| step type | requirements | statement |
0 | instantiation | 1, 2, 3 | ⊢ |
| : , : , : |
1 | reference | 431 | ⊢ |
2 | instantiation | 4, 635, 5, 6, 7, 8 | ⊢ |
| : , : , : |
3 | instantiation | 473, 9, 10, 11 | ⊢ |
| : , : , : , : |
4 | theorem | | ⊢ |
| proveit.numbers.exponentiation.exp_pos_less |
5 | instantiation | 642, 547, 30 | ⊢ |
| : , : , : |
6 | instantiation | 642, 12, 13 | ⊢ |
| : , : , : |
7 | instantiation | 353, 14, 15 | ⊢ |
| : , : |
8 | instantiation | 582, 624 | ⊢ |
| : |
9 | instantiation | 299, 564, 16, 17, 18* | ⊢ |
| : , : |
10 | instantiation | 577 | ⊢ |
| : |
11 | instantiation | 416, 19 | ⊢ |
| : , : |
12 | theorem | | ⊢ |
| proveit.numbers.number_sets.real_numbers.real_nonneg_within_real |
13 | instantiation | 20, 36 | ⊢ |
| : |
14 | instantiation | 21, 22 | ⊢ |
| : |
15 | instantiation | 431, 23, 24 | ⊢ |
| : , : , : |
16 | instantiation | 642, 634, 25 | ⊢ |
| : , : , : |
17 | instantiation | 26, 486, 628, 427 | ⊢ |
| : , : |
18 | instantiation | 62, 486, 635, 575, 427, 27* | ⊢ |
| : , : , : |
19 | instantiation | 586, 28, 29 | ⊢ |
| : , : , : |
20 | theorem | | ⊢ |
| proveit.numbers.absolute_value.abs_complex_closure |
21 | theorem | | ⊢ |
| proveit.numbers.number_sets.real_numbers.nonneg_if_in_real_nonneg |
22 | instantiation | 642, 169, 30 | ⊢ |
| : , : , : |
23 | instantiation | 411, 85, 31, 32, 33, 120, 34* | ⊢ |
| : , : , : |
24 | instantiation | 35, 36, 37, 38, 39* | ⊢ |
| : , : |
25 | instantiation | 40, 516, 644 | ⊢ |
| : , : |
26 | theorem | | ⊢ |
| proveit.numbers.exponentiation.exp_not_eq_zero |
27 | instantiation | 41, 628, 550, 612* | ⊢ |
| : , : |
28 | instantiation | 594, 42 | ⊢ |
| : , : , : |
29 | instantiation | 43, 628, 424, 624, 44*, 45* | ⊢ |
| : , : , : |
30 | instantiation | 46, 131, 546, 427 | ⊢ |
| : , : |
31 | instantiation | 604, 68, 335, 206 | ⊢ |
| : , : |
32 | instantiation | 604, 198, 258, 197 | ⊢ |
| : , : |
33 | instantiation | 408, 47, 48 | ⊢ |
| : , : , : |
34 | instantiation | 586, 49, 50 | ⊢ |
| : , : , : |
35 | theorem | | ⊢ |
| proveit.numbers.absolute_value.abs_eq |
36 | instantiation | 51, 52 | ⊢ |
| : |
37 | instantiation | 419, 56, 57 | ⊢ |
| : , : |
38 | instantiation | 470, 53, 54 | ⊢ |
| : , : , : |
39 | instantiation | 493, 624, 55, 56, 57, 58*, 59* | ⊢ |
| : , : |
40 | theorem | | ⊢ |
| proveit.numbers.exponentiation.exp_real_closure_nat_power |
41 | theorem | | ⊢ |
| proveit.numbers.multiplication.mult_neg_right |
42 | instantiation | 299, 628, 486, 427 | ⊢ |
| : , : |
43 | theorem | | ⊢ |
| proveit.numbers.exponentiation.posnat_power_of_product |
44 | instantiation | 473, 60, 61, 562 | ⊢ |
| : , : , : , : |
45 | instantiation | 62, 486, 575, 635, 427, 63* | ⊢ |
| : , : , : |
46 | theorem | | ⊢ |
| proveit.numbers.division.div_real_pos_closure |
47 | instantiation | 64, 98, 65, 373, 66 | ⊢ |
| : , : , : |
48 | instantiation | 67, 258, 68, 198, 69, 259 | ⊢ |
| : , : , : |
49 | instantiation | 586, 70, 71 | ⊢ |
| : , : , : |
50 | instantiation | 473, 72, 73, 74 | ⊢ |
| : , : , : , : |
51 | theorem | | ⊢ |
| proveit.physics.quantum.QPE._alpha_are_complex |
52 | instantiation | 75, 632, 617 | ⊢ |
| : , : |
53 | instantiation | 470, 76, 77, 78* | ⊢ |
| : , : , : |
54 | instantiation | 79, 158, 159, 80, 81, 82, 83*, 84* | ⊢ |
| : , : , : , : |
55 | instantiation | 625 | ⊢ |
| : , : |
56 | instantiation | 642, 634, 85 | ⊢ |
| : , : , : |
57 | instantiation | 207, 88, 89, 90 | ⊢ |
| : , : |
58 | instantiation | 522, 86 | ⊢ |
| : |
59 | instantiation | 87, 88, 89, 90, 91* | ⊢ |
| : , : |
60 | instantiation | 92, 624, 628 | ⊢ |
| : , : |
61 | instantiation | 93, 644, 94, 610, 95 | ⊢ |
| : , : , : , : |
62 | theorem | | ⊢ |
| proveit.numbers.exponentiation.real_power_of_real_power |
63 | instantiation | 549, 550, 628, 611* | ⊢ |
| : , : |
64 | theorem | | ⊢ |
| proveit.numbers.division.strong_div_from_denom_bound__all_pos |
65 | instantiation | 96, 258, 259 | ⊢ |
| : |
66 | instantiation | 97, 373 | ⊢ |
| : |
67 | theorem | | ⊢ |
| proveit.numbers.division.weak_div_from_numer_bound__pos_denom |
68 | instantiation | 642, 547, 98 | ⊢ |
| : , : , : |
69 | instantiation | 99, 100, 101, 102* | ⊢ |
| : |
70 | instantiation | 594, 103 | ⊢ |
| : , : , : |
71 | instantiation | 470, 104, 105 | ⊢ |
| : , : , : |
72 | instantiation | 594, 106 | ⊢ |
| : , : , : |
73 | instantiation | 594, 107 | ⊢ |
| : , : , : |
74 | instantiation | 312, 108, 321, 628 | ⊢ |
| : , : , : |
75 | theorem | | ⊢ |
| proveit.numbers.modular.mod_natpos_in_interval |
76 | instantiation | 109, 632 | ⊢ |
| : |
77 | instantiation | 110, 632 | ⊢ |
| : |
78 | instantiation | 586, 111, 112 | ⊢ |
| : , : , : |
79 | theorem | | ⊢ |
| proveit.numbers.summation.gen_finite_geom_sum |
80 | theorem | | ⊢ |
| proveit.numbers.number_sets.integers.zero_is_int |
81 | instantiation | 113, 114, 618 | ⊢ |
| : , : |
82 | instantiation | 115, 116 | ⊢ |
| : , : |
83 | instantiation | 479, 158 | ⊢ |
| : |
84 | instantiation | 586, 117, 118 | ⊢ |
| : , : , : |
85 | instantiation | 642, 638, 119 | ⊢ |
| : , : , : |
86 | instantiation | 555, 120 | ⊢ |
| : , : |
87 | theorem | | ⊢ |
| proveit.numbers.absolute_value.abs_frac |
88 | instantiation | 122, 550, 121 | ⊢ |
| : , : |
89 | instantiation | 122, 550, 123 | ⊢ |
| : , : |
90 | instantiation | 124, 125 | ⊢ |
| : , : |
91 | instantiation | 586, 126, 127 | ⊢ |
| : , : , : |
92 | theorem | | ⊢ |
| proveit.numbers.exponentiation.exp_nat_pos_expansion |
93 | theorem | | ⊢ |
| proveit.core_expr_types.operations.operands_substitution_via_tuple |
94 | instantiation | 128, 644 | ⊢ |
| : , : |
95 | instantiation | 129 | ⊢ |
| : |
96 | theorem | | ⊢ |
| proveit.numbers.number_sets.real_numbers.pos_real_is_real_pos |
97 | theorem | | ⊢ |
| proveit.trigonometry.sine_linear_bound_by_arg_pos |
98 | instantiation | 130, 421, 290, 131, 132, 548 | ⊢ |
| : , : |
99 | theorem | | ⊢ |
| proveit.trigonometry.sine_linear_bound_nonneg |
100 | instantiation | 133, 421, 348, 134, 135, 136 | ⊢ |
| : , : |
101 | instantiation | 431, 137, 138 | ⊢ |
| : , : , : |
102 | instantiation | 586, 139, 140 | ⊢ |
| : , : , : |
103 | instantiation | 586, 141, 142 | ⊢ |
| : , : , : |
104 | instantiation | 470, 143, 144 | ⊢ |
| : , : , : |
105 | instantiation | 586, 145, 146 | ⊢ |
| : , : , : |
106 | instantiation | 465, 628, 487 | ⊢ |
| : , : |
107 | instantiation | 465, 486, 487 | ⊢ |
| : , : |
108 | instantiation | 642, 528, 147 | ⊢ |
| : , : , : |
109 | theorem | | ⊢ |
| proveit.physics.quantum.QPE._alpha_m_mod_as_geometric_sum |
110 | theorem | | ⊢ |
| proveit.physics.quantum.QPE._phase_from_best_with_delta_b |
111 | instantiation | 538, 539, 644, 637, 540, 148, 180, 602, 149 | ⊢ |
| : , : , : , : , : , : |
112 | instantiation | 150, 180, 602, 151 | ⊢ |
| : , : , : |
113 | theorem | | ⊢ |
| proveit.numbers.addition.add_int_closure_bin |
114 | instantiation | 642, 152, 617 | ⊢ |
| : , : , : |
115 | theorem | | ⊢ |
| proveit.numbers.addition.subtraction.nonneg_difference |
116 | instantiation | 572, 617 | ⊢ |
| : |
117 | instantiation | 594, 153 | ⊢ |
| : , : , : |
118 | instantiation | 154, 308, 186, 544, 155* | ⊢ |
| : , : , : |
119 | instantiation | 642, 557, 156 | ⊢ |
| : , : , : |
120 | instantiation | 440, 156 | ⊢ |
| : |
121 | instantiation | 351, 157 | ⊢ |
| : |
122 | theorem | | ⊢ |
| proveit.numbers.addition.add_complex_closure_bin |
123 | instantiation | 351, 158 | ⊢ |
| : |
124 | theorem | | ⊢ |
| proveit.numbers.addition.subtraction.nonzero_difference_if_different |
125 | instantiation | 229, 159 | ⊢ |
| : , : |
126 | instantiation | 608, 644, 160, 161, 162, 163 | ⊢ |
| : , : , : , : |
127 | instantiation | 312, 503, 164, 165 | ⊢ |
| : , : , : |
128 | theorem | | ⊢ |
| proveit.core_expr_types.tuples.range_from1_len_typical_eq |
129 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.reduce_2_repeats |
130 | theorem | | ⊢ |
| proveit.numbers.multiplication.mult_real_pos_closure |
131 | instantiation | 642, 166, 585 | ⊢ |
| : , : , : |
132 | instantiation | 642, 166, 184 | ⊢ |
| : , : , : |
133 | theorem | | ⊢ |
| proveit.numbers.multiplication.mult_real_nonneg_closure |
134 | instantiation | 642, 167, 168 | ⊢ |
| : , : , : |
135 | instantiation | 642, 169, 546 | ⊢ |
| : , : , : |
136 | instantiation | 642, 169, 548 | ⊢ |
| : , : , : |
137 | instantiation | 431, 410, 170 | ⊢ |
| : , : , : |
138 | instantiation | 299, 486, 628, 606, 171* | ⊢ |
| : , : |
139 | instantiation | 594, 172 | ⊢ |
| : , : , : |
140 | instantiation | 586, 173, 174 | ⊢ |
| : , : , : |
141 | instantiation | 400, 539, 637, 540, 628, 544, 487 | ⊢ |
| : , : , : , : , : , : , : |
142 | instantiation | 420, 637, 644, 539, 175, 540, 544, 628, 487 | ⊢ |
| : , : , : , : , : , : |
143 | instantiation | 501, 550, 205, 502, 176, 177 | ⊢ |
| : , : , : , : , : |
144 | instantiation | 594, 178 | ⊢ |
| : , : , : |
145 | instantiation | 594, 506 | ⊢ |
| : , : , : |
146 | instantiation | 626, 179 | ⊢ |
| : |
147 | instantiation | 642, 477, 548 | ⊢ |
| : , : , : |
148 | instantiation | 625 | ⊢ |
| : , : |
149 | instantiation | 351, 180 | ⊢ |
| : |
150 | theorem | | ⊢ |
| proveit.numbers.addition.subtraction.add_cancel_triple_13 |
151 | instantiation | 577 | ⊢ |
| : |
152 | theorem | | ⊢ |
| proveit.numbers.number_sets.integers.nat_pos_within_int |
153 | instantiation | 586, 181, 182 | ⊢ |
| : , : , : |
154 | theorem | | ⊢ |
| proveit.numbers.exponentiation.complex_power_of_complex_power |
155 | instantiation | 463, 539, 636, 637, 540, 183, 628, 486, 324, 602, 544 | ⊢ |
| : , : , : , : , : , : |
156 | instantiation | 583, 584, 184 | ⊢ |
| : , : |
157 | instantiation | 449, 252, 185 | ⊢ |
| : , : |
158 | instantiation | 449, 252, 186 | ⊢ |
| : , : |
159 | instantiation | 431, 187, 188 | ⊢ |
| : , : , : |
160 | instantiation | 625 | ⊢ |
| : , : |
161 | instantiation | 625 | ⊢ |
| : , : |
162 | instantiation | 192, 412, 189, 193*, 190*, 191* | ⊢ |
| : , : |
163 | instantiation | 192, 412, 217, 193*, 194*, 195* | ⊢ |
| : , : |
164 | instantiation | 601, 196, 197 | ⊢ |
| : |
165 | instantiation | 642, 634, 198 | ⊢ |
| : , : , : |
166 | theorem | | ⊢ |
| proveit.numbers.number_sets.real_numbers.rational_pos_within_real_pos |
167 | theorem | | ⊢ |
| proveit.numbers.number_sets.real_numbers.rational_nonneg_within_real_nonneg |
168 | instantiation | 642, 199, 597 | ⊢ |
| : , : , : |
169 | theorem | | ⊢ |
| proveit.numbers.number_sets.real_numbers.real_pos_within_real_nonneg |
170 | instantiation | 400, 539, 637, 540, 544, 486, 487 | ⊢ |
| : , : , : , : , : , : , : |
171 | instantiation | 586, 200, 439 | ⊢ |
| : , : , : |
172 | instantiation | 463, 637, 421, 539, 348, 540, 628, 544, 486, 487 | ⊢ |
| : , : , : , : , : , : |
173 | instantiation | 586, 201, 202 | ⊢ |
| : , : , : |
174 | instantiation | 595, 234 | ⊢ |
| : |
175 | instantiation | 625 | ⊢ |
| : , : |
176 | instantiation | 642, 528, 203 | ⊢ |
| : , : , : |
177 | instantiation | 642, 528, 237 | ⊢ |
| : , : , : |
178 | instantiation | 594, 204 | ⊢ |
| : , : , : |
179 | instantiation | 207, 205, 313, 206 | ⊢ |
| : , : |
180 | instantiation | 207, 208, 544, 209 | ⊢ |
| : , : |
181 | instantiation | 538, 539, 644, 637, 540, 210, 544, 542, 550 | ⊢ |
| : , : , : , : , : , : |
182 | instantiation | 211, 550, 544, 545 | ⊢ |
| : , : , : |
183 | instantiation | 344 | ⊢ |
| : , : , : , : |
184 | instantiation | 642, 607, 617 | ⊢ |
| : , : , : |
185 | instantiation | 470, 212, 213 | ⊢ |
| : , : , : |
186 | instantiation | 470, 214, 215 | ⊢ |
| : , : , : |
187 | instantiation | 216, 217, 218, 219* | ⊢ |
| : |
188 | instantiation | 594, 220 | ⊢ |
| : , : , : |
189 | instantiation | 470, 384, 364 | ⊢ |
| : , : , : |
190 | instantiation | 416, 221 | ⊢ |
| : , : |
191 | instantiation | 586, 222, 223 | ⊢ |
| : , : , : |
192 | theorem | | ⊢ |
| proveit.trigonometry.complex_unit_circle_chord_length |
193 | instantiation | 586, 224, 225 | ⊢ |
| : , : , : |
194 | instantiation | 416, 226 | ⊢ |
| : , : |
195 | instantiation | 586, 227, 228 | ⊢ |
| : , : , : |
196 | instantiation | 642, 634, 258 | ⊢ |
| : , : , : |
197 | instantiation | 229, 230 | ⊢ |
| : , : |
198 | instantiation | 231, 232 | ⊢ |
| : |
199 | theorem | | ⊢ |
| proveit.numbers.number_sets.rational_numbers.nat_within_rational_nonneg |
200 | instantiation | 594, 358 | ⊢ |
| : , : , : |
201 | instantiation | 594, 233 | ⊢ |
| : , : , : |
202 | instantiation | 312, 321, 502, 234, 235* | ⊢ |
| : , : , : |
203 | instantiation | 642, 567, 236 | ⊢ |
| : , : , : |
204 | instantiation | 626, 544 | ⊢ |
| : |
205 | instantiation | 419, 628, 487 | ⊢ |
| : , : |
206 | instantiation | 452, 237 | ⊢ |
| : |
207 | theorem | | ⊢ |
| proveit.numbers.division.div_complex_closure |
208 | instantiation | 642, 634, 238 | ⊢ |
| : , : , : |
209 | instantiation | 623, 617 | ⊢ |
| : |
210 | instantiation | 625 | ⊢ |
| : , : |
211 | theorem | | ⊢ |
| proveit.numbers.addition.subtraction.add_cancel_triple_32 |
212 | instantiation | 419, 404, 239 | ⊢ |
| : , : |
213 | instantiation | 586, 240, 241 | ⊢ |
| : , : , : |
214 | instantiation | 419, 404, 293 | ⊢ |
| : , : |
215 | instantiation | 586, 242, 243 | ⊢ |
| : , : , : |
216 | theorem | | ⊢ |
| proveit.numbers.exponentiation.unit_complex_polar_num_neq_one |
217 | instantiation | 470, 388, 372 | ⊢ |
| : , : , : |
218 | instantiation | 431, 244, 245 | ⊢ |
| : , : , : |
219 | instantiation | 416, 246 | ⊢ |
| : , : |
220 | instantiation | 400, 644, 637, 539, 405, 540, 628, 486, 324, 602 | ⊢ |
| : , : , : , : , : , : , : |
221 | instantiation | 594, 247 | ⊢ |
| : , : , : |
222 | instantiation | 594, 248 | ⊢ |
| : , : , : |
223 | instantiation | 586, 249, 250 | ⊢ |
| : , : , : |
224 | instantiation | 594, 251 | ⊢ |
| : , : , : |
225 | instantiation | 479, 252 | ⊢ |
| : |
226 | instantiation | 594, 253 | ⊢ |
| : , : , : |
227 | instantiation | 594, 254 | ⊢ |
| : , : , : |
228 | instantiation | 586, 255, 256 | ⊢ |
| : , : , : |
229 | theorem | | ⊢ |
| proveit.logic.equality.not_equals_symmetry |
230 | instantiation | 257, 412, 258, 259 | ⊢ |
| : , : |
231 | theorem | | ⊢ |
| proveit.trigonometry.real_closure |
232 | instantiation | 470, 349, 331 | ⊢ |
| : , : , : |
233 | instantiation | 586, 260, 261 | ⊢ |
| : , : , : |
234 | instantiation | 470, 262, 263 | ⊢ |
| : , : , : |
235 | instantiation | 627, 486 | ⊢ |
| : |
236 | instantiation | 642, 592, 264 | ⊢ |
| : , : , : |
237 | instantiation | 642, 477, 373 | ⊢ |
| : , : , : |
238 | instantiation | 642, 638, 265 | ⊢ |
| : , : , : |
239 | instantiation | 470, 266, 267 | ⊢ |
| : , : , : |
240 | instantiation | 463, 637, 421, 539, 268, 540, 404, 324, 602, 544 | ⊢ |
| : , : , : , : , : , : |
241 | instantiation | 463, 539, 644, 421, 540, 405, 268, 628, 486, 324, 602, 544 | ⊢ |
| : , : , : , : , : , : |
242 | instantiation | 463, 637, 644, 539, 294, 540, 404, 324, 602 | ⊢ |
| : , : , : , : , : , : |
243 | instantiation | 463, 539, 644, 540, 405, 294, 628, 486, 324, 602 | ⊢ |
| : , : , : , : , : , : |
244 | instantiation | 269, 270, 271, 319, 317 | ⊢ |
| : , : |
245 | instantiation | 473, 272, 551, 273 | ⊢ |
| : , : , : , : |
246 | instantiation | 594, 274 | ⊢ |
| : , : , : |
247 | instantiation | 586, 275, 276 | ⊢ |
| : , : , : |
248 | instantiation | 586, 277, 278 | ⊢ |
| : , : , : |
249 | instantiation | 586, 279, 280 | ⊢ |
| : , : , : |
250 | instantiation | 595, 307 | ⊢ |
| : |
251 | instantiation | 466, 324 | ⊢ |
| : |
252 | instantiation | 642, 634, 281 | ⊢ |
| : , : , : |
253 | instantiation | 586, 282, 303 | ⊢ |
| : , : , : |
254 | instantiation | 586, 283, 284 | ⊢ |
| : , : , : |
255 | instantiation | 586, 285, 286 | ⊢ |
| : , : , : |
256 | instantiation | 595, 313 | ⊢ |
| : |
257 | theorem | | ⊢ |
| proveit.numbers.ordering.less_is_not_eq |
258 | instantiation | 287, 412, 605, 289 | ⊢ |
| : , : , : |
259 | instantiation | 288, 412, 605, 289 | ⊢ |
| : , : , : |
260 | instantiation | 400, 539, 644, 637, 540, 292, 628, 544, 486, 487 | ⊢ |
| : , : , : , : , : , : , : |
261 | instantiation | 420, 637, 421, 539, 290, 540, 486, 628, 544, 487 | ⊢ |
| : , : , : , : , : , : |
262 | instantiation | 642, 634, 291 | ⊢ |
| : , : , : |
263 | instantiation | 463, 539, 644, 637, 540, 292, 628, 544, 487 | ⊢ |
| : , : , : , : , : , : |
264 | instantiation | 642, 615, 617 | ⊢ |
| : , : , : |
265 | instantiation | 642, 640, 632 | ⊢ |
| : , : , : |
266 | instantiation | 419, 293, 544 | ⊢ |
| : , : |
267 | instantiation | 463, 539, 644, 637, 540, 294, 324, 602, 544 | ⊢ |
| : , : , : , : , : , : |
268 | instantiation | 448 | ⊢ |
| : , : , : |
269 | theorem | | ⊢ |
| proveit.logic.booleans.disjunction.right_if_not_left |
270 | instantiation | 295, 296 | ⊢ |
| : |
271 | instantiation | 297, 298 | ⊢ |
| : , : |
272 | instantiation | 299, 352, 404, 300, 301* | ⊢ |
| : , : |
273 | instantiation | 577 | ⊢ |
| : |
274 | instantiation | 586, 302, 303 | ⊢ |
| : , : , : |
275 | instantiation | 400, 539, 644, 540, 405, 406, 628, 486, 324, 602, 544 | ⊢ |
| : , : , : , : , : , : , : |
276 | instantiation | 420, 637, 636, 539, 326, 540, 324, 628, 486, 602, 544 | ⊢ |
| : , : , : , : , : , : |
277 | instantiation | 594, 304 | ⊢ |
| : , : , : |
278 | instantiation | 519, 343, 305* | ⊢ |
| : |
279 | instantiation | 594, 306 | ⊢ |
| : , : , : |
280 | instantiation | 312, 503, 502, 307, 612* | ⊢ |
| : , : , : |
281 | instantiation | 642, 547, 308 | ⊢ |
| : , : , : |
282 | instantiation | 400, 539, 644, 637, 540, 405, 628, 486, 324, 602 | ⊢ |
| : , : , : , : , : , : , : |
283 | instantiation | 594, 309 | ⊢ |
| : , : , : |
284 | instantiation | 519, 352, 310* | ⊢ |
| : |
285 | instantiation | 594, 311 | ⊢ |
| : , : , : |
286 | instantiation | 312, 503, 502, 313, 612* | ⊢ |
| : , : , : |
287 | theorem | | ⊢ |
| proveit.numbers.number_sets.real_numbers.all_in_interval_oc__is__real |
288 | theorem | | ⊢ |
| proveit.numbers.number_sets.real_numbers.interval_oc_lower_bound |
289 | instantiation | 314, 315 | ⊢ |
| : |
290 | instantiation | 448 | ⊢ |
| : , : , : |
291 | instantiation | 497, 316, 517 | ⊢ |
| : , : |
292 | instantiation | 625 | ⊢ |
| : , : |
293 | instantiation | 419, 324, 602 | ⊢ |
| : , : |
294 | instantiation | 625 | ⊢ |
| : , : |
295 | axiom | | ⊢ |
| proveit.logic.booleans.negation.operand_is_bool |
296 | instantiation | 318, 317 | ⊢ |
| : |
297 | axiom | | ⊢ |
| proveit.logic.booleans.disjunction.right_in_bool |
298 | instantiation | 318, 319 | ⊢ |
| : |
299 | theorem | | ⊢ |
| proveit.numbers.division.div_as_mult |
300 | instantiation | 320, 644, 405, 503, 321 | ⊢ |
| : , : |
301 | instantiation | 586, 322, 323 | ⊢ |
| : , : , : |
302 | instantiation | 400, 539, 421, 540, 397, 628, 486, 602, 324 | ⊢ |
| : , : , : , : , : , : , : |
303 | instantiation | 420, 637, 421, 539, 397, 540, 324, 628, 486, 602 | ⊢ |
| : , : , : , : , : , : |
304 | instantiation | 442, 325 | ⊢ |
| : |
305 | instantiation | 493, 590, 326, 628, 486, 602, 544, 327* | ⊢ |
| : , : |
306 | instantiation | 586, 328, 329 | ⊢ |
| : , : , : |
307 | instantiation | 470, 330, 331 | ⊢ |
| : , : , : |
308 | theorem | | ⊢ |
| proveit.numbers.number_sets.real_numbers.e_is_real_pos |
309 | instantiation | 442, 332 | ⊢ |
| : |
310 | instantiation | 493, 333, 397, 628, 486, 602, 367*, 368* | ⊢ |
| : , : |
311 | instantiation | 420, 637, 644, 539, 347, 540, 628, 486, 487 | ⊢ |
| : , : , : , : , : , : |
312 | theorem | | ⊢ |
| proveit.numbers.division.frac_cancel_left |
313 | instantiation | 642, 634, 335 | ⊢ |
| : , : , : |
314 | theorem | | ⊢ |
| proveit.trigonometry.sine_pos_interval |
315 | instantiation | 334, 412, 516, 335, 336 | ⊢ |
| : , : , : |
316 | instantiation | 497, 635, 576 | ⊢ |
| : , : |
317 | instantiation | 337, 603 | ⊢ |
| : , : |
318 | theorem | | ⊢ |
| proveit.logic.booleans.in_bool_if_true |
319 | instantiation | 338, 339 | ⊢ |
| : |
320 | theorem | | ⊢ |
| proveit.numbers.multiplication.mult_not_eq_zero |
321 | instantiation | 642, 528, 453 | ⊢ |
| : , : , : |
322 | instantiation | 594, 340 | ⊢ |
| : , : , : |
323 | instantiation | 586, 341, 342 | ⊢ |
| : , : , : |
324 | theorem | | ⊢ |
| proveit.numbers.number_sets.complex_numbers.i_is_complex |
325 | instantiation | 351, 343 | ⊢ |
| : |
326 | instantiation | 344 | ⊢ |
| : , : , : , : |
327 | instantiation | 586, 345, 346 | ⊢ |
| : , : , : |
328 | instantiation | 400, 539, 637, 644, 540, 347, 544, 628, 486, 487 | ⊢ |
| : , : , : , : , : , : , : |
329 | instantiation | 420, 637, 421, 539, 348, 540, 628, 544, 486, 487 | ⊢ |
| : , : , : , : , : , : |
330 | instantiation | 642, 634, 349 | ⊢ |
| : , : , : |
331 | instantiation | 463, 539, 644, 637, 540, 350, 544, 486, 487 | ⊢ |
| : , : , : , : , : , : |
332 | instantiation | 351, 352 | ⊢ |
| : |
333 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.posnat3 |
334 | theorem | | ⊢ |
| proveit.numbers.number_sets.real_numbers.in_IntervalOO |
335 | instantiation | 642, 547, 373 | ⊢ |
| : , : , : |
336 | instantiation | 353, 354, 355 | ⊢ |
| : , : |
337 | theorem | | ⊢ |
| proveit.logic.equality.unfold_not_equals |
338 | theorem | | ⊢ |
| proveit.physics.quantum.QPE._delta_b_is_zero_or_non_int |
339 | instantiation | 356, 637, 539, 540 | ⊢ |
| : , : , : , : , : |
340 | instantiation | 357, 628, 486, 575, 606, 427, 358* | ⊢ |
| : , : , : |
341 | instantiation | 586, 359, 360 | ⊢ |
| : , : , : |
342 | instantiation | 586, 361, 362 | ⊢ |
| : , : , : |
343 | instantiation | 470, 363, 364 | ⊢ |
| : , : , : |
344 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.tuple_len_4_typical_eq |
345 | instantiation | 608, 421, 365, 366, 367, 368, 495 | ⊢ |
| : , : , : , : |
346 | instantiation | 400, 539, 421, 540, 369, 628, 486, 487, 544 | ⊢ |
| : , : , : , : , : , : , : |
347 | instantiation | 625 | ⊢ |
| : , : |
348 | instantiation | 448 | ⊢ |
| : , : , : |
349 | instantiation | 497, 370, 517 | ⊢ |
| : , : |
350 | instantiation | 625 | ⊢ |
| : , : |
351 | theorem | | ⊢ |
| proveit.numbers.negation.complex_closure |
352 | instantiation | 470, 371, 372 | ⊢ |
| : , : , : |
353 | theorem | | ⊢ |
| proveit.logic.booleans.conjunction.and_if_both |
354 | instantiation | 496, 373 | ⊢ |
| : |
355 | instantiation | 374, 375, 376 | ⊢ |
| : , : , : |
356 | theorem | | ⊢ |
| proveit.logic.sets.enumeration.in_enumerated_set |
357 | theorem | | ⊢ |
| proveit.numbers.exponentiation.real_power_of_product |
358 | instantiation | 377, 503, 614, 537* | ⊢ |
| : , : |
359 | instantiation | 586, 378, 379 | ⊢ |
| : , : , : |
360 | instantiation | 586, 380, 381 | ⊢ |
| : , : , : |
361 | instantiation | 485, 539, 421, 540, 423, 486, 602, 424 | ⊢ |
| : , : , : , : |
362 | instantiation | 586, 382, 383 | ⊢ |
| : , : , : |
363 | instantiation | 642, 634, 384 | ⊢ |
| : , : , : |
364 | instantiation | 586, 385, 386 | ⊢ |
| : , : , : |
365 | instantiation | 448 | ⊢ |
| : , : , : |
366 | instantiation | 448 | ⊢ |
| : , : , : |
367 | instantiation | 522, 387 | ⊢ |
| : |
368 | instantiation | 522, 437 | ⊢ |
| : |
369 | instantiation | 448 | ⊢ |
| : , : , : |
370 | instantiation | 497, 576, 516 | ⊢ |
| : , : |
371 | instantiation | 642, 634, 388 | ⊢ |
| : , : , : |
372 | instantiation | 463, 539, 644, 637, 540, 405, 628, 486, 602 | ⊢ |
| : , : , : , : , : , : |
373 | instantiation | 389, 546, 548 | ⊢ |
| : , : |
374 | axiom | | ⊢ |
| proveit.numbers.ordering.transitivity_less_less |
375 | instantiation | 470, 390, 433 | ⊢ |
| : , : , : |
376 | instantiation | 480, 468, 391, 392, 393*, 394* | ⊢ |
| : , : , : |
377 | theorem | | ⊢ |
| proveit.numbers.exponentiation.neg_power_as_div |
378 | instantiation | 463, 539, 421, 637, 540, 397, 628, 486, 602, 395 | ⊢ |
| : , : , : , : , : , : |
379 | instantiation | 463, 421, 644, 539, 397, 396, 540, 628, 486, 602, 467, 424 | ⊢ |
| : , : , : , : , : , : |
380 | instantiation | 400, 539, 421, 637, 540, 397, 628, 486, 602, 467, 424 | ⊢ |
| : , : , : , : , : , : , : |
381 | instantiation | 586, 398, 399 | ⊢ |
| : , : , : |
382 | instantiation | 400, 637, 539, 540, 486, 602, 424 | ⊢ |
| : , : , : , : , : , : , : |
383 | instantiation | 420, 539, 644, 637, 540, 401, 486, 424, 602, 402* | ⊢ |
| : , : , : , : , : , : |
384 | instantiation | 497, 430, 403 | ⊢ |
| : , : |
385 | instantiation | 463, 637, 644, 539, 406, 540, 404, 602, 544 | ⊢ |
| : , : , : , : , : , : |
386 | instantiation | 463, 539, 644, 540, 405, 406, 628, 486, 602, 544 | ⊢ |
| : , : , : , : , : , : |
387 | instantiation | 407, 644 | ⊢ |
| : |
388 | instantiation | 497, 430, 621 | ⊢ |
| : , : |
389 | theorem | | ⊢ |
| proveit.numbers.multiplication.mult_real_pos_closure_bin |
390 | instantiation | 408, 409, 410 | ⊢ |
| : , : , : |
391 | instantiation | 497, 498, 412 | ⊢ |
| : , : |
392 | instantiation | 411, 498, 412, 516, 462, 413 | ⊢ |
| : , : , : |
393 | instantiation | 586, 414, 415 | ⊢ |
| : , : , : |
394 | instantiation | 416, 417, 418* | ⊢ |
| : , : |
395 | instantiation | 419, 467, 424 | ⊢ |
| : , : |
396 | instantiation | 625 | ⊢ |
| : , : |
397 | instantiation | 448 | ⊢ |
| : , : , : |
398 | instantiation | 420, 539, 644, 421, 540, 422, 423, 467, 628, 486, 602, 424 | ⊢ |
| : , : , : , : , : , : |
399 | instantiation | 594, 425 | ⊢ |
| : , : , : |
400 | theorem | | ⊢ |
| proveit.numbers.multiplication.leftward_commutation |
401 | instantiation | 625 | ⊢ |
| : , : |
402 | instantiation | 426, 486, 605, 575, 427, 428*, 429* | ⊢ |
| : , : , : |
403 | instantiation | 497, 621, 576 | ⊢ |
| : , : |
404 | instantiation | 642, 634, 430 | ⊢ |
| : , : , : |
405 | instantiation | 625 | ⊢ |
| : , : |
406 | instantiation | 625 | ⊢ |
| : , : |
407 | theorem | | ⊢ |
| proveit.numbers.number_sets.natural_numbers.natural_lower_bound |
408 | theorem | | ⊢ |
| proveit.numbers.ordering.transitivity_less_less_eq |
409 | instantiation | 431, 432, 433 | ⊢ |
| : , : , : |
410 | instantiation | 434, 516, 435, 581, 436, 437, 438*, 439* | ⊢ |
| : , : , : |
411 | theorem | | ⊢ |
| proveit.numbers.multiplication.strong_bound_via_right_factor_bound |
412 | theorem | | ⊢ |
| proveit.numbers.number_sets.real_numbers.zero_is_real |
413 | instantiation | 440, 558 | ⊢ |
| : |
414 | instantiation | 594, 441 | ⊢ |
| : , : , : |
415 | instantiation | 442, 443 | ⊢ |
| : |
416 | theorem | | ⊢ |
| proveit.logic.equality.equals_reversal |
417 | instantiation | 444, 539, 644, 637, 540, 445, 467, 486 | ⊢ |
| : , : , : , : , : , : |
418 | instantiation | 586, 446, 447 | ⊢ |
| : , : , : |
419 | theorem | | ⊢ |
| proveit.numbers.multiplication.mult_complex_closure_bin |
420 | theorem | | ⊢ |
| proveit.numbers.multiplication.association |
421 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.nat3 |
422 | instantiation | 625 | ⊢ |
| : , : |
423 | instantiation | 448 | ⊢ |
| : , : , : |
424 | instantiation | 449, 486, 542 | ⊢ |
| : , : |
425 | instantiation | 470, 450, 451 | ⊢ |
| : , : , : |
426 | theorem | | ⊢ |
| proveit.numbers.exponentiation.product_of_real_powers |
427 | instantiation | 452, 453 | ⊢ |
| : |
428 | instantiation | 574, 486 | ⊢ |
| : |
429 | instantiation | 586, 454, 455 | ⊢ |
| : , : , : |
430 | instantiation | 497, 635, 516 | ⊢ |
| : , : |
431 | theorem | | ⊢ |
| proveit.logic.equality.sub_left_side_into |
432 | instantiation | 456, 637, 546, 548, 457, 458* | ⊢ |
| : , : , : , : , : , : |
433 | instantiation | 594, 459 | ⊢ |
| : , : , : |
434 | theorem | | ⊢ |
| proveit.numbers.multiplication.weak_bound_via_right_factor_bound |
435 | instantiation | 497, 576, 517 | ⊢ |
| : , : |
436 | instantiation | 470, 460, 461 | ⊢ |
| : , : , : |
437 | instantiation | 555, 462 | ⊢ |
| : , : |
438 | instantiation | 463, 637, 644, 539, 464, 540, 486, 544, 487 | ⊢ |
| : , : , : , : , : , : |
439 | instantiation | 465, 486, 467 | ⊢ |
| : , : |
440 | theorem | | ⊢ |
| proveit.numbers.number_sets.rational_numbers.positive_if_in_rational_pos |
441 | instantiation | 466, 467 | ⊢ |
| : |
442 | theorem | | ⊢ |
| proveit.numbers.addition.elim_zero_left |
443 | instantiation | 642, 634, 468 | ⊢ |
| : , : , : |
444 | theorem | | ⊢ |
| proveit.numbers.multiplication.distribute_through_sum |
445 | instantiation | 625 | ⊢ |
| : , : |
446 | instantiation | 594, 469 | ⊢ |
| : , : , : |
447 | instantiation | 626, 486 | ⊢ |
| : |
448 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.tuple_len_3_typical_eq |
449 | theorem | | ⊢ |
| proveit.numbers.exponentiation.exp_complex_closure |
450 | instantiation | 470, 471, 472 | ⊢ |
| : , : , : |
451 | instantiation | 473, 474, 475, 476 | ⊢ |
| : , : , : , : |
452 | theorem | | ⊢ |
| proveit.numbers.number_sets.real_numbers.nonzero_if_in_real_nonzero |
453 | instantiation | 642, 477, 546 | ⊢ |
| : , : , : |
454 | instantiation | 594, 478 | ⊢ |
| : , : , : |
455 | instantiation | 479, 486 | ⊢ |
| : |
456 | theorem | | ⊢ |
| proveit.numbers.multiplication.strong_bound_via_factor_bound |
457 | instantiation | 480, 575, 635, 481, 482, 483*, 484* | ⊢ |
| : , : , : |
458 | instantiation | 485, 637, 486, 487 | ⊢ |
| : , : , : , : |
459 | instantiation | 586, 488, 489 | ⊢ |
| : , : , : |
460 | instantiation | 490, 491, 492 | ⊢ |
| : , : |
461 | instantiation | 493, 624, 494, 544, 602, 495* | ⊢ |
| : , : |
462 | instantiation | 496, 546 | ⊢ |
| : |
463 | theorem | | ⊢ |
| proveit.numbers.multiplication.disassociation |
464 | instantiation | 625 | ⊢ |
| : , : |
465 | theorem | | ⊢ |
| proveit.numbers.multiplication.commutation |
466 | theorem | | ⊢ |
| proveit.numbers.multiplication.mult_zero_right |
467 | instantiation | 642, 634, 581 | ⊢ |
| : , : , : |
468 | instantiation | 497, 498, 516 | ⊢ |
| : , : |
469 | instantiation | 499, 633, 641, 500* | ⊢ |
| : , : , : , : |
470 | theorem | | ⊢ |
| proveit.logic.equality.sub_right_side_into |
471 | instantiation | 501, 550, 502, 503 | ⊢ |
| : , : , : , : , : |
472 | instantiation | 586, 504, 505 | ⊢ |
| : , : , : |
473 | theorem | | ⊢ |
| proveit.logic.equality.four_chain_transitivity |
474 | instantiation | 594, 506 | ⊢ |
| : , : , : |
475 | instantiation | 594, 506 | ⊢ |
| : , : , : |
476 | instantiation | 627, 550 | ⊢ |
| : |
477 | theorem | | ⊢ |
| proveit.numbers.number_sets.real_numbers.real_pos_within_real_nonzero |
478 | instantiation | 507, 550, 545 | ⊢ |
| : , : |
479 | theorem | | ⊢ |
| proveit.numbers.exponentiation.exp_zero_eq_one |
480 | theorem | | ⊢ |
| proveit.numbers.addition.strong_bound_via_left_term_bound |
481 | instantiation | 642, 638, 508 | ⊢ |
| : , : , : |
482 | instantiation | 509, 635, 576, 605, 510, 511 | ⊢ |
| : , : , : |
483 | instantiation | 512, 550, 628, 513 | ⊢ |
| : , : , : |
484 | instantiation | 586, 514, 515 | ⊢ |
| : , : , : |
485 | theorem | | ⊢ |
| proveit.numbers.multiplication.elim_one_any |
486 | instantiation | 642, 634, 516 | ⊢ |
| : , : , : |
487 | instantiation | 642, 634, 517 | ⊢ |
| : , : , : |
488 | instantiation | 594, 518 | ⊢ |
| : , : , : |
489 | instantiation | 519, 602 | ⊢ |
| : |
490 | theorem | | ⊢ |
| proveit.numbers.absolute_value.weak_upper_bound |
491 | instantiation | 520, 553, 581, 554 | ⊢ |
| : , : , : |
492 | instantiation | 555, 521 | ⊢ |
| : , : |
493 | theorem | | ⊢ |
| proveit.numbers.absolute_value.abs_prod |
494 | instantiation | 625 | ⊢ |
| : , : |
495 | instantiation | 522, 523 | ⊢ |
| : |
496 | theorem | | ⊢ |
| proveit.numbers.number_sets.real_numbers.positive_if_in_real_pos |
497 | theorem | | ⊢ |
| proveit.numbers.multiplication.mult_real_closure_bin |
498 | instantiation | 642, 638, 524 | ⊢ |
| : , : , : |
499 | theorem | | ⊢ |
| proveit.numbers.addition.rational_pair_addition |
500 | instantiation | 586, 525, 526 | ⊢ |
| : , : , : |
501 | theorem | | ⊢ |
| proveit.numbers.division.mult_frac_cancel_denom_left |
502 | instantiation | 642, 528, 527 | ⊢ |
| : , : , : |
503 | instantiation | 642, 528, 529 | ⊢ |
| : , : , : |
504 | instantiation | 594, 530 | ⊢ |
| : , : , : |
505 | instantiation | 594, 531 | ⊢ |
| : , : , : |
506 | instantiation | 595, 550 | ⊢ |
| : |
507 | theorem | | ⊢ |
| proveit.numbers.addition.subtraction.add_cancel_basic |
508 | instantiation | 642, 640, 532 | ⊢ |
| : , : , : |
509 | theorem | | ⊢ |
| proveit.numbers.ordering.less_eq_add_right_strong |
510 | instantiation | 533, 635, 605, 534, 535, 536, 537* | ⊢ |
| : , : , : |
511 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.less_0_1 |
512 | theorem | | ⊢ |
| proveit.numbers.addition.subtraction.subtract_from_add |
513 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.add_1_1 |
514 | instantiation | 538, 539, 644, 637, 540, 541, 544, 550, 542 | ⊢ |
| : , : , : , : , : , : |
515 | instantiation | 543, 550, 544, 545 | ⊢ |
| : , : , : |
516 | instantiation | 642, 547, 546 | ⊢ |
| : , : , : |
517 | instantiation | 642, 547, 548 | ⊢ |
| : , : , : |
518 | instantiation | 549, 550, 602, 551* | ⊢ |
| : , : |
519 | theorem | | ⊢ |
| proveit.numbers.absolute_value.abs_even |
520 | theorem | | ⊢ |
| proveit.numbers.number_sets.real_numbers.interval_co_lower_bound |
521 | instantiation | 552, 553, 581, 554 | ⊢ |
| : , : , : |
522 | theorem | | ⊢ |
| proveit.numbers.absolute_value.abs_non_neg_elim |
523 | instantiation | 555, 556 | ⊢ |
| : , : |
524 | instantiation | 642, 557, 558 | ⊢ |
| : , : , : |
525 | instantiation | 608, 644, 559, 560, 561, 562 | ⊢ |
| : , : , : , : |
526 | instantiation | 563, 564, 565 | ⊢ |
| : |
527 | instantiation | 642, 567, 566 | ⊢ |
| : , : , : |
528 | theorem | | ⊢ |
| proveit.numbers.number_sets.complex_numbers.real_nonzero_within_complex_nonzero |
529 | instantiation | 642, 567, 568 | ⊢ |
| : , : , : |
530 | instantiation | 594, 611 | ⊢ |
| : , : , : |
531 | instantiation | 586, 569, 570 | ⊢ |
| : , : , : |
532 | instantiation | 642, 643, 571 | ⊢ |
| : , : , : |
533 | theorem | | ⊢ |
| proveit.numbers.exponentiation.exp_monotonicity_large_base_less_eq |
534 | instantiation | 599, 600, 573 | ⊢ |
| : , : , : |
535 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.less_1_2 |
536 | instantiation | 572, 573 | ⊢ |
| : |
537 | instantiation | 574, 628 | ⊢ |
| : |
538 | theorem | | ⊢ |
| proveit.numbers.addition.disassociation |
539 | axiom | | ⊢ |
| proveit.numbers.number_sets.natural_numbers.zero_in_nats |
540 | theorem | | ⊢ |
| proveit.core_expr_types.tuples.tuple_len_0_typical_eq |
541 | instantiation | 625 | ⊢ |
| : , : |
542 | instantiation | 642, 634, 575 | ⊢ |
| : , : , : |
543 | theorem | | ⊢ |
| proveit.numbers.addition.subtraction.add_cancel_triple_23 |
544 | instantiation | 642, 634, 576 | ⊢ |
| : , : , : |
545 | instantiation | 577 | ⊢ |
| : |
546 | theorem | | ⊢ |
| proveit.numbers.number_sets.real_numbers.pi_is_real_pos |
547 | theorem | | ⊢ |
| proveit.numbers.number_sets.real_numbers.real_pos_within_real |
548 | instantiation | 578, 579 | ⊢ |
| : |
549 | theorem | | ⊢ |
| proveit.numbers.multiplication.mult_neg_left |
550 | instantiation | 642, 634, 605 | ⊢ |
| : , : , : |
551 | instantiation | 626, 602 | ⊢ |
| : |
552 | theorem | | ⊢ |
| proveit.numbers.number_sets.real_numbers.interval_co_upper_bound |
553 | instantiation | 580, 581 | ⊢ |
| : |
554 | theorem | | ⊢ |
| proveit.physics.quantum.QPE._scaled_delta_b_round_in_interval |
555 | theorem | | ⊢ |
| proveit.numbers.ordering.relax_less |
556 | instantiation | 582, 617 | ⊢ |
| : |
557 | theorem | | ⊢ |
| proveit.numbers.number_sets.rational_numbers.rational_pos_within_rational |
558 | instantiation | 583, 584, 585 | ⊢ |
| : , : |
559 | instantiation | 625 | ⊢ |
| : , : |
560 | instantiation | 625 | ⊢ |
| : , : |
561 | instantiation | 586, 587, 588 | ⊢ |
| : , : , : |
562 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.mult_2_2 |
563 | theorem | | ⊢ |
| proveit.numbers.division.frac_cancel_complete |
564 | instantiation | 642, 634, 589 | ⊢ |
| : , : , : |
565 | instantiation | 623, 590 | ⊢ |
| : |
566 | instantiation | 642, 592, 591 | ⊢ |
| : , : , : |
567 | theorem | | ⊢ |
| proveit.numbers.number_sets.real_numbers.rational_nonzero_within_real_nonzero |
568 | instantiation | 642, 592, 593 | ⊢ |
| : , : , : |
569 | instantiation | 594, 612 | ⊢ |
| : , : , : |
570 | instantiation | 595, 628 | ⊢ |
| : |
571 | instantiation | 596, 597, 637 | ⊢ |
| : , : |
572 | theorem | | ⊢ |
| proveit.numbers.number_sets.natural_numbers.natural_pos_lower_bound |
573 | axiom | | ⊢ |
| proveit.physics.quantum.QPE._t_in_natural_pos |
574 | theorem | | ⊢ |
| proveit.numbers.exponentiation.complex_x_to_first_power_is_x |
575 | instantiation | 642, 638, 598 | ⊢ |
| : , : , : |
576 | instantiation | 599, 600, 617 | ⊢ |
| : , : , : |
577 | axiom | | ⊢ |
| proveit.logic.equality.equals_reflexivity |
578 | theorem | | ⊢ |
| proveit.numbers.absolute_value.abs_nonzero_closure |
579 | instantiation | 601, 602, 603 | ⊢ |
| : |
580 | theorem | | ⊢ |
| proveit.numbers.negation.real_closure |
581 | instantiation | 604, 605, 635, 606 | ⊢ |
| : , : |
582 | theorem | | ⊢ |
| proveit.numbers.number_sets.natural_numbers.natural_pos_is_pos |
583 | theorem | | ⊢ |
| proveit.numbers.division.div_rational_pos_closure |
584 | instantiation | 642, 607, 614 | ⊢ |
| : , : , : |
585 | instantiation | 642, 607, 624 | ⊢ |
| : , : , : |
586 | axiom | | ⊢ |
| proveit.logic.equality.equals_transitivity |
587 | instantiation | 608, 644, 609, 610, 611, 612 | ⊢ |
| : , : , : , : |
588 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.add_2_2 |
589 | instantiation | 642, 638, 613 | ⊢ |
| : , : , : |
590 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.posnat4 |
591 | instantiation | 642, 615, 614 | ⊢ |
| : , : , : |
592 | theorem | | ⊢ |
| proveit.numbers.number_sets.rational_numbers.nonzero_int_within_rational_nonzero |
593 | instantiation | 642, 615, 624 | ⊢ |
| : , : , : |
594 | axiom | | ⊢ |
| proveit.logic.equality.substitution |
595 | theorem | | ⊢ |
| proveit.numbers.division.frac_one_denom |
596 | theorem | | ⊢ |
| proveit.numbers.addition.add_nat_closure_bin |
597 | instantiation | 642, 616, 617 | ⊢ |
| : , : , : |
598 | instantiation | 642, 640, 618 | ⊢ |
| : , : , : |
599 | theorem | | ⊢ |
| proveit.logic.sets.inclusion.unfold_subset_eq |
600 | instantiation | 619, 620 | ⊢ |
| : , : |
601 | theorem | | ⊢ |
| proveit.numbers.number_sets.complex_numbers.nonzero_complex_is_complex_nonzero |
602 | instantiation | 642, 634, 621 | ⊢ |
| : , : , : |
603 | assumption | | ⊢ |
604 | theorem | | ⊢ |
| proveit.numbers.division.div_real_closure |
605 | instantiation | 642, 638, 622 | ⊢ |
| : , : , : |
606 | instantiation | 623, 624 | ⊢ |
| : |
607 | theorem | | ⊢ |
| proveit.numbers.number_sets.rational_numbers.nat_pos_within_rational_pos |
608 | axiom | | ⊢ |
| proveit.core_expr_types.operations.operands_substitution |
609 | instantiation | 625 | ⊢ |
| : , : |
610 | instantiation | 625 | ⊢ |
| : , : |
611 | instantiation | 626, 628 | ⊢ |
| : |
612 | instantiation | 627, 628 | ⊢ |
| : |
613 | instantiation | 642, 640, 629 | ⊢ |
| : , : , : |
614 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.posnat1 |
615 | theorem | | ⊢ |
| proveit.numbers.number_sets.integers.nat_pos_within_nonzero_int |
616 | theorem | | ⊢ |
| proveit.numbers.number_sets.natural_numbers.nat_pos_within_nat |
617 | theorem | | ⊢ |
| proveit.physics.quantum.QPE._two_pow_t_is_nat_pos |
618 | instantiation | 630, 633 | ⊢ |
| : |
619 | theorem | | ⊢ |
| proveit.logic.sets.inclusion.relax_proper_subset |
620 | theorem | | ⊢ |
| proveit.numbers.number_sets.real_numbers.nat_pos_within_real |
621 | instantiation | 631, 632 | ⊢ |
| : |
622 | instantiation | 642, 640, 633 | ⊢ |
| : , : , : |
623 | theorem | | ⊢ |
| proveit.numbers.number_sets.natural_numbers.nonzero_if_is_nat_pos |
624 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.posnat2 |
625 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.tuple_len_2_typical_eq |
626 | theorem | | ⊢ |
| proveit.numbers.multiplication.elim_one_left |
627 | theorem | | ⊢ |
| proveit.numbers.multiplication.elim_one_right |
628 | instantiation | 642, 634, 635 | ⊢ |
| : , : , : |
629 | instantiation | 642, 643, 636 | ⊢ |
| : , : , : |
630 | theorem | | ⊢ |
| proveit.numbers.negation.int_closure |
631 | theorem | | ⊢ |
| proveit.physics.quantum.QPE._delta_b_is_real |
632 | theorem | | ⊢ |
| proveit.physics.quantum.QPE._best_round_is_int |
633 | instantiation | 642, 643, 637 | ⊢ |
| : , : , : |
634 | theorem | | ⊢ |
| proveit.numbers.number_sets.complex_numbers.real_within_complex |
635 | instantiation | 642, 638, 639 | ⊢ |
| : , : , : |
636 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.nat4 |
637 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.nat1 |
638 | theorem | | ⊢ |
| proveit.numbers.number_sets.real_numbers.rational_within_real |
639 | instantiation | 642, 640, 641 | ⊢ |
| : , : , : |
640 | theorem | | ⊢ |
| proveit.numbers.number_sets.rational_numbers.int_within_rational |
641 | instantiation | 642, 643, 644 | ⊢ |
| : , : , : |
642 | theorem | | ⊢ |
| proveit.logic.sets.inclusion.superset_membership_from_proper_subset |
643 | theorem | | ⊢ |
| proveit.numbers.number_sets.integers.nat_within_int |
644 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.nat2 |
*equality replacement requirements |