| step type | requirements | statement |
0 | generalization | 1 | ⊢ |
1 | instantiation | 471, 2, 3 | ⊢ |
| : , : , : |
2 | instantiation | 79, 4, 5 | ⊢ |
| : , : , : |
3 | instantiation | 243, 527, 6, 7, 8, 9 | ⊢ |
| : , : , : , : |
4 | instantiation | 79, 10, 11 | ⊢ |
| : , : , : |
5 | instantiation | 147, 12, 13, 14, 15 | ⊢ |
| : , : , : |
6 | instantiation | 461 | ⊢ |
| : , : |
7 | instantiation | 461 | ⊢ |
| : , : |
8 | instantiation | 205, 16 | ⊢ |
| : , : |
9 | instantiation | 205, 17 | ⊢ |
| : , : |
10 | instantiation | 18, 516 | ⊢ |
| : |
11 | instantiation | 471, 19, 20, 21* | ⊢ |
| : , : , : |
12 | instantiation | 22, 179, 204 | ⊢ |
| : , : |
13 | instantiation | 22, 175, 314 | ⊢ |
| : , : |
14 | instantiation | 22, 175, 23 | ⊢ |
| : , : |
15 | instantiation | 114, 175, 314, 23, 24, 25 | ⊢ |
| : , : , : |
16 | instantiation | 29, 26, 27, 28 | ⊢ |
| : , : , : , : |
17 | instantiation | 29, 30, 31, 32 | ⊢ |
| : , : , : , : |
18 | theorem | | ⊢ |
| proveit.physics.quantum.QPE._failure_upper_bound_lemma |
19 | instantiation | 471, 33, 34 | ⊢ |
| : , : , : |
20 | instantiation | 35, 499, 481, 133 | ⊢ |
| : , : , : , : |
21 | instantiation | 406, 36, 37 | ⊢ |
| : , : , : |
22 | theorem | | ⊢ |
| proveit.numbers.multiplication.mult_real_closure_bin |
23 | instantiation | 371, 495, 458, 224 | ⊢ |
| : , : |
24 | instantiation | 79, 38, 39 | ⊢ |
| : , : , : |
25 | instantiation | 402, 40 | ⊢ |
| : , : |
26 | instantiation | 110, 485, 41, 42, 43* | ⊢ |
| : , : |
27 | instantiation | 325 | ⊢ |
| : |
28 | instantiation | 205, 44 | ⊢ |
| : , : |
29 | theorem | | ⊢ |
| proveit.logic.equality.four_chain_transitivity |
30 | instantiation | 110, 485, 45, 46, 47* | ⊢ |
| : , : |
31 | instantiation | 325 | ⊢ |
| : |
32 | instantiation | 205, 48 | ⊢ |
| : , : |
33 | instantiation | 471, 49, 50 | ⊢ |
| : , : , : |
34 | instantiation | 51, 453, 454, 52*, 53*, 54* | ⊢ |
| : , : , : , : |
35 | theorem | | ⊢ |
| proveit.numbers.summation.sum_split_first |
36 | instantiation | 234, 55 | ⊢ |
| : , : , : |
37 | instantiation | 239, 517, 527, 446, 56, 447, 144, 57, 163, 58* | ⊢ |
| : , : , : , : , : , : |
38 | instantiation | 59, 60, 61, 480, 481, 62, 63, 83* | ⊢ |
| : , : , : , : |
39 | instantiation | 64, 65, 66, 67 | ⊢ |
| : , : |
40 | instantiation | 194, 262 | ⊢ |
| : |
41 | instantiation | 93, 463, 226 | ⊢ |
| : , : |
42 | instantiation | 73, 527, 68, 249, 69 | ⊢ |
| : , : |
43 | instantiation | 406, 70, 71 | ⊢ |
| : , : , : |
44 | instantiation | 234, 72 | ⊢ |
| : , : , : |
45 | instantiation | 93, 286, 140 | ⊢ |
| : , : |
46 | instantiation | 73, 527, 74, 177, 75 | ⊢ |
| : , : |
47 | instantiation | 406, 76, 77 | ⊢ |
| : , : , : |
48 | instantiation | 234, 78 | ⊢ |
| : , : , : |
49 | instantiation | 79, 80, 81 | ⊢ |
| : , : , : |
50 | instantiation | 82, 480, 519, 493, 83*, 84* | ⊢ |
| : , : , : , : , : |
51 | theorem | | ⊢ |
| proveit.numbers.summation.index_negate |
52 | instantiation | 280, 85 | ⊢ |
| : |
53 | instantiation | 86, 87, 485, 88* | ⊢ |
| : , : |
54 | instantiation | 89, 90, 517, 267* | , ⊢ |
| : , : |
55 | instantiation | 406, 91, 92 | ⊢ |
| : , : , : |
56 | instantiation | 461 | ⊢ |
| : , : |
57 | instantiation | 93, 463, 283 | ⊢ |
| : , : |
58 | instantiation | 406, 94, 95 | ⊢ |
| : , : , : |
59 | theorem | | ⊢ |
| proveit.numbers.summation.integral_upper_bound_of_sum |
60 | theorem | | ⊢ |
| proveit.numbers.functions.one_over_x_sqrd_in_mon_dec_fxns |
61 | instantiation | 496, 96 | ⊢ |
| : , : |
62 | instantiation | 147, 495, 458, 215, 216, 173* | ⊢ |
| : , : , : |
63 | instantiation | 97, 98 | ⊢ |
| : , : , : |
64 | theorem | | ⊢ |
| proveit.numbers.integration.boundedInvSqrdIntegral |
65 | instantiation | 525, 330, 99 | ⊢ |
| : , : , : |
66 | instantiation | 169, 253, 100 | ⊢ |
| : |
67 | instantiation | 402, 133 | ⊢ |
| : , : |
68 | instantiation | 461 | ⊢ |
| : , : |
69 | instantiation | 525, 287, 101 | ⊢ |
| : , : , : |
70 | instantiation | 234, 102 | ⊢ |
| : , : , : |
71 | instantiation | 406, 103, 104 | ⊢ |
| : , : , : |
72 | instantiation | 110, 485, 226, 224, 105* | ⊢ |
| : , : |
73 | theorem | | ⊢ |
| proveit.numbers.multiplication.mult_not_eq_zero |
74 | instantiation | 461 | ⊢ |
| : , : |
75 | instantiation | 106, 140, 238 | ⊢ |
| : |
76 | instantiation | 234, 107 | ⊢ |
| : , : , : |
77 | instantiation | 406, 108, 109 | ⊢ |
| : , : , : |
78 | instantiation | 110, 485, 140, 238, 111* | ⊢ |
| : , : |
79 | theorem | | ⊢ |
| proveit.numbers.ordering.transitivity_less_eq_less_eq |
80 | instantiation | 114, 179, 112, 115, 113, 118 | ⊢ |
| : , : , : |
81 | instantiation | 114, 179, 115, 116, 117, 118 | ⊢ |
| : , : , : |
82 | theorem | | ⊢ |
| proveit.numbers.summation.index_shift |
83 | instantiation | 406, 119, 120 | ⊢ |
| : , : , : |
84 | instantiation | 406, 121, 122 | , ⊢ |
| : , : , : |
85 | instantiation | 525, 494, 123 | ⊢ |
| : , : , : |
86 | theorem | | ⊢ |
| proveit.numbers.negation.distribute_neg_through_binary_sum |
87 | instantiation | 525, 494, 124 | ⊢ |
| : , : , : |
88 | instantiation | 280, 260 | ⊢ |
| : |
89 | theorem | | ⊢ |
| proveit.numbers.exponentiation.even_pow_is_even_fn |
90 | instantiation | 525, 494, 391 | , ⊢ |
| : , : , : |
91 | instantiation | 256, 517, 527, 446, 125, 447, 283, 163 | ⊢ |
| : , : , : , : , : , : |
92 | instantiation | 406, 126, 127 | ⊢ |
| : , : , : |
93 | theorem | | ⊢ |
| proveit.numbers.multiplication.mult_complex_closure_bin |
94 | instantiation | 426, 517, 527, 446, 128, 447, 144, 463, 283 | ⊢ |
| : , : , : , : , : , : |
95 | instantiation | 129, 446, 527, 517, 447, 130, 144, 463, 283, 131* | ⊢ |
| : , : , : , : , : , : |
96 | theorem | | ⊢ |
| proveit.numbers.number_sets.real_numbers.real_pos_within_real |
97 | theorem | | ⊢ |
| proveit.logic.sets.inclusion.fold_subset_eq |
98 | generalization | 132 | ⊢ |
99 | instantiation | 525, 349, 492 | ⊢ |
| : , : , : |
100 | instantiation | 421, 500, 133 | ⊢ |
| : , : , : |
101 | instantiation | 525, 316, 282 | ⊢ |
| : , : , : |
102 | instantiation | 139, 463, 226, 386, 134, 224, 135* | ⊢ |
| : , : , : |
103 | instantiation | 426, 517, 527, 446, 136, 447, 485, 137, 138 | ⊢ |
| : , : , : , : , : , : |
104 | instantiation | 445, 446, 527, 447, 136, 137, 138 | ⊢ |
| : , : , : , : |
105 | instantiation | 285, 138 | ⊢ |
| : |
106 | theorem | | ⊢ |
| proveit.numbers.number_sets.complex_numbers.nonzero_complex_is_complex_nonzero |
107 | instantiation | 139, 286, 140, 386, 141, 238, 142*, 180* | ⊢ |
| : , : , : |
108 | instantiation | 426, 517, 527, 446, 143, 447, 485, 144, 181 | ⊢ |
| : , : , : , : , : , : |
109 | instantiation | 445, 446, 527, 447, 143, 144, 181 | ⊢ |
| : , : , : , : |
110 | theorem | | ⊢ |
| proveit.numbers.division.div_as_mult |
111 | instantiation | 406, 145, 146 | ⊢ |
| : , : , : |
112 | instantiation | 398, 148, 151 | ⊢ |
| : , : |
113 | instantiation | 147, 151, 148, 150, 149 | ⊢ |
| : , : , : |
114 | theorem | | ⊢ |
| proveit.numbers.multiplication.weak_bound_via_right_factor_bound |
115 | instantiation | 398, 150, 151 | ⊢ |
| : , : |
116 | instantiation | 398, 150, 152 | ⊢ |
| : , : |
117 | instantiation | 343, 150, 151, 152, 153 | ⊢ |
| : , : , : |
118 | instantiation | 402, 154 | ⊢ |
| : , : |
119 | instantiation | 256, 446, 527, 517, 447, 155, 226, 485, 427 | ⊢ |
| : , : , : , : , : , : |
120 | instantiation | 201, 485, 226, 203 | ⊢ |
| : , : , : |
121 | instantiation | 234, 156 | ⊢ |
| : , : , : |
122 | instantiation | 406, 157, 158 | , ⊢ |
| : , : , : |
123 | instantiation | 525, 503, 159 | ⊢ |
| : , : , : |
124 | instantiation | 525, 503, 160 | ⊢ |
| : , : , : |
125 | instantiation | 461 | ⊢ |
| : , : |
126 | instantiation | 161, 517, 446, 447, 283, 163 | ⊢ |
| : , : , : , : , : , : , : |
127 | instantiation | 258, 446, 527, 517, 447, 162, 283, 163, 164* | ⊢ |
| : , : , : , : , : , : |
128 | instantiation | 461 | ⊢ |
| : , : |
129 | theorem | | ⊢ |
| proveit.numbers.multiplication.association |
130 | instantiation | 461 | ⊢ |
| : , : |
131 | instantiation | 165, 485, 463, 177, 166, 167*, 168* | ⊢ |
| : , : , : , : |
132 | instantiation | 169, 170, 171 | , ⊢ |
| : |
133 | instantiation | 471, 172, 173 | ⊢ |
| : , : , : |
134 | instantiation | 307, 432 | ⊢ |
| : |
135 | instantiation | 176, 249, 510, 174* | ⊢ |
| : , : |
136 | instantiation | 461 | ⊢ |
| : , : |
137 | instantiation | 525, 494, 175 | ⊢ |
| : , : , : |
138 | instantiation | 462, 226, 427 | ⊢ |
| : , : |
139 | theorem | | ⊢ |
| proveit.numbers.exponentiation.real_power_of_product |
140 | instantiation | 525, 494, 237 | ⊢ |
| : , : , : |
141 | instantiation | 307, 321 | ⊢ |
| : |
142 | instantiation | 176, 177, 510, 178* | ⊢ |
| : , : |
143 | instantiation | 461 | ⊢ |
| : , : |
144 | instantiation | 525, 494, 179 | ⊢ |
| : , : , : |
145 | instantiation | 234, 180 | ⊢ |
| : , : , : |
146 | instantiation | 285, 181 | ⊢ |
| : |
147 | theorem | | ⊢ |
| proveit.numbers.addition.weak_bound_via_left_term_bound |
148 | modus ponens | 182, 183 | ⊢ |
149 | modus ponens | 184, 185 | ⊢ |
150 | modus ponens | 186, 187 | ⊢ |
151 | modus ponens | 188, 189 | ⊢ |
152 | modus ponens | 190, 191 | ⊢ |
153 | modus ponens | 192, 193 | ⊢ |
154 | instantiation | 194, 265 | ⊢ |
| : |
155 | instantiation | 461 | ⊢ |
| : , : |
156 | instantiation | 195, 432, 196, 197, 198, 199 | ⊢ |
| : , : , : |
157 | instantiation | 256, 446, 527, 517, 447, 200, 202, 485, 427 | , ⊢ |
| : , : , : , : , : , : |
158 | instantiation | 201, 485, 202, 203 | , ⊢ |
| : , : , : |
159 | instantiation | 525, 511, 480 | ⊢ |
| : , : , : |
160 | instantiation | 525, 511, 469 | ⊢ |
| : , : , : |
161 | theorem | | ⊢ |
| proveit.numbers.addition.leftward_commutation |
162 | instantiation | 461 | ⊢ |
| : , : |
163 | instantiation | 525, 494, 204 | ⊢ |
| : , : , : |
164 | instantiation | 205, 206, 319* | ⊢ |
| : , : |
165 | theorem | | ⊢ |
| proveit.numbers.division.prod_of_fracs |
166 | instantiation | 525, 287, 207 | ⊢ |
| : , : , : |
167 | instantiation | 208, 463 | ⊢ |
| : |
168 | instantiation | 406, 209, 210 | ⊢ |
| : , : , : |
169 | theorem | | ⊢ |
| proveit.numbers.number_sets.real_numbers.pos_real_is_real_pos |
170 | instantiation | 211, 252, 253, 254 | , ⊢ |
| : , : , : |
171 | instantiation | 506, 212, 213 | , ⊢ |
| : , : , : |
172 | instantiation | 214, 458, 215, 495, 216, 507 | ⊢ |
| : , : , : |
173 | instantiation | 406, 217, 218 | ⊢ |
| : , : , : |
174 | instantiation | 221, 463 | ⊢ |
| : |
175 | instantiation | 525, 503, 219 | ⊢ |
| : , : , : |
176 | theorem | | ⊢ |
| proveit.numbers.exponentiation.neg_power_as_div |
177 | instantiation | 525, 287, 220 | ⊢ |
| : , : , : |
178 | instantiation | 221, 286 | ⊢ |
| : |
179 | instantiation | 525, 503, 222 | ⊢ |
| : , : , : |
180 | instantiation | 223, 226, 474, 386, 224, 225* | ⊢ |
| : , : , : |
181 | instantiation | 462, 226, 320 | ⊢ |
| : , : |
182 | instantiation | 353 | ⊢ |
| : , : , : |
183 | generalization | 227 | ⊢ |
184 | instantiation | 232 | ⊢ |
| : , : , : |
185 | generalization | 228 | ⊢ |
186 | instantiation | 353 | ⊢ |
| : , : , : |
187 | generalization | 229 | ⊢ |
188 | instantiation | 353 | ⊢ |
| : , : , : |
189 | generalization | 230 | ⊢ |
190 | instantiation | 353 | ⊢ |
| : , : , : |
191 | generalization | 231 | ⊢ |
192 | instantiation | 232 | ⊢ |
| : , : , : |
193 | generalization | 233 | ⊢ |
194 | theorem | | ⊢ |
| proveit.numbers.number_sets.rational_numbers.positive_if_in_rational_pos |
195 | theorem | | ⊢ |
| proveit.core_expr_types.tuples.tuple_eq_via_elem_eq |
196 | instantiation | 461 | ⊢ |
| : , : |
197 | instantiation | 461 | ⊢ |
| : , : |
198 | instantiation | 234, 235 | ⊢ |
| : , : , : |
199 | instantiation | 325 | ⊢ |
| : |
200 | instantiation | 461 | ⊢ |
| : , : |
201 | theorem | | ⊢ |
| proveit.numbers.addition.subtraction.add_cancel_triple_23 |
202 | instantiation | 525, 494, 236 | , ⊢ |
| : , : , : |
203 | instantiation | 325 | ⊢ |
| : |
204 | instantiation | 371, 495, 237, 238 | ⊢ |
| : , : |
205 | theorem | | ⊢ |
| proveit.logic.equality.equals_reversal |
206 | instantiation | 239, 446, 527, 517, 447, 240, 485, 283, 241* | ⊢ |
| : , : , : , : , : , : |
207 | instantiation | 525, 316, 242 | ⊢ |
| : , : , : |
208 | theorem | | ⊢ |
| proveit.numbers.division.frac_one_denom |
209 | instantiation | 243, 527, 244, 245, 246, 247 | ⊢ |
| : , : , : , : |
210 | instantiation | 248, 249, 485, 267*, 250* | ⊢ |
| : , : , : |
211 | theorem | | ⊢ |
| proveit.numbers.number_sets.real_numbers.all_in_interval_cc__is__real |
212 | instantiation | 423, 442 | ⊢ |
| : , : |
213 | instantiation | 251, 252, 253, 254 | , ⊢ |
| : , : , : |
214 | theorem | | ⊢ |
| proveit.numbers.ordering.less_eq_add_right_strong |
215 | instantiation | 525, 503, 255 | ⊢ |
| : , : , : |
216 | instantiation | 433, 514, 515, 516 | ⊢ |
| : , : , : |
217 | instantiation | 256, 446, 527, 517, 447, 257, 260, 320, 485 | ⊢ |
| : , : , : , : , : , : |
218 | instantiation | 258, 517, 527, 446, 259, 447, 260, 320, 485, 261* | ⊢ |
| : , : , : , : , : , : |
219 | instantiation | 525, 264, 262 | ⊢ |
| : , : , : |
220 | instantiation | 525, 316, 263 | ⊢ |
| : , : , : |
221 | theorem | | ⊢ |
| proveit.numbers.exponentiation.complex_x_to_first_power_is_x |
222 | instantiation | 525, 264, 265 | ⊢ |
| : , : , : |
223 | theorem | | ⊢ |
| proveit.numbers.exponentiation.real_power_of_real_power |
224 | instantiation | 307, 492 | ⊢ |
| : |
225 | instantiation | 266, 463, 485, 267* | ⊢ |
| : , : |
226 | instantiation | 525, 494, 458 | ⊢ |
| : , : , : |
227 | instantiation | 371, 495, 268, 269 | , ⊢ |
| : , : |
228 | instantiation | 270, 271, 326, 322, 272 | , ⊢ |
| : , : , : |
229 | instantiation | 371, 495, 273, 274 | , ⊢ |
| : , : |
230 | instantiation | 371, 495, 275, 276 | , ⊢ |
| : , : |
231 | instantiation | 371, 495, 277, 278 | , ⊢ |
| : , : |
232 | theorem | | ⊢ |
| proveit.numbers.summation.weak_summation_from_summands_bound |
233 | instantiation | 402, 279 | , ⊢ |
| : , : |
234 | axiom | | ⊢ |
| proveit.logic.equality.substitution |
235 | instantiation | 280, 485 | ⊢ |
| : |
236 | instantiation | 525, 503, 281 | , ⊢ |
| : , : , : |
237 | instantiation | 390, 458, 527 | ⊢ |
| : , : |
238 | instantiation | 392, 282, 394 | ⊢ |
| : , : |
239 | theorem | | ⊢ |
| proveit.numbers.multiplication.distribute_through_sum |
240 | instantiation | 461 | ⊢ |
| : , : |
241 | instantiation | 285, 283 | ⊢ |
| : |
242 | instantiation | 525, 411, 284 | ⊢ |
| : , : , : |
243 | axiom | | ⊢ |
| proveit.core_expr_types.operations.operands_substitution |
244 | instantiation | 461 | ⊢ |
| : , : |
245 | instantiation | 461 | ⊢ |
| : , : |
246 | instantiation | 285, 463 | ⊢ |
| : |
247 | instantiation | 425, 286 | ⊢ |
| : |
248 | theorem | | ⊢ |
| proveit.numbers.division.frac_cancel_left |
249 | instantiation | 525, 287, 288 | ⊢ |
| : , : , : |
250 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.mult_2_2 |
251 | theorem | | ⊢ |
| proveit.numbers.number_sets.real_numbers.interval_cc_lower_bound |
252 | instantiation | 525, 503, 289 | ⊢ |
| : , : , : |
253 | instantiation | 525, 503, 290 | ⊢ |
| : , : , : |
254 | assumption | | ⊢ |
255 | instantiation | 525, 511, 515 | ⊢ |
| : , : , : |
256 | theorem | | ⊢ |
| proveit.numbers.addition.disassociation |
257 | instantiation | 461 | ⊢ |
| : , : |
258 | theorem | | ⊢ |
| proveit.numbers.addition.association |
259 | instantiation | 461 | ⊢ |
| : , : |
260 | instantiation | 525, 494, 291 | ⊢ |
| : , : , : |
261 | instantiation | 471, 292, 293 | ⊢ |
| : , : , : |
262 | instantiation | 296, 329, 294 | ⊢ |
| : , : |
263 | instantiation | 525, 411, 295 | ⊢ |
| : , : , : |
264 | theorem | | ⊢ |
| proveit.numbers.number_sets.rational_numbers.rational_pos_within_rational |
265 | instantiation | 296, 329, 297 | ⊢ |
| : , : |
266 | theorem | | ⊢ |
| proveit.numbers.multiplication.mult_neg_right |
267 | instantiation | 425, 463 | ⊢ |
| : |
268 | instantiation | 390, 357, 527 | , ⊢ |
| : , : |
269 | instantiation | 305, 298 | , ⊢ |
| : |
270 | theorem | | ⊢ |
| proveit.numbers.division.weak_div_from_denom_bound__all_pos |
271 | instantiation | 525, 299, 300 | ⊢ |
| : , : , : |
272 | instantiation | 301, 474, 357, 378, 302, 303 | , ⊢ |
| : , : , : |
273 | instantiation | 390, 378, 527 | , ⊢ |
| : , : |
274 | instantiation | 305, 304 | , ⊢ |
| : |
275 | instantiation | 390, 380, 527 | , ⊢ |
| : , : |
276 | instantiation | 305, 306 | , ⊢ |
| : |
277 | instantiation | 390, 333, 527 | , ⊢ |
| : , : |
278 | instantiation | 307, 350 | , ⊢ |
| : |
279 | instantiation | 308, 309, 310, 328, 311 | , ⊢ |
| : , : , : |
280 | theorem | | ⊢ |
| proveit.numbers.negation.double_negation |
281 | instantiation | 525, 511, 312 | , ⊢ |
| : , : , : |
282 | instantiation | 525, 411, 313 | ⊢ |
| : , : , : |
283 | instantiation | 525, 494, 314 | ⊢ |
| : , : , : |
284 | instantiation | 525, 431, 510 | ⊢ |
| : , : , : |
285 | theorem | | ⊢ |
| proveit.numbers.multiplication.elim_one_left |
286 | instantiation | 525, 494, 315 | ⊢ |
| : , : , : |
287 | theorem | | ⊢ |
| proveit.numbers.number_sets.complex_numbers.real_nonzero_within_complex_nonzero |
288 | instantiation | 525, 316, 394 | ⊢ |
| : , : , : |
289 | instantiation | 525, 511, 317 | ⊢ |
| : , : , : |
290 | instantiation | 525, 511, 481 | ⊢ |
| : , : , : |
291 | instantiation | 488, 489, 522 | ⊢ |
| : , : , : |
292 | instantiation | 318, 485, 463, 319 | ⊢ |
| : , : , : |
293 | instantiation | 484, 485, 320 | ⊢ |
| : , : |
294 | instantiation | 525, 349, 432 | ⊢ |
| : , : , : |
295 | instantiation | 525, 431, 321 | ⊢ |
| : , : , : |
296 | theorem | | ⊢ |
| proveit.numbers.division.div_rational_pos_closure |
297 | instantiation | 525, 349, 321 | ⊢ |
| : , : , : |
298 | instantiation | 525, 327, 322 | , ⊢ |
| : , : , : |
299 | theorem | | ⊢ |
| proveit.numbers.number_sets.real_numbers.rational_nonneg_within_real_nonneg |
300 | instantiation | 525, 323, 517 | ⊢ |
| : , : , : |
301 | theorem | | ⊢ |
| proveit.numbers.exponentiation.exp_even_neg_base_lesseq |
302 | instantiation | 351, 324, 395 | , ⊢ |
| : , : |
303 | instantiation | 325 | ⊢ |
| : |
304 | instantiation | 525, 327, 326 | , ⊢ |
| : , : , : |
305 | theorem | | ⊢ |
| proveit.numbers.number_sets.real_numbers.nonzero_if_in_real_nonzero |
306 | instantiation | 525, 327, 328 | , ⊢ |
| : , : , : |
307 | theorem | | ⊢ |
| proveit.numbers.number_sets.natural_numbers.nonzero_if_is_nat_pos |
308 | theorem | | ⊢ |
| proveit.numbers.division.strong_div_from_denom_bound__all_pos |
309 | instantiation | 525, 330, 329 | ⊢ |
| : , : , : |
310 | instantiation | 525, 330, 331 | , ⊢ |
| : , : , : |
311 | instantiation | 332, 474, 333, 380, 334, 335 | , ⊢ |
| : , : , : |
312 | instantiation | 525, 336, 337 | , ⊢ |
| : , : , : |
313 | instantiation | 525, 431, 492 | ⊢ |
| : , : , : |
314 | modus ponens | 338, 339 | ⊢ |
315 | instantiation | 525, 503, 340 | ⊢ |
| : , : , : |
316 | theorem | | ⊢ |
| proveit.numbers.number_sets.real_numbers.rational_nonzero_within_real_nonzero |
317 | instantiation | 518, 480, 493 | ⊢ |
| : , : |
318 | theorem | | ⊢ |
| proveit.numbers.addition.subtraction.subtract_from_add_reversed |
319 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.add_1_1 |
320 | instantiation | 525, 494, 341 | ⊢ |
| : , : , : |
321 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.posnat4 |
322 | instantiation | 347, 357, 342 | , ⊢ |
| : |
323 | theorem | | ⊢ |
| proveit.numbers.number_sets.rational_numbers.nat_within_rational_nonneg |
324 | instantiation | 343, 378, 400, 457, 344, 345* | , ⊢ |
| : , : , : |
325 | axiom | | ⊢ |
| proveit.logic.equality.equals_reflexivity |
326 | instantiation | 347, 378, 346 | , ⊢ |
| : |
327 | theorem | | ⊢ |
| proveit.numbers.number_sets.real_numbers.real_pos_within_real_nonzero |
328 | instantiation | 347, 380, 348 | , ⊢ |
| : |
329 | instantiation | 525, 349, 510 | ⊢ |
| : , : , : |
330 | theorem | | ⊢ |
| proveit.numbers.number_sets.real_numbers.rational_pos_within_real_pos |
331 | instantiation | 525, 349, 350 | , ⊢ |
| : , : , : |
332 | theorem | | ⊢ |
| proveit.numbers.exponentiation.exp_pos_less |
333 | instantiation | 398, 399, 386 | , ⊢ |
| : , : |
334 | instantiation | 351, 384, 352 | , ⊢ |
| : , : |
335 | instantiation | 478, 432 | ⊢ |
| : |
336 | instantiation | 512, 499, 481 | ⊢ |
| : , : |
337 | assumption | | ⊢ |
338 | instantiation | 353 | ⊢ |
| : , : , : |
339 | generalization | 354 | ⊢ |
340 | instantiation | 525, 511, 355 | ⊢ |
| : , : , : |
341 | instantiation | 525, 503, 356 | ⊢ |
| : , : , : |
342 | instantiation | 379, 357, 457, 358 | , ⊢ |
| : , : |
343 | theorem | | ⊢ |
| proveit.numbers.addition.weak_bound_via_right_term_bound |
344 | instantiation | 359, 386, 457, 420, 396, 360, 389*, 361* | ⊢ |
| : , : , : |
345 | instantiation | 483, 362 | , ⊢ |
| : |
346 | instantiation | 363, 417, 364, 395 | , ⊢ |
| : , : |
347 | theorem | | ⊢ |
| proveit.numbers.exponentiation.sqrd_pos_closure |
348 | instantiation | 365, 366 | , ⊢ |
| : , : |
349 | theorem | | ⊢ |
| proveit.numbers.number_sets.rational_numbers.nat_pos_within_rational_pos |
350 | instantiation | 367, 368, 527 | , ⊢ |
| : , : |
351 | theorem | | ⊢ |
| proveit.logic.booleans.conjunction.and_if_both |
352 | instantiation | 369, 399, 386, 400, 370 | , ⊢ |
| : , : , : |
353 | theorem | | ⊢ |
| proveit.numbers.summation.summation_real_closure |
354 | instantiation | 371, 495, 372, 373 | , ⊢ |
| : , : |
355 | instantiation | 525, 526, 374 | ⊢ |
| : , : , : |
356 | instantiation | 525, 511, 520 | ⊢ |
| : , : , : |
357 | instantiation | 398, 378, 400 | , ⊢ |
| : , : |
358 | instantiation | 375, 376 | , ⊢ |
| : , : |
359 | theorem | | ⊢ |
| proveit.numbers.multiplication.reversed_weak_bound_via_right_factor_bound |
360 | instantiation | 402, 387 | ⊢ |
| : , : |
361 | instantiation | 377, 427 | ⊢ |
| : |
362 | instantiation | 525, 494, 378 | , ⊢ |
| : , : , : |
363 | theorem | | ⊢ |
| proveit.numbers.ordering.less_is_not_eq_int |
364 | theorem | | ⊢ |
| proveit.numbers.number_sets.integers.zero_is_int |
365 | theorem | | ⊢ |
| proveit.logic.equality.not_equals_symmetry |
366 | instantiation | 379, 457, 380, 381 | , ⊢ |
| : , : |
367 | theorem | | ⊢ |
| proveit.numbers.exponentiation.exp_natpos_closure |
368 | instantiation | 382, 383, 384 | , ⊢ |
| : |
369 | theorem | | ⊢ |
| proveit.numbers.addition.strong_bound_via_right_term_bound |
370 | instantiation | 385, 386, 420, 495, 422, 387, 388*, 389* | ⊢ |
| : , : , : |
371 | theorem | | ⊢ |
| proveit.numbers.division.div_real_closure |
372 | instantiation | 390, 391, 527 | , ⊢ |
| : , : |
373 | instantiation | 392, 393, 394 | , ⊢ |
| : , : |
374 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.nat4 |
375 | theorem | | ⊢ |
| proveit.numbers.addition.subtraction.neg_difference |
376 | instantiation | 506, 395, 396 | , ⊢ |
| : , : , : |
377 | theorem | | ⊢ |
| proveit.numbers.multiplication.mult_zero_right |
378 | instantiation | 525, 503, 397 | , ⊢ |
| : , : , : |
379 | theorem | | ⊢ |
| proveit.numbers.ordering.less_is_not_eq |
380 | instantiation | 398, 399, 400 | , ⊢ |
| : , : |
381 | instantiation | 423, 401 | , ⊢ |
| : , : |
382 | theorem | | ⊢ |
| proveit.numbers.number_sets.integers.nonneg_int_is_natural |
383 | instantiation | 518, 438, 493 | , ⊢ |
| : , : |
384 | instantiation | 402, 403 | , ⊢ |
| : , : |
385 | theorem | | ⊢ |
| proveit.numbers.multiplication.reversed_strong_bound_via_right_factor_bound |
386 | instantiation | 419, 495 | ⊢ |
| : |
387 | instantiation | 434, 502 | ⊢ |
| : |
388 | instantiation | 404, 485, 405* | ⊢ |
| : , : |
389 | instantiation | 406, 407, 408 | ⊢ |
| : , : , : |
390 | theorem | | ⊢ |
| proveit.numbers.exponentiation.exp_real_closure_nat_power |
391 | instantiation | 525, 503, 409 | , ⊢ |
| : , : , : |
392 | theorem | | ⊢ |
| proveit.numbers.exponentiation.exp_rational_non_zero__not_zero |
393 | instantiation | 525, 411, 410 | , ⊢ |
| : , : , : |
394 | instantiation | 525, 411, 412 | ⊢ |
| : , : , : |
395 | instantiation | 413, 414, 415 | , ⊢ |
| : , : , : |
396 | instantiation | 416, 457, 495, 441 | ⊢ |
| : , : , : |
397 | instantiation | 525, 511, 417 | , ⊢ |
| : , : , : |
398 | theorem | | ⊢ |
| proveit.numbers.addition.add_real_closure_bin |
399 | instantiation | 525, 503, 418 | , ⊢ |
| : , : , : |
400 | instantiation | 419, 420 | ⊢ |
| : |
401 | instantiation | 421, 422, 424 | , ⊢ |
| : , : , : |
402 | theorem | | ⊢ |
| proveit.numbers.ordering.relax_less |
403 | instantiation | 423, 424 | , ⊢ |
| : , : |
404 | theorem | | ⊢ |
| proveit.numbers.multiplication.mult_neg_left |
405 | instantiation | 425, 485 | ⊢ |
| : |
406 | axiom | | ⊢ |
| proveit.logic.equality.equals_transitivity |
407 | instantiation | 426, 517, 527, 446, 448, 447, 427, 449, 450 | ⊢ |
| : , : , : , : , : , : |
408 | instantiation | 428, 446, 527, 447, 448, 485, 449, 450, 429* | ⊢ |
| : , : , : , : , : |
409 | instantiation | 525, 511, 451 | , ⊢ |
| : , : , : |
410 | instantiation | 525, 431, 430 | , ⊢ |
| : , : , : |
411 | theorem | | ⊢ |
| proveit.numbers.number_sets.rational_numbers.nonzero_int_within_rational_nonzero |
412 | instantiation | 525, 431, 432 | ⊢ |
| : , : , : |
413 | theorem | | ⊢ |
| proveit.numbers.ordering.transitivity_less_eq_less |
414 | instantiation | 433, 453, 454, 437 | , ⊢ |
| : , : , : |
415 | instantiation | 434, 435 | ⊢ |
| : |
416 | theorem | | ⊢ |
| proveit.numbers.number_sets.real_numbers.interval_co_lower_bound |
417 | instantiation | 525, 436, 437 | , ⊢ |
| : , : , : |
418 | instantiation | 525, 511, 438 | , ⊢ |
| : , : , : |
419 | theorem | | ⊢ |
| proveit.numbers.negation.real_closure |
420 | instantiation | 439, 457, 495, 441 | ⊢ |
| : , : , : |
421 | axiom | | ⊢ |
| proveit.numbers.ordering.transitivity_less_less |
422 | instantiation | 440, 457, 495, 441 | ⊢ |
| : , : , : |
423 | theorem | | ⊢ |
| proveit.numbers.addition.subtraction.pos_difference |
424 | instantiation | 506, 442, 443 | , ⊢ |
| : , : , : |
425 | theorem | | ⊢ |
| proveit.numbers.multiplication.elim_one_right |
426 | theorem | | ⊢ |
| proveit.numbers.multiplication.disassociation |
427 | instantiation | 444, 485 | ⊢ |
| : |
428 | theorem | | ⊢ |
| proveit.numbers.multiplication.mult_neg_any |
429 | instantiation | 445, 446, 527, 447, 448, 449, 450 | ⊢ |
| : , : , : , : |
430 | instantiation | 498, 451, 452 | , ⊢ |
| : |
431 | theorem | | ⊢ |
| proveit.numbers.number_sets.integers.nat_pos_within_nonzero_int |
432 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.posnat2 |
433 | theorem | | ⊢ |
| proveit.numbers.number_sets.integers.interval_upper_bound |
434 | theorem | | ⊢ |
| proveit.numbers.number_sets.integers.negative_if_in_neg_int |
435 | instantiation | 509, 479 | ⊢ |
| : |
436 | instantiation | 512, 453, 454 | ⊢ |
| : , : |
437 | assumption | | ⊢ |
438 | instantiation | 525, 455, 460 | , ⊢ |
| : , : , : |
439 | theorem | | ⊢ |
| proveit.numbers.number_sets.real_numbers.all_in_interval_co__is__real |
440 | theorem | | ⊢ |
| proveit.numbers.number_sets.real_numbers.interval_co_upper_bound |
441 | theorem | | ⊢ |
| proveit.physics.quantum.QPE._scaled_delta_b_floor_in_interval |
442 | instantiation | 456, 495, 457, 458, 500, 459* | ⊢ |
| : , : , : |
443 | instantiation | 513, 480, 519, 460 | , ⊢ |
| : , : , : |
444 | theorem | | ⊢ |
| proveit.numbers.negation.complex_closure |
445 | theorem | | ⊢ |
| proveit.numbers.multiplication.elim_one_any |
446 | axiom | | ⊢ |
| proveit.numbers.number_sets.natural_numbers.zero_in_nats |
447 | theorem | | ⊢ |
| proveit.core_expr_types.tuples.tuple_len_0_typical_eq |
448 | instantiation | 461 | ⊢ |
| : , : |
449 | instantiation | 462, 463, 464 | ⊢ |
| : , : |
450 | instantiation | 525, 494, 465 | ⊢ |
| : , : , : |
451 | instantiation | 525, 466, 482 | , ⊢ |
| : , : , : |
452 | instantiation | 506, 467, 468 | , ⊢ |
| : , : , : |
453 | instantiation | 518, 469, 514 | ⊢ |
| : , : |
454 | instantiation | 523, 480 | ⊢ |
| : |
455 | instantiation | 512, 480, 519 | ⊢ |
| : , : |
456 | theorem | | ⊢ |
| proveit.numbers.addition.strong_bound_via_left_term_bound |
457 | theorem | | ⊢ |
| proveit.numbers.number_sets.real_numbers.zero_is_real |
458 | instantiation | 525, 503, 470 | ⊢ |
| : , : , : |
459 | instantiation | 471, 472, 473 | ⊢ |
| : , : , : |
460 | assumption | | ⊢ |
461 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.tuple_len_2_typical_eq |
462 | theorem | | ⊢ |
| proveit.numbers.exponentiation.exp_complex_closure |
463 | instantiation | 525, 494, 474 | ⊢ |
| : , : , : |
464 | instantiation | 525, 494, 475 | ⊢ |
| : , : , : |
465 | instantiation | 476, 477 | ⊢ |
| : |
466 | instantiation | 512, 480, 481 | ⊢ |
| : , : |
467 | instantiation | 478, 479 | ⊢ |
| : |
468 | instantiation | 513, 480, 481, 482 | , ⊢ |
| : , : , : |
469 | instantiation | 523, 519 | ⊢ |
| : |
470 | instantiation | 525, 511, 499 | ⊢ |
| : , : , : |
471 | theorem | | ⊢ |
| proveit.logic.equality.sub_right_side_into |
472 | instantiation | 483, 485 | ⊢ |
| : |
473 | instantiation | 484, 485, 486 | ⊢ |
| : , : |
474 | instantiation | 525, 503, 487 | ⊢ |
| : , : , : |
475 | instantiation | 488, 489, 490 | ⊢ |
| : , : , : |
476 | theorem | | ⊢ |
| proveit.physics.quantum.QPE._delta_b_is_real |
477 | theorem | | ⊢ |
| proveit.physics.quantum.QPE._best_floor_is_int |
478 | theorem | | ⊢ |
| proveit.numbers.number_sets.natural_numbers.natural_pos_is_pos |
479 | instantiation | 491, 492, 510 | ⊢ |
| : , : |
480 | instantiation | 518, 499, 514 | ⊢ |
| : , : |
481 | instantiation | 518, 519, 493 | ⊢ |
| : , : |
482 | assumption | | ⊢ |
483 | theorem | | ⊢ |
| proveit.numbers.addition.elim_zero_right |
484 | theorem | | ⊢ |
| proveit.numbers.addition.commutation |
485 | instantiation | 525, 494, 495 | ⊢ |
| : , : , : |
486 | theorem | | ⊢ |
| proveit.numbers.number_sets.complex_numbers.zero_is_complex |
487 | instantiation | 525, 511, 524 | ⊢ |