, 551 | ⊢ |
| : , : , : , : |
44 | instantiation | 62, 479, 564, 622, 420, 63* | ⊢ |
| : , : , : |
45 | conjecture | | ⊢ |
| proveit.numbers.division.div_real_pos_closure |
46 | conjecture | | ⊢ |
| proveit.numbers.division.div_real_closure |
47 | instantiation | 64, 273, 65, 362, 66 | ⊢ |
| : , : , : |
48 | instantiation | 67, 241, 245, 183, 68, 242 | ⊢ |
| : , : , : |
49 | instantiation | 573, 69, 70 | ⊢ |
| : , : , : |
50 | instantiation | 466, 71, 72, 73 | ⊢ |
| : , : , : , : |
51 | conjecture | | ⊢ |
| proveit.physics.quantum.QPE._alpha_are_complex |
52 | instantiation | 74, 617, 602 | ⊢ |
| : , : |
53 | instantiation | 463, 75, 76, 77* | ⊢ |
| : , : , : |
54 | instantiation | 78, 148, 149, 79, 80, 81, 82*, 83* | ⊢ |
| : , : , : , : |
55 | instantiation | 609 | ⊢ |
| : , : |
56 | instantiation | 632, 621, 84 | ⊢ |
| : , : , : |
57 | instantiation | 191, 87, 88, 89 | ⊢ |
| : , : |
58 | instantiation | 514, 85 | ⊢ |
| : |
59 | instantiation | 86, 87, 88, 89, 90* | ⊢ |
| : , : |
60 | instantiation | 91, 627, 612 | ⊢ |
| : , : |
61 | instantiation | 92, 634, 93, 596, 94 | ⊢ |
| : , : , : , : |
62 | conjecture | | ⊢ |
| proveit.numbers.exponentiation.real_power_of_real_power |
63 | instantiation | 540, 541, 612, 597* | ⊢ |
| : , : |
64 | conjecture | | ⊢ |
| proveit.numbers.division.strong_div_from_denom_bound__all_pos |
65 | instantiation | 95, 241, 242 | ⊢ |
| : |
66 | instantiation | 96, 362 | ⊢ |
| : |
67 | conjecture | | ⊢ |
| proveit.numbers.division.weak_div_from_numer_bound__pos_denom |
68 | instantiation | 97, 334, 98, 99* | ⊢ |
| : |
69 | instantiation | 582, 100 | ⊢ |
| : , : , : |
70 | instantiation | 463, 101, 102 | ⊢ |
| : , : , : |
71 | instantiation | 582, 103 | ⊢ |
| : , : , : |
72 | instantiation | 582, 104 | ⊢ |
| : , : , : |
73 | instantiation | 293, 105, 305, 612 | ⊢ |
| : , : , : |
74 | conjecture | | ⊢ |
| proveit.numbers.modular.mod_natpos_in_interval |
75 | instantiation | 106, 617 | ⊢ |
| : |
76 | instantiation | 107, 617 | ⊢ |
| : |
77 | instantiation | 573, 108, 109 | ⊢ |
| : , : , : |
78 | conjecture | | ⊢ |
| proveit.numbers.summation.gen_finite_geom_sum |
79 | conjecture | | ⊢ |
| proveit.numbers.number_sets.integers.zero_is_int |
80 | instantiation | 110, 111, 603 | ⊢ |
| : , : |
81 | instantiation | 112, 113 | ⊢ |
| : , : |
82 | instantiation | 472, 148 | ⊢ |
| : |
83 | instantiation | 573, 114, 115 | ⊢ |
| : , : , : |
84 | instantiation | 632, 628, 116 | ⊢ |
| : , : , : |
85 | instantiation | 546, 117 | ⊢ |
| : , : |
86 | conjecture | | ⊢ |
| proveit.numbers.absolute_value.abs_frac |
87 | instantiation | 119, 541, 118 | ⊢ |
| : , : |
88 | instantiation | 119, 541, 120 | ⊢ |
| : , : |
89 | instantiation | 121, 122 | ⊢ |
| : , : |
90 | instantiation | 573, 123, 124 | ⊢ |
| : , : , : |
91 | conjecture | | ⊢ |
| proveit.numbers.exponentiation.exp_nat_pos_expansion |
92 | conjecture | | ⊢ |
| proveit.core_expr_types.operations.operands_substitution_via_tuple |
93 | instantiation | 125, 634 | ⊢ |
| : , : |
94 | instantiation | 126 | ⊢ |
| : |
95 | conjecture | | ⊢ |
| proveit.numbers.number_sets.real_numbers.pos_real_is_real_pos |
96 | conjecture | | ⊢ |
| proveit.trigonometry.sine_linear_bound_by_arg_pos |
97 | conjecture | | ⊢ |
| proveit.trigonometry.sine_linear_bound_nonneg |
98 | instantiation | 424, 127, 128 | ⊢ |
| : , : , : |
99 | instantiation | 573, 129, 130 | ⊢ |
| : , : , : |
100 | instantiation | 573, 131, 132 | ⊢ |
| : , : , : |
101 | instantiation | 463, 133, 134 | ⊢ |
| : , : , : |
102 | instantiation | 573, 135, 136 | ⊢ |
| : , : , : |
103 | instantiation | 458, 612, 480 | ⊢ |
| : , : |
104 | instantiation | 458, 479, 480 | ⊢ |
| : , : |
105 | instantiation | 632, 519, 137 | ⊢ |
| : , : , : |
106 | conjecture | | ⊢ |
| proveit.physics.quantum.QPE._alpha_m_mod_as_geometric_sum |
107 | conjecture | | ⊢ |
| proveit.physics.quantum.QPE._phase_from_best_with_delta_b |
108 | instantiation | 529, 530, 634, 624, 531, 138, 166, 590, 139 | ⊢ |
| : , : , : , : , : , : |
109 | instantiation | 140, 166, 590, 141 | ⊢ |
| : , : , : |
110 | conjecture | | ⊢ |
| proveit.numbers.addition.add_int_closure_bin |
111 | instantiation | 632, 142, 602 | ⊢ |
| : , : , : |
112 | conjecture | | ⊢ |
| proveit.numbers.addition.subtraction.nonneg_difference |
113 | instantiation | 561, 602 | ⊢ |
| : |
114 | instantiation | 582, 143 | ⊢ |
| : , : , : |
115 | instantiation | 144, 289, 171, 535, 145* | ⊢ |
| : , : , : |
116 | instantiation | 632, 607, 146 | ⊢ |
| : , : , : |
117 | instantiation | 433, 146 | ⊢ |
| : |
118 | instantiation | 335, 147 | ⊢ |
| : |
119 | conjecture | | ⊢ |
| proveit.numbers.addition.add_complex_closure_bin |
120 | instantiation | 335, 148 | ⊢ |
| : |
121 | conjecture | | ⊢ |
| proveit.numbers.addition.subtraction.nonzero_difference_if_different |
122 | instantiation | 213, 149 | ⊢ |
| : , : |
123 | instantiation | 594, 634, 150, 151, 152, 153 | ⊢ |
| : , : , : , : |
124 | instantiation | 293, 495, 154, 155 | ⊢ |
| : , : , : |
125 | conjecture | | ⊢ |
| proveit.core_expr_types.tuples.range_from1_len_typical_eq |
126 | conjecture | | ⊢ |
| proveit.numbers.numerals.decimals.reduce_2_repeats |
127 | instantiation | 424, 403, 156 | ⊢ |
| : , : , : |
128 | instantiation | 280, 479, 612, 342, 157* | ⊢ |
| : , : |
129 | instantiation | 582, 158 | ⊢ |
| : , : , : |
130 | instantiation | 573, 159, 160 | ⊢ |
| : , : , : |
131 | instantiation | 392, 530, 624, 531, 612, 535, 480 | ⊢ |
| : , : , : , : , : , : , : |
132 | instantiation | 413, 624, 634, 530, 161, 531, 535, 612, 480 | ⊢ |
| : , : , : , : , : , : |
133 | instantiation | 493, 541, 189, 494, 162, 163 | ⊢ |
| : , : , : , : , : |
134 | instantiation | 582, 164 | ⊢ |
| : , : , : |
135 | instantiation | 582, 498 | ⊢ |
| : , : , : |
136 | instantiation | 610, 165 | ⊢ |
| : |
137 | instantiation | 632, 470, 539 | ⊢ |
| : , : , : |
138 | instantiation | 609 | ⊢ |
| : , : |
139 | instantiation | 335, 166 | ⊢ |
| : |
140 | conjecture | | ⊢ |
| proveit.numbers.addition.subtraction.add_cancel_triple_13 |
141 | instantiation | 566 | ⊢ |
| : |
142 | conjecture | | ⊢ |
| proveit.numbers.number_sets.integers.nat_pos_within_int |
143 | instantiation | 573, 167, 168 | ⊢ |
| : , : , : |
144 | conjecture | | ⊢ |
| proveit.numbers.exponentiation.complex_power_of_complex_power |
145 | instantiation | 456, 530, 623, 624, 531, 169, 612, 479, 308, 590, 535 | ⊢ |
| : , : , : , : , : , : |
146 | instantiation | 618, 619, 321 | ⊢ |
| : , : |
147 | instantiation | 442, 235, 170 | ⊢ |
| : , : |
148 | instantiation | 442, 235, 171 | ⊢ |
| : , : |
149 | instantiation | 424, 172, 173 | ⊢ |
| : , : , : |
150 | instantiation | 609 | ⊢ |
| : , : |
151 | instantiation | 609 | ⊢ |
| : , : |
152 | instantiation | 177, 405, 174, 178*, 175*, 176* | ⊢ |
| : , : |
153 | instantiation | 177, 405, 201, 178*, 179*, 180* | ⊢ |
| : , : |
154 | instantiation | 589, 181, 182 | ⊢ |
| : |
155 | instantiation | 632, 621, 183 | ⊢ |
| : , : , : |
156 | instantiation | 392, 530, 624, 531, 535, 479, 480 | ⊢ |
| : , : , : , : , : , : , : |
157 | instantiation | 573, 184, 432 | ⊢ |
| : , : , : |
158 | instantiation | 456, 624, 414, 530, 356, 531, 612, 535, 479, 480 | ⊢ |
| : , : , : , : , : , : |
159 | instantiation | 573, 185, 186 | ⊢ |
| : , : , : |
160 | instantiation | 583, 217 | ⊢ |
| : |
161 | instantiation | 609 | ⊢ |
| : , : |
162 | instantiation | 632, 519, 187 | ⊢ |
| : , : , : |
163 | instantiation | 632, 519, 220 | ⊢ |
| : , : , : |
164 | instantiation | 582, 188 | ⊢ |
| : , : , : |
165 | instantiation | 191, 189, 294, 190 | ⊢ |
| : , : |
166 | instantiation | 191, 192, 535, 193 | ⊢ |
| : , : |
167 | instantiation | 529, 530, 634, 624, 531, 194, 535, 533, 541 | ⊢ |
| : , : , : , : , : , : |
168 | instantiation | 195, 541, 535, 536 | ⊢ |
| : , : , : |
169 | instantiation | 329 | ⊢ |
| : , : , : , : |
170 | instantiation | 463, 196, 197 | ⊢ |
| : , : , : |
171 | instantiation | 463, 198, 199 | ⊢ |
| : , : , : |
172 | instantiation | 200, 201, 202, 203* | ⊢ |
| : |
173 | instantiation | 582, 204 | ⊢ |
| : , : , : |
174 | instantiation | 463, 373, 349 | ⊢ |
| : , : , : |
175 | instantiation | 409, 205 | ⊢ |
| : , : |
176 | instantiation | 573, 206, 207 | ⊢ |
| : , : , : |
177 | conjecture | | ⊢ |
| proveit.trigonometry.complex_unit_circle_chord_length |
178 | instantiation | 573, 208, 209 | ⊢ |
| : , : , : |
179 | instantiation | 409, 210 | ⊢ |
| : , : |
180 | instantiation | 573, 211, 212 | ⊢ |
| : , : , : |
181 | instantiation | 632, 621, 241 | ⊢ |
| : , : , : |
182 | instantiation | 213, 214 | ⊢ |
| : , : |
183 | instantiation | 215, 314 | ⊢ |
| : |
184 | instantiation | 582, 343 | ⊢ |
| : , : , : |
185 | instantiation | 582, 216 | ⊢ |
| : , : , : |
186 | instantiation | 293, 305, 494, 217, 218* | ⊢ |
| : , : , : |
187 | instantiation | 632, 556, 219 | ⊢ |
| : , : , : |
188 | instantiation | 610, 535 | ⊢ |
| : |
189 | instantiation | 412, 612, 480 | ⊢ |
| : , : |
190 | instantiation | 445, 220 | ⊢ |
| : |
191 | conjecture | | ⊢ |
| proveit.numbers.division.div_complex_closure |
192 | instantiation | 632, 621, 221 | ⊢ |
| : , : , : |
193 | instantiation | 577, 602 | ⊢ |
| : |
194 | instantiation | 609 | ⊢ |
| : , : |
195 | conjecture | | ⊢ |
| proveit.numbers.addition.subtraction.add_cancel_triple_32 |
196 | instantiation | 412, 396, 222 | ⊢ |
| : , : |
197 | instantiation | 573, 223, 224 | ⊢ |
| : , : , : |
198 | instantiation | 412, 396, 274 | ⊢ |
| : , : |
199 | instantiation | 573, 225, 226 | ⊢ |
| : , : , : |
200 | conjecture | | ⊢ |
| proveit.numbers.exponentiation.unit_complex_polar_num_neq_one |
201 | instantiation | 463, 380, 361 | ⊢ |
| : , : , : |
202 | instantiation | 424, 227, 228 | ⊢ |
| : , : , : |
203 | instantiation | 409, 229 | ⊢ |
| : , : |
204 | instantiation | 392, 634, 624, 530, 397, 531, 612, 479, 308, 590 | ⊢ |
| : , : , : , : , : , : , : |
205 | instantiation | 582, 230 | ⊢ |
| : , : , : |
206 | instantiation | 582, 231 | ⊢ |
| : , : , : |
207 | instantiation | 573, 232, 233 | ⊢ |
| : , : , : |
208 | instantiation | 582, 234 | ⊢ |
| : , : , : |
209 | instantiation | 472, 235 | ⊢ |
| : |
210 | instantiation | 582, 236 | ⊢ |
| : , : , : |
211 | instantiation | 582, 237 | ⊢ |
| : , : , : |
212 | instantiation | 573, 238, 239 | ⊢ |
| : , : , : |
213 | theorem | | ⊢ |
| proveit.logic.equality.not_equals_symmetry |
214 | instantiation | 240, 405, 241, 242 | ⊢ |
| : , : |
215 | conjecture | | ⊢ |
| proveit.trigonometry.real_closure |
216 | instantiation | 573, 243, 244 | ⊢ |
| : , : , : |
217 | instantiation | 632, 621, 245 | ⊢ |
| : , : , : |
218 | instantiation | 611, 479 | ⊢ |
| : |
219 | instantiation | 632, 580, 246 | ⊢ |
| : , : , : |
220 | instantiation | 632, 470, 362 | ⊢ |
| : , : , : |
221 | instantiation | 632, 628, 247 | ⊢ |
| : , : , : |
222 | instantiation | 463, 248, 249 | ⊢ |
| : , : , : |
223 | instantiation | 456, 624, 414, 530, 250, 531, 396, 308, 590, 535 | ⊢ |
| : , : , : , : , : , : |
224 | instantiation | 456, 530, 634, 414, 531, 397, 250, 612, 479, 308, 590, 535 | ⊢ |
| : , : , : , : , : , : |
225 | instantiation | 456, 624, 634, 530, 275, 531, 396, 308, 590 | ⊢ |
| : , : , : , : , : , : |
226 | instantiation | 456, 530, 634, 531, 397, 275, 612, 479, 308, 590 | ⊢ |
| : , : , : , : , : , : |
227 | instantiation | 251, 252, 253, 303, 301 | ⊢ |
| : , : |
228 | instantiation | 466, 254, 542, 255 | ⊢ |
| : , : , : , : |
229 | instantiation | 582, 256 | ⊢ |
| : , : , : |
230 | instantiation | 573, 257, 258 | ⊢ |
| : , : , : |
231 | instantiation | 573, 259, 260 | ⊢ |
| : , : , : |
232 | instantiation | 573, 261, 262 | ⊢ |
| : , : , : |
233 | instantiation | 583, 288 | ⊢ |
| : |
234 | instantiation | 459, 308 | ⊢ |
| : |
235 | instantiation | 632, 621, 263 | ⊢ |
| : , : , : |
236 | instantiation | 573, 264, 284 | ⊢ |
| : , : , : |
237 | instantiation | 573, 265, 266 | ⊢ |
| : , : , : |
238 | instantiation | 573, 267, 268 | ⊢ |
| : , : , : |
239 | instantiation | 583, 294 | ⊢ |
| : |
240 | conjecture | | ⊢ |
| proveit.numbers.ordering.less_is_not_eq |
241 | instantiation | 269, 405, 569, 271 | ⊢ |
| : , : , : |
242 | instantiation | 270, 405, 569, 271 | ⊢ |
| : , : , : |
243 | instantiation | 392, 530, 634, 624, 531, 272, 612, 535, 479, 480 | ⊢ |
| : , : , : , : , : , : , : |
244 | instantiation | 413, 624, 414, 530, 298, 531, 479, 612, 535, 480 | ⊢ |
| : , : , : , : , : , : |
245 | instantiation | 632, 538, 273 | ⊢ |
| : , : , : |
246 | instantiation | 632, 600, 602 | ⊢ |
| : , : , : |
247 | instantiation | 632, 630, 617 | ⊢ |
| : , : , : |
248 | instantiation | 412, 274, 535 | ⊢ |
| : , : |
249 | instantiation | 456, 530, 634, 624, 531, 275, 308, 590, 535 | ⊢ |
| : , : , : , : , : , : |
250 | instantiation | 441 | ⊢ |
| : , : , : |
251 | theorem | | ⊢ |
| proveit.logic.booleans.disjunction.right_if_not_left |
252 | instantiation | 276, 277 | ⊢ |
| : |
253 | instantiation | 278, 279 | ⊢ |
| : , : |
254 | instantiation | 280, 336, 396, 281, 282* | ⊢ |
| : , : |
255 | instantiation | 566 | ⊢ |
| : |
256 | instantiation | 573, 283, 284 | ⊢ |
| : , : , : |
257 | instantiation | 392, 530, 634, 531, 397, 398, 612, 479, 308, 590, 535 | ⊢ |
| : , : , : , : , : , : , : |
258 | instantiation | 413, 624, 623, 530, 310, 531, 308, 612, 479, 590, 535 | ⊢ |
| : , : , : , : , : , : |
259 | instantiation | 582, 285 | ⊢ |
| : , : , : |
260 | instantiation | 511, 328, 286* | ⊢ |
| : |
261 | instantiation | 582, 287 | ⊢ |
| : , : , : |
262 | instantiation | 293, 495, 494, 288, 598* | ⊢ |
| : , : , : |
263 | instantiation | 632, 538, 289 | ⊢ |
| : , : , : |
264 | instantiation | 392, 530, 634, 624, 531, 397, 612, 479, 308, 590 | ⊢ |
| : , : , : , : , : , : , : |
265 | instantiation | 582, 290 | ⊢ |
| : , : , : |
266 | instantiation | 511, 336, 291* | ⊢ |
| : |
267 | instantiation | 582, 292 | ⊢ |
| : , : , : |
268 | instantiation | 293, 495, 494, 294, 598* | ⊢ |
| : , : , : |
269 | conjecture | | ⊢ |
| proveit.numbers.number_sets.real_numbers.all_in_interval_oc__is__real |
270 | conjecture | | ⊢ |
| proveit.numbers.number_sets.real_numbers.interval_oc_lower_bound |
271 | instantiation | 295, 296 | ⊢ |
| : |
272 | instantiation | 609 | ⊢ |
| : , : |
273 | instantiation | 297, 414, 298, 299, 300, 539 | ⊢ |
| : , : |
274 | instantiation | 412, 308, 590 | ⊢ |
| : , : |
275 | instantiation | 609 | ⊢ |
| : , : |
276 | axiom | | ⊢ |
| proveit.logic.booleans.negation.operand_is_bool |
277 | instantiation | 302, 301 | ⊢ |
| : |
278 | axiom | | ⊢ |
| proveit.logic.booleans.disjunction.right_in_bool |
279 | instantiation | 302, 303 | ⊢ |
| : |
280 | conjecture | | ⊢ |
| proveit.numbers.division.div_as_mult |
281 | instantiation | 304, 634, 397, 495, 305 | ⊢ |
| : , : |
282 | instantiation | 573, 306, 307 | ⊢ |
| : , : , : |
283 | instantiation | 392, 530, 414, 531, 389, 612, 479, 590, 308 | ⊢ |
| : , : , : , : , : , : , : |
284 | instantiation | 413, 624, 414, 530, 389, 531, 308, 612, 479, 590 | ⊢ |
| : , : , : , : , : , : |
285 | instantiation | 435, 309 | ⊢ |
| : |
286 | instantiation | 486, 578, 310, 612, 479, 590, 535, 311* | ⊢ |
| : , : |
287 | instantiation | 573, 312, 313 | ⊢ |
| : , : , : |
288 | instantiation | 632, 621, 314 | ⊢ |
| : , : , : |
289 | conjecture | | ⊢ |
| proveit.numbers.number_sets.real_numbers.e_is_real_pos |
290 | instantiation | 435, 315 | ⊢ |
| : |
291 | instantiation | 486, 316, 389, 612, 479, 590, 352*, 353* | ⊢ |
| : , : |
292 | instantiation | 413, 624, 634, 530, 332, 531, 612, 479, 480 | ⊢ |
| : , : , : , : , : , : |
293 | conjecture | | ⊢ |
| proveit.numbers.division.frac_cancel_left |
294 | instantiation | 632, 621, 318 | ⊢ |
| : , : , : |
295 | conjecture | | ⊢ |
| proveit.trigonometry.sine_pos_interval |
296 | instantiation | 317, 405, 508, 318, 319 | ⊢ |
| : , : , : |
297 | conjecture | | ⊢ |
| proveit.numbers.multiplication.mult_real_pos_closure |
298 | instantiation | 441 | ⊢ |
| : , : , : |
299 | instantiation | 632, 320, 620 | ⊢ |
| : , : , : |
300 | instantiation | 632, 320, 321 | ⊢ |
| : , : , : |
301 | instantiation | 322, 591 | ⊢ |
| : , : |
302 | conjecture | | ⊢ |
| proveit.logic.booleans.in_bool_if_true |
303 | instantiation | 323, 324 | ⊢ |
| : |
304 | conjecture | | ⊢ |
| proveit.numbers.multiplication.mult_not_eq_zero |
305 | instantiation | 632, 519, 446 | ⊢ |
| : , : , : |
306 | instantiation | 582, 325 | ⊢ |
| : , : , : |
307 | instantiation | 573, 326, 327 | ⊢ |
| : , : , : |
308 | conjecture | | ⊢ |
| proveit.numbers.number_sets.complex_numbers.i_is_complex |
309 | instantiation | 335, 328 | ⊢ |
| : |
310 | instantiation | 329 | ⊢ |
| : , : , : , : |
311 | instantiation | 573, 330, 331 | ⊢ |
| : , : , : |
312 | instantiation | 392, 530, 624, 634, 531, 332, 535, 612, 479, 480 | ⊢ |
| : , : , : , : , : , : , : |
313 | instantiation | 413, 624, 414, 530, 356, 531, 612, 535, 479, 480 | ⊢ |
| : , : , : , : , : , : |
314 | instantiation | 632, 333, 334 | ⊢ |
| : , : , : |
315 | instantiation | 335, 336 | ⊢ |
| : |
316 | conjecture | | ⊢ |
| proveit.numbers.numerals.decimals.posnat3 |
317 | conjecture | | ⊢ |
| proveit.numbers.number_sets.real_numbers.in_IntervalOO |
318 | instantiation | 632, 538, 362 | ⊢ |
| : , : , : |
319 | instantiation | 337, 338, 339 | ⊢ |
| : , : |
320 | conjecture | | ⊢ |
| proveit.numbers.number_sets.real_numbers.rational_pos_within_real_pos |
321 | instantiation | 632, 626, 602 | ⊢ |
| : , : , : |
322 | theorem | | ⊢ |
| proveit.logic.equality.unfold_not_equals |
323 | conjecture | | ⊢ |
| proveit.physics.quantum.QPE._delta_b_is_zero_or_non_int |
324 | instantiation | 340, 624, 530, 531 | ⊢ |
| : , : , : , : , : |
325 | instantiation | 341, 612, 479, 564, 342, 420, 343* | ⊢ |
| : , : , : |
326 | instantiation | 573, 344, 345 | ⊢ |
| : , : , : |
327 | instantiation | 573, 346, 347 | ⊢ |
| : , : , : |
328 | instantiation | 463, 348, 349 | ⊢ |
| : , : , : |
329 | conjecture | | ⊢ |
| proveit.numbers.numerals.decimals.tuple_len_4_typical_eq |
330 | instantiation | 594, 414, 350, 351, 352, 353, 488 | ⊢ |
| : , : , : , : |
331 | instantiation | 392, 530, 414, 531, 354, 612, 479, 480, 535 | ⊢ |
| : , : , : , : , : , : , : |
332 | instantiation | 609 | ⊢ |
| : , : |
333 | conjecture | | ⊢ |
| proveit.numbers.number_sets.real_numbers.real_nonneg_within_real |
334 | instantiation | 355, 414, 356, 357, 358, 359 | ⊢ |
| : , : |
335 | conjecture | | ⊢ |
| proveit.numbers.negation.complex_closure |
336 | instantiation | 463, 360, 361 | ⊢ |
| : , : , : |
337 | theorem | | ⊢ |
| proveit.logic.booleans.conjunction.and_if_both |
338 | instantiation | 489, 362 | ⊢ |
| : |
339 | instantiation | 363, 364, 365 | ⊢ |
| : , : , : |
340 | conjecture | | ⊢ |
| proveit.logic.sets.enumeration.in_enumerated_set |
341 | conjecture | | ⊢ |
| proveit.numbers.exponentiation.real_power_of_product |
342 | instantiation | 577, 627 | ⊢ |
| : |
343 | instantiation | 366, 495, 625, 528* | ⊢ |
| : , : |
344 | instantiation | 573, 367, 368 | ⊢ |
| : , : , : |
345 | instantiation | 573, 369, 370 | ⊢ |
| : , : , : |
346 | instantiation | 478, 530, 414, 531, 416, 479, 590, 417 | ⊢ |
| : , : , : , : |
347 | instantiation | 573, 371, 372 | ⊢ |
| : , : , : |
348 | instantiation | 632, 621, 373 | ⊢ |
| : , : , : |
349 | instantiation | 573, 374, 375 | ⊢ |
| : , : , : |
350 | instantiation | 441 | ⊢ |
| : , : , : |
351 | instantiation | 441 | ⊢ |
| : , : , : |
352 | instantiation | 514, 376 | ⊢ |
| : |
353 | instantiation | 514, 430 | ⊢ |
| : |
354 | instantiation | 441 | ⊢ |
| : , : , : |
355 | conjecture | | ⊢ |
| proveit.numbers.multiplication.mult_real_nonneg_closure |
356 | instantiation | 441 | ⊢ |
| : , : , : |
357 | instantiation | 632, 377, 378 | ⊢ |
| : , : , : |
358 | instantiation | 632, 379, 537 | ⊢ |
| : , : , : |
359 | instantiation | 632, 379, 539 | ⊢ |
| : , : , : |
360 | instantiation | 632, 621, 380 | ⊢ |
| : , : , : |
361 | instantiation | 456, 530, 634, 624, 531, 397, 612, 479, 590 | ⊢ |
| : , : , : , : , : , : |
362 | instantiation | 381, 537, 539 | ⊢ |
| : , : |
363 | axiom | | ⊢ |
| proveit.numbers.ordering.transitivity_less_less |
364 | instantiation | 463, 382, 426 | ⊢ |
| : , : , : |
365 | instantiation | 473, 461, 383, 384, 385*, 386* | ⊢ |
| : , : , : |
366 | conjecture | | ⊢ |
| proveit.numbers.exponentiation.neg_power_as_div |
367 | instantiation | 456, 530, 414, 624, 531, 389, 612, 479, 590, 387 | ⊢ |
| : , : , : , : , : , : |
368 | instantiation | 456, 414, 634, 530, 389, 388, 531, 612, 479, 590, 460, 417 | ⊢ |
| : , : , : , : , : , : |
369 | instantiation | 392, 530, 414, 624, 531, 389, 612, 479, 590, 460, 417 | ⊢ |
| : , : , : , : , : , : , : |
370 | instantiation | 573, 390, 391 | ⊢ |
| : , : , : |
371 | instantiation | 392, 624, 530, 531, 479, 590, 417 | ⊢ |
| : , : , : , : , : , : , : |
372 | instantiation | 413, 530, 634, 624, 531, 393, 479, 417, 590, 394* | ⊢ |
| : , : , : , : , : , : |
373 | instantiation | 490, 423, 395 | ⊢ |
| : , : |
374 | instantiation | 456, 624, 634, 530, 398, 531, 396, 590, 535 | ⊢ |
| : , : , : , : , : , : |
375 | instantiation | 456, 530, 634, 531, 397, 398, 612, 479, 590, 535 | ⊢ |
| : , : , : , : , : , : |
376 | instantiation | 399, 634 | ⊢ |
| : |
377 | conjecture | | ⊢ |
| proveit.numbers.number_sets.real_numbers.rational_nonneg_within_real_nonneg |
378 | instantiation | 632, 400, 585 | ⊢ |
| : , : , : |
379 | conjecture | | ⊢ |
| proveit.numbers.number_sets.real_numbers.real_pos_within_real_nonneg |
380 | instantiation | 490, 423, 606 | ⊢ |
| : , : |
381 | conjecture | | ⊢ |
| proveit.numbers.multiplication.mult_real_pos_closure_bin |
382 | instantiation | 401, 402, 403 | ⊢ |
| : , : , : |
383 | instantiation | 490, 571, 405 | ⊢ |
| : , : |
384 | instantiation | 404, 571, 405, 508, 455, 406 | ⊢ |
| : , : , : |
385 | instantiation | 573, 407, 408 | ⊢ |
| : , : , : |
386 | instantiation | 409, 410, 411* | ⊢ |
| : , : |
387 | instantiation | 412, 460, 417 | ⊢ |
| : , : |
388 | instantiation | 609 | ⊢ |
| : , : |
389 | instantiation | 441 | ⊢ |
| : , : , : |
390 | instantiation | 413, 530, 634, 414, 531, 415, 416, 460, 612, 479, 590, 417 | ⊢ |
| : , : , : , : , : , : |
391 | instantiation | 582, 418 | ⊢ |
| : , : , : |
392 | conjecture | | ⊢ |
| proveit.numbers.multiplication.leftward_commutation |
393 | instantiation | 609 | ⊢ |
| : , : |
394 | instantiation | 419, 479, 569, 564, 420, 421*, 422* | ⊢ |
| : , : , : |
395 | instantiation | 490, 606, 565 | ⊢ |
| : , : |
396 | instantiation | 632, 621, 423 | ⊢ |
| : , : , : |
397 | instantiation | 609 | ⊢ |
| : , : |
398 | instantiation | 609 | ⊢ |
| : , : |
399 | conjecture | | ⊢ |
| proveit.numbers.number_sets.natural_numbers.natural_lower_bound |
400 | conjecture | | ⊢ |
| proveit.numbers.number_sets.rational_numbers.nat_within_rational_nonneg |
401 | conjecture | | ⊢ |
| proveit.numbers.ordering.transitivity_less_less_eq |
402 | instantiation | 424, 425, 426 | ⊢ |
| : , : , : |
403 | instantiation | 427, 508, 428, 571, 429, 430, 431*, 432* | ⊢ |
| : , : , : |
404 | conjecture | | ⊢ |
| proveit.numbers.multiplication.strong_bound_via_right_factor_bound |
405 | conjecture | | ⊢ |
| proveit.numbers.number_sets.real_numbers.zero_is_real |
406 | instantiation | 433, 608 | ⊢ |
| : |
407 | instantiation | 582, 434 | ⊢ |
| : , : , : |
408 | instantiation | 435, 436 | ⊢ |
| : |
409 | theorem | | ⊢ |
| proveit.logic.equality.equals_reversal |
410 | instantiation | 437, 530, 634, 624, 531, 438, 460, 479 | ⊢ |
| : , : , : , : , : , : |
411 | instantiation | 573, 439, 440 | ⊢ |
| : , : , : |
412 | conjecture | | ⊢ |
| proveit.numbers.multiplication.mult_complex_closure_bin |
413 | conjecture | | ⊢ |
| proveit.numbers.multiplication.association |
414 | conjecture | | ⊢ |
| proveit.numbers.numerals.decimals.nat3 |
415 | instantiation | 609 | ⊢ |
| : , : |
416 | instantiation | 441 | ⊢ |
| : , : , : |
417 | instantiation | 442, 479, 533 | ⊢ |
| : , : |
418 | instantiation | 463, 443, 444 | ⊢ |
| : , : , : |
419 | conjecture | | ⊢ |
| proveit.numbers.exponentiation.product_of_real_powers |
420 | instantiation | 445, 446 | ⊢ |
| : |
421 | instantiation | 563, 479 | ⊢ |
| : |
422 | instantiation | 573, 447, 448 | ⊢ |
| : , : , : |
423 | instantiation | 490, 622, 508 | ⊢ |
| : , : |
424 | theorem | | ⊢ |
| proveit.logic.equality.sub_left_side_into |
425 | instantiation | 449, 624, 537, 539, 450, 451* | ⊢ |
| : , : , : , : , : , : |
426 | instantiation | 582, 452 | ⊢ |
| : , : , : |
427 | conjecture | | ⊢ |
| proveit.numbers.multiplication.weak_bound_via_right_factor_bound |
428 | instantiation | 490, 565, 509 | ⊢ |
| : , : |
429 | instantiation | 463, 453, 454 | ⊢ |
| : , : , : |
430 | instantiation | 546, 455 | ⊢ |
| : , : |
431 | instantiation | 456, 624, 634, 530, 457, 531, 479, 535, 480 | ⊢ |
| : , : , : , : , : , : |
432 | instantiation | 458, 479, 460 | ⊢ |
| : , : |
433 | conjecture | | ⊢ |
| proveit.numbers.number_sets.rational_numbers.positive_if_in_rational_pos |
434 | instantiation | 459, 460 | ⊢ |
| : |
435 | conjecture | | ⊢ |
| proveit.numbers.addition.elim_zero_left |
436 | instantiation | 632, 621, 461 | ⊢ |
| : , : , : |
437 | conjecture | | ⊢ |
| proveit.numbers.multiplication.distribute_through_sum |
438 | instantiation | 609 | ⊢ |
| : , : |
439 | instantiation | 582, 462 | ⊢ |
| : , : , : |
440 | instantiation | 610, 479 | ⊢ |
| : |
441 | conjecture | | ⊢ |
| proveit.numbers.numerals.decimals.tuple_len_3_typical_eq |
442 | conjecture | | ⊢ |
| proveit.numbers.exponentiation.exp_complex_closure |
443 | instantiation | 463, 464, 465 | ⊢ |
| : , : , : |
444 | instantiation | 466, 467, 468, 469 | ⊢ |
| : , : , : , : |
445 | conjecture | | ⊢ |
| proveit.numbers.number_sets.real_numbers.nonzero_if_in_real_nonzero |
446 | instantiation | 632, 470, 537 | ⊢ |
| : , : , : |
447 | instantiation | 582, 471 | ⊢ |
| : , : , : |
448 | instantiation | 472, 479 | ⊢ |
| : |
449 | conjecture | | ⊢ |
| proveit.numbers.multiplication.strong_bound_via_factor_bound |
450 | instantiation | 473, 564, 622, 474, 475, 476*, 477* | ⊢ |
| : , : , : |
451 | instantiation | 478, 624, 479, 480 | ⊢ |
| : , : , : , : |
452 | instantiation | 573, 481, 482 | ⊢ |
| : , : , : |
453 | instantiation | 483, 484, 485 | ⊢ |
| : , : |
454 | instantiation | 486, 627, 487, 535, 590, 488* | ⊢ |
| : , : |
455 | instantiation | 489, 537 | ⊢ |
| : |
456 | conjecture | | ⊢ |
| proveit.numbers.multiplication.disassociation |
457 | instantiation | 609 | ⊢ |
| : , : |
458 | conjecture | | ⊢ |
| proveit.numbers.multiplication.commutation |
459 | conjecture | | ⊢ |
| proveit.numbers.multiplication.mult_zero_right |
460 | instantiation | 632, 621, 571 | ⊢ |
| : , : , : |
461 | instantiation | 490, 571, 508 | ⊢ |
| : , : |
462 | instantiation | 491, 615, 631, 492* | ⊢ |
| : , : , : , : |
463 | theorem | | ⊢ |
| proveit.logic.equality.sub_right_side_into |
464 | instantiation | 493, 541, 494, 495 | ⊢ |
| : , : , : , : , : |
465 | instantiation | 573, 496, 497 | ⊢ |
| : , : , : |
466 | conjecture | | ⊢ |
| proveit.logic.equality.four_chain_transitivity |
467 | instantiation | 582, 498 | ⊢ |
| : , : , : |
468 | instantiation | 582, 498 | ⊢ |
| : , : , : |
469 | instantiation | 611, 541 | ⊢ |
| : |
470 | conjecture | | ⊢ |
| proveit.numbers.number_sets.real_numbers.real_pos_within_real_nonzero |
471 | instantiation | 499, 541, 536 | ⊢ |
| : , : |
472 | conjecture | | ⊢ |
| proveit.numbers.exponentiation.exp_zero_eq_one |
473 | conjecture | | ⊢ |
| proveit.numbers.addition.strong_bound_via_left_term_bound |
474 | instantiation | 632, 628, 500 | ⊢ |
| : , : , : |
475 | instantiation | 501, 622, 565, 569, 502, 503 | ⊢ |
| : , : , : |
476 | instantiation | 504, 541, 612, 505 | ⊢ |
| : , : , : |
477 | instantiation | 573, 506, 507 | ⊢ |
| : , : , : |
478 | conjecture | | ⊢ |
| proveit.numbers.multiplication.elim_one_any |
479 | instantiation | 632, 621, 508 | ⊢ |
| : , : , : |
480 | instantiation | 632, 621, 509 | ⊢ |
| : , : , : |
481 | instantiation | 582, 510 | ⊢ |
| : , : , : |
482 | instantiation | 511, 590 | ⊢ |
| : |
483 | conjecture | | ⊢ |
| proveit.numbers.absolute_value.weak_upper_bound |
484 | instantiation | 512, 544, 571, 545 | ⊢ |
| : , : , : |
485 | instantiation | 546, 513 | ⊢ |
| : , : |
486 | conjecture | | ⊢ |
| proveit.numbers.absolute_value.abs_prod |
487 | instantiation | 609 | ⊢ |
| : , : |
488 | instantiation | 514, 515 | ⊢ |
| : |
489 | conjecture | | ⊢ |
| proveit.numbers.number_sets.real_numbers.positive_if_in_real_pos |
490 | conjecture | | ⊢ |
| proveit.numbers.multiplication.mult_real_closure_bin |
491 | conjecture | | ⊢ |
| proveit.numbers.addition.rational_pair_addition |
492 | instantiation | 573, 516, 517 | ⊢ |
| : , : , : |
493 | conjecture | | ⊢ |
| proveit.numbers.division.mult_frac_cancel_denom_left |
494 | instantiation | 632, 519, 518 | ⊢ |
| : , : , : |
495 | instantiation | 632, 519, 520 | ⊢ |
| : , : , : |
496 | instantiation | 582, 521 | ⊢ |
| : , : , : |
497 | instantiation | 582, 522 | ⊢ |
| : , : , : |
498 | instantiation | 583, 541 | ⊢ |
| : |
499 | conjecture | | ⊢ |
| proveit.numbers.addition.subtraction.add_cancel_basic |
500 | instantiation | 632, 630, 523 | ⊢ |
| : , : , : |
501 | conjecture | | ⊢ |
| proveit.numbers.ordering.less_eq_add_right_strong |
502 | instantiation | 524, 622, 569, 525, 526, 527, 528* | ⊢ |
| : , : , : |
503 | conjecture | | ⊢ |
| proveit.numbers.numerals.decimals.less_0_1 |
504 | conjecture | | ⊢ |
| proveit.numbers.addition.subtraction.subtract_from_add |
505 | conjecture | | ⊢ |
| proveit.numbers.numerals.decimals.add_1_1 |
506 | instantiation | 529, 530, 634, 624, 531, 532, 535, 541, 533 | ⊢ |
| : , : , : , : , : , : |
507 | instantiation | 534, 541, 535, 536 | ⊢ |
| : , : , : |
508 | instantiation | 632, 538, 537 | ⊢ |
| : , : , : |
509 | instantiation | 632, 538, 539 | ⊢ |
| : , : , : |
510 | instantiation | 540, 541, 590, 542* | ⊢ |
| : , : |
511 | conjecture | | ⊢ |
| proveit.numbers.absolute_value.abs_even |
512 | conjecture | | ⊢ |
| proveit.numbers.number_sets.real_numbers.interval_co_lower_bound |
513 | instantiation | 543, 544, 571, 545 | ⊢ |
| : , : , : |
514 | conjecture | | ⊢ |
| proveit.numbers.absolute_value.abs_non_neg_elim |
515 | instantiation | 546, 547 | ⊢ |
| : , : |
516 | instantiation | 594, 634, 548, 549, 550, 551 | ⊢ |
| : , : , : , : |
517 | instantiation | 552, 553, 554 | ⊢ |
| : |
518 | instantiation | 632, 556, 555 | ⊢ |
| : , : , : |
519 | conjecture | | ⊢ |
| proveit.numbers.number_sets.complex_numbers.real_nonzero_within_complex_nonzero |
520 | instantiation | 632, 556, 557 | ⊢ |
| : , : , : |
521 | instantiation | 582, 597 | ⊢ |
| : , : , : |
522 | instantiation | 573, 558, 559 | ⊢ |
| : , : , : |
523 | instantiation | 632, 633, 560 | ⊢ |
| : , : , : |
524 | conjecture | | ⊢ |
| proveit.numbers.exponentiation.exp_monotonicity_large_base_less_eq |
525 | instantiation | 587, 588, 562 | ⊢ |
| : , : , : |
526 | conjecture | | ⊢ |
| proveit.numbers.numerals.decimals.less_1_2 |
527 | instantiation | 561, 562 | ⊢ |
| : |
528 | instantiation | 563, 612 | ⊢ |
| : |
529 | conjecture | | ⊢ |
| proveit.numbers.addition.disassociation |
530 | axiom | | ⊢ |
| proveit.numbers.number_sets.natural_numbers.zero_in_nats |
531 | conjecture | | ⊢ |
| proveit.core_expr_types.tuples.tuple_len_0_typical_eq |
532 | instantiation | 609 | ⊢ |
| : , : |
533 | instantiation | 632, 621, 564 | ⊢ |
| : , : , : |
534 | conjecture | | ⊢ |
| proveit.numbers.addition.subtraction.add_cancel_triple_23 |
535 | instantiation | 632, 621, 565 | ⊢ |
| : , : , : |
536 | instantiation | 566 | ⊢ |
| : |
537 | conjecture | | ⊢ |
| proveit.numbers.number_sets.real_numbers.pi_is_real_pos |
538 | conjecture | | ⊢ |
| proveit.numbers.number_sets.real_numbers.real_pos_within_real |
539 | instantiation | 567, 568 | ⊢ |
| : |
540 | conjecture | | ⊢ |
| proveit.numbers.multiplication.mult_neg_left |
541 | instantiation | 632, 621, 569 | ⊢ |
| : , : , : |
542 | instantiation | 610, 590 | ⊢ |
| : |
543 | conjecture | | ⊢ |
| proveit.numbers.number_sets.real_numbers.interval_co_upper_bound |
544 | instantiation | 570, 571 | ⊢ |
| : |
545 | conjecture | | ⊢ |
| proveit.physics.quantum.QPE._scaled_delta_b_round_in_interval |
546 | conjecture | | ⊢ |
| proveit.numbers.ordering.relax_less |
547 | instantiation | 572, 602 | ⊢ |
| : |
548 | instantiation | 609 | ⊢ |
| : , : |
549 | instantiation | 609 | ⊢ |
| : , : |
550 | instantiation | 573, 574, 575 | ⊢ |
| : , : , : |
551 | conjecture | | ⊢ |
| proveit.numbers.numerals.decimals.mult_2_2 |
552 | conjecture | | ⊢ |
| proveit.numbers.division.frac_cancel_complete |
553 | instantiation | 632, 621, 576 | ⊢ |
| : , : , : |
554 | instantiation | 577, 578 | ⊢ |
| : |
555 | instantiation | 632, 580, 579 | ⊢ |
| : , : , : |
556 | conjecture | | ⊢ |
| proveit.numbers.number_sets.real_numbers.rational_nonzero_within_real_nonzero |
557 | instantiation | 632, 580, 581 | ⊢ |
| : , : , : |
558 | instantiation | 582, 598 | ⊢ |
| : , : , : |
559 | instantiation | 583, 612 | ⊢ |
| : |
560 | instantiation | 584, 585, 624 | ⊢ |
| : , : |
561 | conjecture | | ⊢ |
| proveit.numbers.number_sets.natural_numbers.natural_pos_lower_bound |
562 | axiom | | ⊢ |
| proveit.physics.quantum.QPE._t_in_natural_pos |
563 | conjecture | | ⊢ |
| proveit.numbers.exponentiation.complex_x_to_first_power_is_x |
564 | instantiation | 632, 628, 586 | ⊢ |
| : , : , : |
565 | instantiation | 587, 588, 602 | ⊢ |
| : , : , : |
566 | axiom | | ⊢ |
| proveit.logic.equality.equals_reflexivity |
567 | conjecture | | ⊢ |
| proveit.numbers.absolute_value.abs_nonzero_closure |
568 | instantiation | 589, 590, 591 | ⊢ |
| : |
569 | instantiation | 632, 628, 592 | ⊢ |
| : , : , : |
570 | conjecture | | ⊢ |
| proveit.numbers.negation.real_closure |
571 | instantiation | 632, 628, 593 | ⊢ |
| : , : , : |
572 | conjecture | | ⊢ |
| proveit.numbers.number_sets.natural_numbers.natural_pos_is_pos |
573 | axiom | | ⊢ |
| proveit.logic.equality.equals_transitivity |
574 | instantiation | 594, 634, 595, 596, 597, 598 | ⊢ |
| : , : , : , : |
575 | conjecture | | ⊢ |
| proveit.numbers.numerals.decimals.add_2_2 |
576 | instantiation | 632, 628, 599 | ⊢ |
| : , : , : |
577 | conjecture | | ⊢ |
| proveit.numbers.number_sets.natural_numbers.nonzero_if_is_nat_pos |
578 | conjecture | | ⊢ |
| proveit.numbers.numerals.decimals.posnat4 |
579 | instantiation | 632, 600, 625 | ⊢ |
| : , : , : |
580 | conjecture | | ⊢ |
| proveit.numbers.number_sets.rational_numbers.nonzero_int_within_rational_nonzero |
581 | instantiation | 632, 600, 627 | ⊢ |
| : , : , : |
582 | axiom | | ⊢ |
| proveit.logic.equality.substitution |
583 | conjecture | | ⊢ |
| proveit.numbers.division.frac_one_denom |
584 | conjecture | | ⊢ |
| proveit.numbers.addition.add_nat_closure_bin |
585 | instantiation | 632, 601, 602 | ⊢ |
| : , : , : |
586 | instantiation | 632, 630, 603 | ⊢ |
| : , : , : |
587 | theorem | | ⊢ |
| proveit.logic.sets.inclusion.unfold_subset_eq |
588 | instantiation | 604, 605 | ⊢ |
| : , : |
589 | conjecture | | ⊢ |
| proveit.numbers.number_sets.complex_numbers.nonzero_complex_is_complex_nonzero |
590 | instantiation | 632, 621, 606 | ⊢ |
| : , : , : |
591 | assumption | | ⊢ |
592 | instantiation | 632, 630, 615 | ⊢ |
| : , : , : |
593 | instantiation | 632, 607, 608 | ⊢ |
| : , : , : |
594 | axiom | | ⊢ |
| proveit.core_expr_types.operations.operands_substitution |
595 | instantiation | 609 | ⊢ |
| : , : |
596 | instantiation | 609 | ⊢ |
| : , : |
597 | instantiation | 610, 612 | ⊢ |
| : |
598 | instantiation | 611, 612 | ⊢ |
| : |
599 | instantiation | 632, 630, 613 | ⊢ |
| : , : , : |
600 | conjecture | | ⊢ |
| proveit.numbers.number_sets.integers.nat_pos_within_nonzero_int |
601 | conjecture | | ⊢ |
| proveit.numbers.number_sets.natural_numbers.nat_pos_within_nat |
602 | conjecture | | ⊢ |
| proveit.physics.quantum.QPE._two_pow_t_is_nat_pos |
603 | instantiation | 614, 615 | ⊢ |
| : |
604 | theorem | | ⊢ |
| proveit.logic.sets.inclusion.relax_proper_subset |
605 | conjecture | | ⊢ |
| proveit.numbers.number_sets.real_numbers.nat_pos_within_real |
606 | instantiation | 616, 617 | ⊢ |
| : |
607 | conjecture | | ⊢ |
| proveit.numbers.number_sets.rational_numbers.rational_pos_within_rational |
608 | instantiation | 618, 619, 620 | ⊢ |
| : , : |
609 | conjecture | | ⊢ |
| proveit.numbers.numerals.decimals.tuple_len_2_typical_eq |
610 | conjecture | | ⊢ |
| proveit.numbers.multiplication.elim_one_left |
611 | conjecture | | ⊢ |
| proveit.numbers.multiplication.elim_one_right |
612 | instantiation | 632, 621, 622 | ⊢ |
| : , : , : |
613 | instantiation | 632, 633, 623 | ⊢ |
| : , : , : |
614 | conjecture | | ⊢ |
| proveit.numbers.negation.int_closure |
615 | instantiation | 632, 633, 624 | ⊢ |
| : , : , : |
616 | conjecture | | ⊢ |
| proveit.physics.quantum.QPE._delta_b_is_real |
617 | conjecture | | ⊢ |
| proveit.physics.quantum.QPE._best_round_is_int |
618 | conjecture | | ⊢ |
| proveit.numbers.division.div_rational_pos_closure |
619 | instantiation | 632, 626, 625 | ⊢ |
| : , : , : |
620 | instantiation | 632, 626, 627 | ⊢ |
| : , : , : |
621 | conjecture | | ⊢ |
| proveit.numbers.number_sets.complex_numbers.real_within_complex |
622 | instantiation | 632, 628, 629 | ⊢ |
| : , : , : |
623 | conjecture | | ⊢ |
| proveit.numbers.numerals.decimals.nat4 |
624 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.nat1 |
625 | conjecture | | ⊢ |
| proveit.numbers.numerals.decimals.posnat1 |
626 | conjecture | | ⊢ |
| proveit.numbers.number_sets.rational_numbers.nat_pos_within_rational_pos |
627 | conjecture | | ⊢ |
| proveit.numbers.numerals.decimals.posnat2 |
628 | conjecture | | ⊢ |
| proveit.numbers.number_sets.real_numbers.rational_within_real |
629 | instantiation | 632, 630, 631 | ⊢ |
| : , : , : |
630 | conjecture | | ⊢ |
| proveit.numbers.number_sets.rational_numbers.int_within_rational |
631 | instantiation | 632, 633, 634 | ⊢ |
| : , : , : |
632 | theorem | | ⊢ |
| proveit.logic.sets.inclusion.superset_membership_from_proper_subset |
633 | conjecture | | ⊢ |
| proveit.numbers.number_sets.integers.nat_within_int |
634 | conjecture | | ⊢ |
| proveit.numbers.numerals.decimals.nat2 |
*equality replacement requirements |