| step type | requirements | statement |
0 | instantiation | 1, 2, 3 | ⊢ |
| : , : , : |
1 | reference | 26 | ⊢ |
2 | instantiation | 4, 404 | ⊢ |
| : |
3 | instantiation | 359, 5, 6, 7* | ⊢ |
| : , : , : |
4 | theorem | | ⊢ |
| proveit.physics.quantum.QPE._failure_upper_bound_lemma |
5 | instantiation | 359, 8, 9 | ⊢ |
| : , : , : |
6 | instantiation | 10, 387, 369, 11 | ⊢ |
| : , : , : , : |
7 | instantiation | 294, 12, 13 | ⊢ |
| : , : , : |
8 | instantiation | 359, 14, 15 | ⊢ |
| : , : , : |
9 | instantiation | 16, 341, 342, 17*, 18*, 19* | ⊢ |
| : , : , : , : |
10 | theorem | | ⊢ |
| proveit.numbers.summation.sum_split_first |
11 | instantiation | 359, 20, 21 | ⊢ |
| : , : , : |
12 | instantiation | 145, 22 | ⊢ |
| : , : , : |
13 | instantiation | 151, 405, 415, 334, 23, 335, 72, 24, 95, 25* | ⊢ |
| : , : , : , : , : , : |
14 | instantiation | 26, 27, 28 | ⊢ |
| : , : , : |
15 | instantiation | 29, 368, 407, 381, 30*, 31* | ⊢ |
| : , : , : , : , : |
16 | theorem | | ⊢ |
| proveit.numbers.summation.index_negate |
17 | instantiation | 179, 32 | ⊢ |
| : |
18 | instantiation | 33, 34, 373, 35* | ⊢ |
| : , : |
19 | instantiation | 36, 37, 405, 165* | , ⊢ |
| : , : |
20 | instantiation | 38, 346, 39, 383, 40, 395 | ⊢ |
| : , : , : |
21 | instantiation | 294, 41, 42 | ⊢ |
| : , : , : |
22 | instantiation | 294, 43, 44 | ⊢ |
| : , : , : |
23 | instantiation | 349 | ⊢ |
| : , : |
24 | instantiation | 45, 351, 183 | ⊢ |
| : , : |
25 | instantiation | 294, 46, 47 | ⊢ |
| : , : , : |
26 | theorem | | ⊢ |
| proveit.numbers.ordering.transitivity_less_eq_less_eq |
27 | instantiation | 50, 97, 48, 51, 49, 54 | ⊢ |
| : , : , : |
28 | instantiation | 50, 97, 51, 52, 53, 54 | ⊢ |
| : , : , : |
29 | theorem | | ⊢ |
| proveit.numbers.summation.index_shift |
30 | instantiation | 294, 55, 56 | ⊢ |
| : , : , : |
31 | instantiation | 294, 57, 58 | , ⊢ |
| : , : , : |
32 | instantiation | 413, 382, 59 | ⊢ |
| : , : , : |
33 | theorem | | ⊢ |
| proveit.numbers.negation.distribute_neg_through_binary_sum |
34 | instantiation | 413, 382, 60 | ⊢ |
| : , : , : |
35 | instantiation | 179, 64 | ⊢ |
| : |
36 | theorem | | ⊢ |
| proveit.numbers.exponentiation.even_pow_is_even_fn |
37 | instantiation | 413, 382, 279 | , ⊢ |
| : , : , : |
38 | theorem | | ⊢ |
| proveit.numbers.ordering.less_eq_add_right_strong |
39 | instantiation | 413, 391, 61 | ⊢ |
| : , : , : |
40 | instantiation | 321, 402, 403, 404 | ⊢ |
| : , : , : |
41 | instantiation | 121, 334, 415, 405, 335, 62, 64, 127, 373 | ⊢ |
| : , : , : , : , : , : |
42 | instantiation | 93, 405, 415, 334, 63, 335, 64, 127, 373, 65* | ⊢ |
| : , : , : , : , : , : |
43 | instantiation | 121, 405, 415, 334, 66, 335, 183, 95 | ⊢ |
| : , : , : , : , : , : |
44 | instantiation | 294, 67, 68 | ⊢ |
| : , : , : |
45 | theorem | | ⊢ |
| proveit.numbers.multiplication.mult_complex_closure_bin |
46 | instantiation | 314, 405, 415, 334, 69, 335, 72, 351, 183 | ⊢ |
| : , : , : , : , : , : |
47 | instantiation | 70, 334, 415, 405, 335, 71, 72, 351, 183, 73* | ⊢ |
| : , : , : , : , : , : |
48 | instantiation | 286, 75, 78 | ⊢ |
| : , : |
49 | instantiation | 74, 78, 75, 77, 76 | ⊢ |
| : , : , : |
50 | theorem | | ⊢ |
| proveit.numbers.multiplication.weak_bound_via_right_factor_bound |
51 | instantiation | 286, 77, 78 | ⊢ |
| : , : |
52 | instantiation | 286, 77, 79 | ⊢ |
| : , : |
53 | instantiation | 232, 77, 78, 79, 80 | ⊢ |
| : , : , : |
54 | instantiation | 290, 81 | ⊢ |
| : , : |
55 | instantiation | 121, 334, 415, 405, 335, 82, 83, 373, 315 | ⊢ |
| : , : , : , : , : , : |
56 | instantiation | 123, 373, 83, 125 | ⊢ |
| : , : , : |
57 | instantiation | 145, 84 | ⊢ |
| : , : , : |
58 | instantiation | 294, 85, 86 | , ⊢ |
| : , : , : |
59 | instantiation | 413, 391, 87 | ⊢ |
| : , : , : |
60 | instantiation | 413, 391, 88 | ⊢ |
| : , : , : |
61 | instantiation | 413, 399, 403 | ⊢ |
| : , : , : |
62 | instantiation | 349 | ⊢ |
| : , : |
63 | instantiation | 349 | ⊢ |
| : , : |
64 | instantiation | 413, 382, 89 | ⊢ |
| : , : , : |
65 | instantiation | 359, 90, 91 | ⊢ |
| : , : , : |
66 | instantiation | 349 | ⊢ |
| : , : |
67 | instantiation | 92, 405, 334, 335, 183, 95 | ⊢ |
| : , : , : , : , : , : , : |
68 | instantiation | 93, 334, 415, 405, 335, 94, 183, 95, 96* | ⊢ |
| : , : , : , : , : , : |
69 | instantiation | 349 | ⊢ |
| : , : |
70 | theorem | | ⊢ |
| proveit.numbers.multiplication.association |
71 | instantiation | 349 | ⊢ |
| : , : |
72 | instantiation | 413, 382, 97 | ⊢ |
| : , : , : |
73 | instantiation | 98, 373, 351, 99, 100, 101*, 102* | ⊢ |
| : , : , : , : |
74 | theorem | | ⊢ |
| proveit.numbers.addition.weak_bound_via_left_term_bound |
75 | modus ponens | 103, 104 | ⊢ |
76 | modus ponens | 105, 106 | ⊢ |
77 | modus ponens | 107, 108 | ⊢ |
78 | modus ponens | 109, 110 | ⊢ |
79 | modus ponens | 111, 112 | ⊢ |
80 | modus ponens | 113, 114 | ⊢ |
81 | instantiation | 115, 155 | ⊢ |
| : |
82 | instantiation | 349 | ⊢ |
| : , : |
83 | instantiation | 413, 382, 346 | ⊢ |
| : , : , : |
84 | instantiation | 116, 320, 117, 118, 119, 120 | ⊢ |
| : , : , : |
85 | instantiation | 121, 334, 415, 405, 335, 122, 124, 373, 315 | , ⊢ |
| : , : , : , : , : , : |
86 | instantiation | 123, 373, 124, 125 | , ⊢ |
| : , : , : |
87 | instantiation | 413, 399, 368 | ⊢ |
| : , : , : |
88 | instantiation | 413, 399, 357 | ⊢ |
| : , : , : |
89 | instantiation | 376, 377, 410 | ⊢ |
| : , : , : |
90 | instantiation | 126, 373, 351, 131 | ⊢ |
| : , : , : |
91 | instantiation | 372, 373, 127 | ⊢ |
| : , : |
92 | theorem | | ⊢ |
| proveit.numbers.addition.leftward_commutation |
93 | theorem | | ⊢ |
| proveit.numbers.addition.association |
94 | instantiation | 349 | ⊢ |
| : , : |
95 | instantiation | 413, 382, 128 | ⊢ |
| : , : , : |
96 | instantiation | 129, 130, 131* | ⊢ |
| : , : |
97 | instantiation | 413, 391, 132 | ⊢ |
| : , : , : |
98 | theorem | | ⊢ |
| proveit.numbers.division.prod_of_fracs |
99 | instantiation | 413, 190, 133 | ⊢ |
| : , : , : |
100 | instantiation | 413, 190, 134 | ⊢ |
| : , : , : |
101 | instantiation | 135, 351 | ⊢ |
| : |
102 | instantiation | 294, 136, 137 | ⊢ |
| : , : , : |
103 | instantiation | 242 | ⊢ |
| : , : , : |
104 | generalization | 138 | ⊢ |
105 | instantiation | 143 | ⊢ |
| : , : , : |
106 | generalization | 139 | ⊢ |
107 | instantiation | 242 | ⊢ |
| : , : , : |
108 | generalization | 140 | ⊢ |
109 | instantiation | 242 | ⊢ |
| : , : , : |
110 | generalization | 141 | ⊢ |
111 | instantiation | 242 | ⊢ |
| : , : , : |
112 | generalization | 142 | ⊢ |
113 | instantiation | 143 | ⊢ |
| : , : , : |
114 | generalization | 144 | ⊢ |
115 | theorem | | ⊢ |
| proveit.numbers.number_sets.rational_numbers.positive_if_in_rational_pos |
116 | theorem | | ⊢ |
| proveit.core_expr_types.tuples.tuple_eq_via_elem_eq |
117 | instantiation | 349 | ⊢ |
| : , : |
118 | instantiation | 349 | ⊢ |
| : , : |
119 | instantiation | 145, 146 | ⊢ |
| : , : , : |
120 | instantiation | 215 | ⊢ |
| : |
121 | theorem | | ⊢ |
| proveit.numbers.addition.disassociation |
122 | instantiation | 349 | ⊢ |
| : , : |
123 | theorem | | ⊢ |
| proveit.numbers.addition.subtraction.add_cancel_triple_23 |
124 | instantiation | 413, 382, 147 | , ⊢ |
| : , : , : |
125 | instantiation | 215 | ⊢ |
| : |
126 | theorem | | ⊢ |
| proveit.numbers.addition.subtraction.subtract_from_add_reversed |
127 | instantiation | 413, 382, 148 | ⊢ |
| : , : , : |
128 | instantiation | 259, 383, 149, 150 | ⊢ |
| : , : |
129 | theorem | | ⊢ |
| proveit.logic.equality.equals_reversal |
130 | instantiation | 151, 334, 415, 405, 335, 152, 373, 183, 153* | ⊢ |
| : , : , : , : , : , : |
131 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.add_1_1 |
132 | instantiation | 413, 154, 155 | ⊢ |
| : , : , : |
133 | instantiation | 413, 211, 156 | ⊢ |
| : , : , : |
134 | instantiation | 413, 211, 157 | ⊢ |
| : , : , : |
135 | theorem | | ⊢ |
| proveit.numbers.division.frac_one_denom |
136 | instantiation | 158, 415, 159, 160, 161, 162 | ⊢ |
| : , : , : , : |
137 | instantiation | 163, 164, 373, 165*, 166* | ⊢ |
| : , : , : |
138 | instantiation | 259, 383, 167, 168 | , ⊢ |
| : , : |
139 | instantiation | 169, 170, 216, 212, 171 | , ⊢ |
| : , : , : |
140 | instantiation | 259, 383, 172, 173 | , ⊢ |
| : , : |
141 | instantiation | 259, 383, 174, 175 | , ⊢ |
| : , : |
142 | instantiation | 259, 383, 176, 177 | , ⊢ |
| : , : |
143 | theorem | | ⊢ |
| proveit.numbers.summation.weak_summation_from_summands_bound |
144 | instantiation | 290, 178 | , ⊢ |
| : , : |
145 | axiom | | ⊢ |
| proveit.logic.equality.substitution |
146 | instantiation | 179, 373 | ⊢ |
| : |
147 | instantiation | 413, 391, 180 | , ⊢ |
| : , : , : |
148 | instantiation | 413, 391, 181 | ⊢ |
| : , : , : |
149 | instantiation | 278, 346, 415 | ⊢ |
| : , : |
150 | instantiation | 280, 182, 282 | ⊢ |
| : , : |
151 | theorem | | ⊢ |
| proveit.numbers.multiplication.distribute_through_sum |
152 | instantiation | 349 | ⊢ |
| : , : |
153 | instantiation | 188, 183 | ⊢ |
| : |
154 | theorem | | ⊢ |
| proveit.numbers.number_sets.rational_numbers.rational_pos_within_rational |
155 | instantiation | 184, 219, 185 | ⊢ |
| : , : |
156 | instantiation | 413, 299, 186 | ⊢ |
| : , : , : |
157 | instantiation | 413, 299, 187 | ⊢ |
| : , : , : |
158 | axiom | | ⊢ |
| proveit.core_expr_types.operations.operands_substitution |
159 | instantiation | 349 | ⊢ |
| : , : |
160 | instantiation | 349 | ⊢ |
| : , : |
161 | instantiation | 188, 351 | ⊢ |
| : |
162 | instantiation | 313, 189 | ⊢ |
| : |
163 | theorem | | ⊢ |
| proveit.numbers.division.frac_cancel_left |
164 | instantiation | 413, 190, 191 | ⊢ |
| : , : , : |
165 | instantiation | 313, 351 | ⊢ |
| : |
166 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.mult_2_2 |
167 | instantiation | 278, 245, 415 | , ⊢ |
| : , : |
168 | instantiation | 199, 192 | , ⊢ |
| : |
169 | theorem | | ⊢ |
| proveit.numbers.division.weak_div_from_denom_bound__all_pos |
170 | instantiation | 413, 193, 194 | ⊢ |
| : , : , : |
171 | instantiation | 195, 362, 245, 266, 196, 197 | , ⊢ |
| : , : , : |
172 | instantiation | 278, 266, 415 | , ⊢ |
| : , : |
173 | instantiation | 199, 198 | , ⊢ |
| : |
174 | instantiation | 278, 268, 415 | , ⊢ |
| : , : |
175 | instantiation | 199, 200 | , ⊢ |
| : |
176 | instantiation | 278, 223, 415 | , ⊢ |
| : , : |
177 | instantiation | 201, 239 | , ⊢ |
| : |
178 | instantiation | 202, 203, 204, 218, 205 | , ⊢ |
| : , : , : |
179 | theorem | | ⊢ |
| proveit.numbers.negation.double_negation |
180 | instantiation | 413, 399, 206 | , ⊢ |
| : , : , : |
181 | instantiation | 413, 399, 408 | ⊢ |
| : , : , : |
182 | instantiation | 413, 299, 207 | ⊢ |
| : , : , : |
183 | instantiation | 413, 382, 208 | ⊢ |
| : , : , : |
184 | theorem | | ⊢ |
| proveit.numbers.division.div_rational_pos_closure |
185 | instantiation | 413, 238, 209 | ⊢ |
| : , : , : |
186 | instantiation | 413, 319, 209 | ⊢ |
| : , : , : |
187 | instantiation | 413, 319, 398 | ⊢ |
| : , : , : |
188 | theorem | | ⊢ |
| proveit.numbers.multiplication.elim_one_left |
189 | instantiation | 413, 382, 210 | ⊢ |
| : , : , : |
190 | theorem | | ⊢ |
| proveit.numbers.number_sets.complex_numbers.real_nonzero_within_complex_nonzero |
191 | instantiation | 413, 211, 282 | ⊢ |
| : , : , : |
192 | instantiation | 413, 217, 212 | , ⊢ |
| : , : , : |
193 | theorem | | ⊢ |
| proveit.numbers.number_sets.real_numbers.rational_nonneg_within_real_nonneg |
194 | instantiation | 413, 213, 405 | ⊢ |
| : , : , : |
195 | theorem | | ⊢ |
| proveit.numbers.exponentiation.exp_even_neg_base_lesseq |
196 | instantiation | 240, 214, 283 | , ⊢ |
| : , : |
197 | instantiation | 215 | ⊢ |
| : |
198 | instantiation | 413, 217, 216 | , ⊢ |
| : , : , : |
199 | theorem | | ⊢ |
| proveit.numbers.number_sets.real_numbers.nonzero_if_in_real_nonzero |
200 | instantiation | 413, 217, 218 | , ⊢ |
| : , : , : |
201 | theorem | | ⊢ |
| proveit.numbers.number_sets.natural_numbers.nonzero_if_is_nat_pos |
202 | theorem | | ⊢ |
| proveit.numbers.division.strong_div_from_denom_bound__all_pos |
203 | instantiation | 413, 220, 219 | ⊢ |
| : , : , : |
204 | instantiation | 413, 220, 221 | , ⊢ |
| : , : , : |
205 | instantiation | 222, 362, 223, 268, 224, 225 | , ⊢ |
| : , : , : |
206 | instantiation | 413, 226, 227 | , ⊢ |
| : , : , : |
207 | instantiation | 413, 319, 380 | ⊢ |
| : , : , : |
208 | modus ponens | 228, 229 | ⊢ |
209 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.posnat4 |
210 | instantiation | 413, 391, 230 | ⊢ |
| : , : , : |
211 | theorem | | ⊢ |
| proveit.numbers.number_sets.real_numbers.rational_nonzero_within_real_nonzero |
212 | instantiation | 236, 245, 231 | , ⊢ |
| : |
213 | theorem | | ⊢ |
| proveit.numbers.number_sets.rational_numbers.nat_within_rational_nonneg |
214 | instantiation | 232, 266, 288, 345, 233, 234* | , ⊢ |
| : , : , : |
215 | axiom | | ⊢ |
| proveit.logic.equality.equals_reflexivity |
216 | instantiation | 236, 266, 235 | , ⊢ |
| : |
217 | theorem | | ⊢ |
| proveit.numbers.number_sets.real_numbers.real_pos_within_real_nonzero |
218 | instantiation | 236, 268, 237 | , ⊢ |
| : |
219 | instantiation | 413, 238, 398 | ⊢ |
| : , : , : |
220 | theorem | | ⊢ |
| proveit.numbers.number_sets.real_numbers.rational_pos_within_real_pos |
221 | instantiation | 413, 238, 239 | , ⊢ |
| : , : , : |
222 | theorem | | ⊢ |
| proveit.numbers.exponentiation.exp_pos_less |
223 | instantiation | 286, 287, 274 | , ⊢ |
| : , : |
224 | instantiation | 240, 272, 241 | , ⊢ |
| : , : |
225 | instantiation | 366, 320 | ⊢ |
| : |
226 | instantiation | 400, 387, 369 | ⊢ |
| : , : |
227 | assumption | | ⊢ |
228 | instantiation | 242 | ⊢ |
| : , : , : |
229 | generalization | 243 | ⊢ |
230 | instantiation | 413, 399, 244 | ⊢ |
| : , : , : |
231 | instantiation | 267, 245, 345, 246 | , ⊢ |
| : , : |
232 | theorem | | ⊢ |
| proveit.numbers.addition.weak_bound_via_right_term_bound |
233 | instantiation | 247, 274, 345, 308, 284, 248, 277*, 249* | ⊢ |
| : , : , : |
234 | instantiation | 371, 250 | , ⊢ |
| : |
235 | instantiation | 251, 305, 252, 283 | , ⊢ |
| : , : |
236 | theorem | | ⊢ |
| proveit.numbers.exponentiation.sqrd_pos_closure |
237 | instantiation | 253, 254 | , ⊢ |
| : , : |
238 | theorem | | ⊢ |
| proveit.numbers.number_sets.rational_numbers.nat_pos_within_rational_pos |
239 | instantiation | 255, 256, 415 | , ⊢ |
| : , : |
240 | theorem | | ⊢ |
| proveit.logic.booleans.conjunction.and_if_both |
241 | instantiation | 257, 287, 274, 288, 258 | , ⊢ |
| : , : , : |
242 | theorem | | ⊢ |
| proveit.numbers.summation.summation_real_closure |
243 | instantiation | 259, 383, 260, 261 | , ⊢ |
| : , : |
244 | instantiation | 413, 414, 262 | ⊢ |
| : , : , : |
245 | instantiation | 286, 266, 288 | , ⊢ |
| : , : |
246 | instantiation | 263, 264 | , ⊢ |
| : , : |
247 | theorem | | ⊢ |
| proveit.numbers.multiplication.reversed_weak_bound_via_right_factor_bound |
248 | instantiation | 290, 275 | ⊢ |
| : , : |
249 | instantiation | 265, 315 | ⊢ |
| : |
250 | instantiation | 413, 382, 266 | , ⊢ |
| : , : , : |
251 | theorem | | ⊢ |
| proveit.numbers.ordering.less_is_not_eq_int |
252 | theorem | | ⊢ |
| proveit.numbers.number_sets.integers.zero_is_int |
253 | theorem | | ⊢ |
| proveit.logic.equality.not_equals_symmetry |
254 | instantiation | 267, 345, 268, 269 | , ⊢ |
| : , : |
255 | theorem | | ⊢ |
| proveit.numbers.exponentiation.exp_natpos_closure |
256 | instantiation | 270, 271, 272 | , ⊢ |
| : |
257 | theorem | | ⊢ |
| proveit.numbers.addition.strong_bound_via_right_term_bound |
258 | instantiation | 273, 274, 308, 383, 310, 275, 276*, 277* | ⊢ |
| : , : , : |
259 | theorem | | ⊢ |
| proveit.numbers.division.div_real_closure |
260 | instantiation | 278, 279, 415 | , ⊢ |
| : , : |
261 | instantiation | 280, 281, 282 | , ⊢ |
| : , : |
262 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.nat4 |
263 | theorem | | ⊢ |
| proveit.numbers.addition.subtraction.neg_difference |
264 | instantiation | 394, 283, 284 | , ⊢ |
| : , : , : |
265 | theorem | | ⊢ |
| proveit.numbers.multiplication.mult_zero_right |
266 | instantiation | 413, 391, 285 | , ⊢ |
| : , : , : |
267 | theorem | | ⊢ |
| proveit.numbers.ordering.less_is_not_eq |
268 | instantiation | 286, 287, 288 | , ⊢ |
| : , : |
269 | instantiation | 311, 289 | , ⊢ |
| : , : |
270 | theorem | | ⊢ |
| proveit.numbers.number_sets.integers.nonneg_int_is_natural |
271 | instantiation | 406, 326, 381 | , ⊢ |
| : , : |
272 | instantiation | 290, 291 | , ⊢ |
| : , : |
273 | theorem | | ⊢ |
| proveit.numbers.multiplication.reversed_strong_bound_via_right_factor_bound |
274 | instantiation | 307, 383 | ⊢ |
| : |
275 | instantiation | 322, 390 | ⊢ |
| : |
276 | instantiation | 292, 373, 293* | ⊢ |
| : , : |
277 | instantiation | 294, 295, 296 | ⊢ |
| : , : , : |
278 | theorem | | ⊢ |
| proveit.numbers.exponentiation.exp_real_closure_nat_power |
279 | instantiation | 413, 391, 297 | , ⊢ |
| : , : , : |
280 | theorem | | ⊢ |
| proveit.numbers.exponentiation.exp_rational_non_zero__not_zero |
281 | instantiation | 413, 299, 298 | , ⊢ |
| : , : , : |
282 | instantiation | 413, 299, 300 | ⊢ |
| : , : , : |
283 | instantiation | 301, 302, 303 | , ⊢ |
| : , : , : |
284 | instantiation | 304, 345, 383, 329 | ⊢ |
| : , : , : |
285 | instantiation | 413, 399, 305 | , ⊢ |
| : , : , : |
286 | theorem | | ⊢ |
| proveit.numbers.addition.add_real_closure_bin |
287 | instantiation | 413, 391, 306 | , ⊢ |
| : , : , : |
288 | instantiation | 307, 308 | ⊢ |
| : |
289 | instantiation | 309, 310, 312 | , ⊢ |
| : , : , : |
290 | theorem | | ⊢ |
| proveit.numbers.ordering.relax_less |
291 | instantiation | 311, 312 | , ⊢ |
| : , : |
292 | theorem | | ⊢ |
| proveit.numbers.multiplication.mult_neg_left |
293 | instantiation | 313, 373 | ⊢ |
| : |
294 | axiom | | ⊢ |
| proveit.logic.equality.equals_transitivity |
295 | instantiation | 314, 405, 415, 334, 336, 335, 315, 337, 338 | ⊢ |
| : , : , : , : , : , : |
296 | instantiation | 316, 334, 415, 335, 336, 373, 337, 338, 317* | ⊢ |
| : , : , : , : , : |
297 | instantiation | 413, 399, 339 | , ⊢ |
| : , : , : |
298 | instantiation | 413, 319, 318 | , ⊢ |
| : , : , : |
299 | theorem | | ⊢ |
| proveit.numbers.number_sets.rational_numbers.nonzero_int_within_rational_nonzero |
300 | instantiation | 413, 319, 320 | ⊢ |
| : , : , : |
301 | theorem | | ⊢ |
| proveit.numbers.ordering.transitivity_less_eq_less |
302 | instantiation | 321, 341, 342, 325 | , ⊢ |
| : , : , : |
303 | instantiation | 322, 323 | ⊢ |
| : |
304 | theorem | | ⊢ |
| proveit.numbers.number_sets.real_numbers.interval_co_lower_bound |
305 | instantiation | 413, 324, 325 | , ⊢ |
| : , : , : |
306 | instantiation | 413, 399, 326 | , ⊢ |
| : , : , : |
307 | theorem | | ⊢ |
| proveit.numbers.negation.real_closure |
308 | instantiation | 327, 345, 383, 329 | ⊢ |
| : , : , : |
309 | axiom | | ⊢ |
| proveit.numbers.ordering.transitivity_less_less |
310 | instantiation | 328, 345, 383, 329 | ⊢ |
| : , : , : |
311 | theorem | | ⊢ |
| proveit.numbers.addition.subtraction.pos_difference |
312 | instantiation | 394, 330, 331 | , ⊢ |
| : , : , : |
313 | theorem | | ⊢ |
| proveit.numbers.multiplication.elim_one_right |
314 | theorem | | ⊢ |
| proveit.numbers.multiplication.disassociation |
315 | instantiation | 332, 373 | ⊢ |
| : |
316 | theorem | | ⊢ |
| proveit.numbers.multiplication.mult_neg_any |
317 | instantiation | 333, 334, 415, 335, 336, 337, 338 | ⊢ |
| : , : , : , : |
318 | instantiation | 386, 339, 340 | , ⊢ |
| : |
319 | theorem | | ⊢ |
| proveit.numbers.number_sets.integers.nat_pos_within_nonzero_int |
320 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.posnat2 |
321 | theorem | | ⊢ |
| proveit.numbers.number_sets.integers.interval_upper_bound |
322 | theorem | | ⊢ |
| proveit.numbers.number_sets.integers.negative_if_in_neg_int |
323 | instantiation | 397, 367 | ⊢ |
| : |
324 | instantiation | 400, 341, 342 | ⊢ |
| : , : |
325 | assumption | | ⊢ |
326 | instantiation | 413, 343, 348 | , ⊢ |
| : , : , : |
327 | theorem | | ⊢ |
| proveit.numbers.number_sets.real_numbers.all_in_interval_co__is__real |
328 | theorem | | ⊢ |
| proveit.numbers.number_sets.real_numbers.interval_co_upper_bound |
329 | theorem | | ⊢ |
| proveit.physics.quantum.QPE._scaled_delta_b_floor_in_interval |
330 | instantiation | 344, 383, 345, 346, 388, 347* | ⊢ |
| : , : , : |
331 | instantiation | 401, 368, 407, 348 | , ⊢ |
| : , : , : |
332 | theorem | | ⊢ |
| proveit.numbers.negation.complex_closure |
333 | theorem | | ⊢ |
| proveit.numbers.multiplication.elim_one_any |
334 | axiom | | ⊢ |
| proveit.numbers.number_sets.natural_numbers.zero_in_nats |
335 | theorem | | ⊢ |
| proveit.core_expr_types.tuples.tuple_len_0_typical_eq |
336 | instantiation | 349 | ⊢ |
| : , : |
337 | instantiation | 350, 351, 352 | ⊢ |
| : , : |
338 | instantiation | 413, 382, 353 | ⊢ |
| : , : , : |
339 | instantiation | 413, 354, 370 | , ⊢ |
| : , : , : |
340 | instantiation | 394, 355, 356 | , ⊢ |
| : , : , : |
341 | instantiation | 406, 357, 402 | ⊢ |
| : , : |
342 | instantiation | 411, 368 | ⊢ |
| : |
343 | instantiation | 400, 368, 407 | ⊢ |
| : , : |
344 | theorem | | ⊢ |
| proveit.numbers.addition.strong_bound_via_left_term_bound |
345 | theorem | | ⊢ |
| proveit.numbers.number_sets.real_numbers.zero_is_real |
346 | instantiation | 413, 391, 358 | ⊢ |
| : , : , : |
347 | instantiation | 359, 360, 361 | ⊢ |
| : , : , : |
348 | assumption | | ⊢ |
349 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.tuple_len_2_typical_eq |
350 | theorem | | ⊢ |
| proveit.numbers.exponentiation.exp_complex_closure |
351 | instantiation | 413, 382, 362 | ⊢ |
| : , : , : |
352 | instantiation | 413, 382, 363 | ⊢ |
| : , : , : |
353 | instantiation | 364, 365 | ⊢ |
| : |
354 | instantiation | 400, 368, 369 | ⊢ |
| : , : |
355 | instantiation | 366, 367 | ⊢ |
| : |
356 | instantiation | 401, 368, 369, 370 | , ⊢ |
| : , : , : |
357 | instantiation | 411, 407 | ⊢ |
| : |
358 | instantiation | 413, 399, 387 | ⊢ |
| : , : , : |
359 | theorem | | ⊢ |
| proveit.logic.equality.sub_right_side_into |
360 | instantiation | 371, 373 | ⊢ |
| : |
361 | instantiation | 372, 373, 374 | ⊢ |
| : , : |
362 | instantiation | 413, 391, 375 | ⊢ |
| : , : , : |
363 | instantiation | 376, 377, 378 | ⊢ |
| : , : , : |
364 | theorem | | ⊢ |
| proveit.physics.quantum.QPE._delta_b_is_real |
365 | theorem | | ⊢ |
| proveit.physics.quantum.QPE._best_floor_is_int |
366 | theorem | | ⊢ |
| proveit.numbers.number_sets.natural_numbers.natural_pos_is_pos |
367 | instantiation | 379, 380, 398 | ⊢ |
| : , : |
368 | instantiation | 406, 387, 402 | ⊢ |
| : , : |
369 | instantiation | 406, 407, 381 | ⊢ |
| : , : |
370 | assumption | | ⊢ |
371 | theorem | | ⊢ |
| proveit.numbers.addition.elim_zero_right |
372 | theorem | | ⊢ |
| proveit.numbers.addition.commutation |
373 | instantiation | 413, 382, 383 | ⊢ |
| : , : , : |
374 | theorem | | ⊢ |
| proveit.numbers.number_sets.complex_numbers.zero_is_complex |
375 | instantiation | 413, 399, 412 | ⊢ |
| : , : , : |
376 | theorem | | ⊢ |
| proveit.logic.sets.inclusion.unfold_subset_eq |
377 | instantiation | 384, 385 | ⊢ |
| : , : |
378 | axiom | | ⊢ |
| proveit.physics.quantum.QPE._t_in_natural_pos |
379 | theorem | | ⊢ |
| proveit.numbers.addition.add_nat_pos_closure_bin |
380 | instantiation | 386, 387, 388 | ⊢ |
| : |
381 | instantiation | 413, 389, 390 | ⊢ |
| : , : , : |
382 | theorem | | ⊢ |
| proveit.numbers.number_sets.complex_numbers.real_within_complex |
383 | instantiation | 413, 391, 392 | ⊢ |
| : , : , : |
384 | theorem | | ⊢ |
| proveit.logic.sets.inclusion.relax_proper_subset |
385 | theorem | | ⊢ |
| proveit.numbers.number_sets.real_numbers.nat_pos_within_real |
386 | theorem | | ⊢ |
| proveit.numbers.number_sets.integers.pos_int_is_natural_pos |
387 | instantiation | 413, 393, 404 | ⊢ |
| : , : , : |
388 | instantiation | 394, 395, 396 | ⊢ |
| : , : , : |
389 | theorem | | ⊢ |
| proveit.numbers.number_sets.integers.neg_int_within_int |
390 | instantiation | 397, 398 | ⊢ |
| : |
391 | theorem | | ⊢ |
| proveit.numbers.number_sets.real_numbers.rational_within_real |
392 | instantiation | 413, 399, 402 | ⊢ |
| : , : , : |
393 | instantiation | 400, 402, 403 | ⊢ |
| : , : |
394 | theorem | | ⊢ |
| proveit.numbers.ordering.transitivity_less_less_eq |
395 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.less_0_1 |
396 | instantiation | 401, 402, 403, 404 | ⊢ |
| : , : , : |
397 | theorem | | ⊢ |
| proveit.numbers.negation.int_neg_closure |
398 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.posnat1 |
399 | theorem | | ⊢ |
| proveit.numbers.number_sets.rational_numbers.int_within_rational |
400 | theorem | | ⊢ |
| proveit.numbers.number_sets.integers.int_interval_within_int |
401 | theorem | | ⊢ |
| proveit.numbers.number_sets.integers.interval_lower_bound |
402 | instantiation | 413, 414, 405 | ⊢ |
| : , : , : |
403 | instantiation | 406, 407, 408 | ⊢ |
| : , : |
404 | assumption | | ⊢ |
405 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.nat1 |
406 | theorem | | ⊢ |
| proveit.numbers.addition.add_int_closure_bin |
407 | instantiation | 413, 409, 410 | ⊢ |
| : , : , : |
408 | instantiation | 411, 412 | ⊢ |
| : |
409 | theorem | | ⊢ |
| proveit.numbers.number_sets.integers.nat_pos_within_int |
410 | theorem | | ⊢ |
| proveit.physics.quantum.QPE._two_pow_t_minus_one_is_nat_pos |
411 | theorem | | ⊢ |
| proveit.numbers.negation.int_closure |
412 | instantiation | 413, 414, 415 | ⊢ |
| : , : , : |
413 | theorem | | ⊢ |
| proveit.logic.sets.inclusion.superset_membership_from_proper_subset |
414 | theorem | | ⊢ |
| proveit.numbers.number_sets.integers.nat_within_int |
415 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.nat2 |
*equality replacement requirements |