| step type | requirements | statement |
0 | instantiation | 1, 2, 3, 4, 5, 6*, 7* | ⊢ |
| : , : |
1 | reference | 315 | ⊢ |
2 | reference | 446 | ⊢ |
3 | instantiation | 447 | ⊢ |
| : , : |
4 | instantiation | 464, 456, 8 | ⊢ |
| : , : , : |
5 | instantiation | 9, 12, 13, 14 | ⊢ |
| : , : |
6 | instantiation | 344, 10 | ⊢ |
| : |
7 | instantiation | 11, 12, 13, 14, 15* | ⊢ |
| : , : |
8 | instantiation | 464, 460, 16 | ⊢ |
| : , : , : |
9 | theorem | | ⊢ |
| proveit.numbers.division.div_complex_closure |
10 | instantiation | 377, 17 | ⊢ |
| : , : |
11 | theorem | | ⊢ |
| proveit.numbers.absolute_value.abs_frac |
12 | instantiation | 19, 372, 18 | ⊢ |
| : , : |
13 | instantiation | 19, 372, 20 | ⊢ |
| : , : |
14 | instantiation | 21, 22 | ⊢ |
| : , : |
15 | instantiation | 408, 23, 24 | ⊢ |
| : , : , : |
16 | instantiation | 464, 379, 25 | ⊢ |
| : , : , : |
17 | instantiation | 262, 25 | ⊢ |
| : |
18 | instantiation | 173, 26 | ⊢ |
| : |
19 | theorem | | ⊢ |
| proveit.numbers.addition.add_complex_closure_bin |
20 | instantiation | 173, 27 | ⊢ |
| : |
21 | theorem | | ⊢ |
| proveit.numbers.addition.subtraction.nonzero_difference_if_different |
22 | instantiation | 67, 28 | ⊢ |
| : , : |
23 | instantiation | 430, 466, 29, 30, 31, 32 | ⊢ |
| : , : , : , : |
24 | instantiation | 135, 325, 33, 34 | ⊢ |
| : , : , : |
25 | instantiation | 405, 406, 35 | ⊢ |
| : , : |
26 | instantiation | 271, 84, 36 | ⊢ |
| : , : |
27 | instantiation | 271, 84, 37 | ⊢ |
| : , : |
28 | instantiation | 253, 38, 39 | ⊢ |
| : , : , : |
29 | instantiation | 447 | ⊢ |
| : , : |
30 | instantiation | 447 | ⊢ |
| : , : |
31 | instantiation | 43, 234, 40, 44*, 41*, 42* | ⊢ |
| : , : |
32 | instantiation | 43, 234, 55, 44*, 45*, 46* | ⊢ |
| : , : |
33 | instantiation | 423, 47, 48 | ⊢ |
| : |
34 | instantiation | 464, 456, 49 | ⊢ |
| : , : , : |
35 | instantiation | 464, 429, 439 | ⊢ |
| : , : , : |
36 | instantiation | 292, 50, 51 | ⊢ |
| : , : , : |
37 | instantiation | 292, 52, 53 | ⊢ |
| : , : , : |
38 | instantiation | 54, 55, 56, 57* | ⊢ |
| : |
39 | instantiation | 416, 58 | ⊢ |
| : , : , : |
40 | instantiation | 292, 206, 186 | ⊢ |
| : , : , : |
41 | instantiation | 238, 59 | ⊢ |
| : , : |
42 | instantiation | 408, 60, 61 | ⊢ |
| : , : , : |
43 | theorem | | ⊢ |
| proveit.trigonometry.complex_unit_circle_chord_length |
44 | instantiation | 408, 62, 63 | ⊢ |
| : , : , : |
45 | instantiation | 238, 64 | ⊢ |
| : , : |
46 | instantiation | 408, 65, 66 | ⊢ |
| : , : , : |
47 | instantiation | 464, 456, 90 | ⊢ |
| : , : , : |
48 | instantiation | 67, 68 | ⊢ |
| : , : |
49 | instantiation | 69, 70 | ⊢ |
| : |
50 | instantiation | 241, 226, 71 | ⊢ |
| : , : |
51 | instantiation | 408, 72, 73 | ⊢ |
| : , : , : |
52 | instantiation | 241, 226, 116 | ⊢ |
| : , : |
53 | instantiation | 408, 74, 75 | ⊢ |
| : , : , : |
54 | theorem | | ⊢ |
| proveit.numbers.exponentiation.unit_complex_polar_num_neq_one |
55 | instantiation | 292, 210, 194 | ⊢ |
| : , : , : |
56 | instantiation | 253, 76, 77 | ⊢ |
| : , : , : |
57 | instantiation | 238, 78 | ⊢ |
| : , : |
58 | instantiation | 222, 466, 459, 361, 227, 362, 450, 308, 146, 424 | ⊢ |
| : , : , : , : , : , : , : |
59 | instantiation | 416, 79 | ⊢ |
| : , : , : |
60 | instantiation | 416, 80 | ⊢ |
| : , : , : |
61 | instantiation | 408, 81, 82 | ⊢ |
| : , : , : |
62 | instantiation | 416, 83 | ⊢ |
| : , : , : |
63 | instantiation | 301, 84 | ⊢ |
| : |
64 | instantiation | 416, 85 | ⊢ |
| : , : , : |
65 | instantiation | 416, 86 | ⊢ |
| : , : , : |
66 | instantiation | 408, 87, 88 | ⊢ |
| : , : , : |
67 | theorem | | ⊢ |
| proveit.logic.equality.not_equals_symmetry |
68 | instantiation | 89, 234, 90, 91 | ⊢ |
| : , : |
69 | theorem | | ⊢ |
| proveit.trigonometry.real_closure |
70 | instantiation | 292, 171, 153 | ⊢ |
| : , : , : |
71 | instantiation | 292, 92, 93 | ⊢ |
| : , : , : |
72 | instantiation | 285, 459, 243, 361, 94, 362, 226, 146, 424, 366 | ⊢ |
| : , : , : , : , : , : |
73 | instantiation | 285, 361, 466, 243, 362, 227, 94, 450, 308, 146, 424, 366 | ⊢ |
| : , : , : , : , : , : |
74 | instantiation | 285, 459, 466, 361, 117, 362, 226, 146, 424 | ⊢ |
| : , : , : , : , : , : |
75 | instantiation | 285, 361, 466, 362, 227, 117, 450, 308, 146, 424 | ⊢ |
| : , : , : , : , : , : |
76 | instantiation | 95, 96, 97, 141, 139 | ⊢ |
| : , : |
77 | instantiation | 295, 98, 373, 99 | ⊢ |
| : , : , : , : |
78 | instantiation | 416, 100 | ⊢ |
| : , : , : |
79 | instantiation | 408, 101, 102 | ⊢ |
| : , : , : |
80 | instantiation | 408, 103, 104 | ⊢ |
| : , : , : |
81 | instantiation | 408, 105, 106 | ⊢ |
| : , : , : |
82 | instantiation | 417, 130 | ⊢ |
| : |
83 | instantiation | 288, 146 | ⊢ |
| : |
84 | instantiation | 464, 456, 107 | ⊢ |
| : , : , : |
85 | instantiation | 408, 108, 126 | ⊢ |
| : , : , : |
86 | instantiation | 408, 109, 110 | ⊢ |
| : , : , : |
87 | instantiation | 408, 111, 112 | ⊢ |
| : , : , : |
88 | instantiation | 417, 136 | ⊢ |
| : |
89 | theorem | | ⊢ |
| proveit.numbers.ordering.less_is_not_eq |
90 | instantiation | 113, 234, 427, 115 | ⊢ |
| : , : , : |
91 | instantiation | 114, 234, 427, 115 | ⊢ |
| : , : , : |
92 | instantiation | 241, 116, 366 | ⊢ |
| : , : |
93 | instantiation | 285, 361, 466, 459, 362, 117, 146, 424, 366 | ⊢ |
| : , : , : , : , : , : |
94 | instantiation | 270 | ⊢ |
| : , : , : |
95 | theorem | | ⊢ |
| proveit.logic.booleans.disjunction.right_if_not_left |
96 | instantiation | 118, 119 | ⊢ |
| : |
97 | instantiation | 120, 121 | ⊢ |
| : , : |
98 | instantiation | 122, 174, 226, 123, 124* | ⊢ |
| : , : |
99 | instantiation | 399 | ⊢ |
| : |
100 | instantiation | 408, 125, 126 | ⊢ |
| : , : , : |
101 | instantiation | 222, 361, 466, 362, 227, 228, 450, 308, 146, 424, 366 | ⊢ |
| : , : , : , : , : , : , : |
102 | instantiation | 242, 459, 458, 361, 148, 362, 146, 450, 308, 424, 366 | ⊢ |
| : , : , : , : , : , : |
103 | instantiation | 416, 127 | ⊢ |
| : , : , : |
104 | instantiation | 341, 165, 128* | ⊢ |
| : |
105 | instantiation | 416, 129 | ⊢ |
| : , : , : |
106 | instantiation | 135, 325, 324, 130, 434* | ⊢ |
| : , : , : |
107 | instantiation | 464, 369, 131 | ⊢ |
| : , : , : |
108 | instantiation | 222, 361, 466, 459, 362, 227, 450, 308, 146, 424 | ⊢ |
| : , : , : , : , : , : , : |
109 | instantiation | 416, 132 | ⊢ |
| : , : , : |
110 | instantiation | 341, 174, 133* | ⊢ |
| : |
111 | instantiation | 416, 134 | ⊢ |
| : , : , : |
112 | instantiation | 135, 325, 324, 136, 434* | ⊢ |
| : , : , : |
113 | theorem | | ⊢ |
| proveit.numbers.number_sets.real_numbers.all_in_interval_oc__is__real |
114 | theorem | | ⊢ |
| proveit.numbers.number_sets.real_numbers.interval_oc_lower_bound |
115 | instantiation | 137, 138 | ⊢ |
| : |
116 | instantiation | 241, 146, 424 | ⊢ |
| : , : |
117 | instantiation | 447 | ⊢ |
| : , : |
118 | axiom | | ⊢ |
| proveit.logic.booleans.negation.operand_is_bool |
119 | instantiation | 140, 139 | ⊢ |
| : |
120 | axiom | | ⊢ |
| proveit.logic.booleans.disjunction.right_in_bool |
121 | instantiation | 140, 141 | ⊢ |
| : |
122 | theorem | | ⊢ |
| proveit.numbers.division.div_as_mult |
123 | instantiation | 142, 466, 227, 325, 143 | ⊢ |
| : , : |
124 | instantiation | 408, 144, 145 | ⊢ |
| : , : , : |
125 | instantiation | 222, 361, 243, 362, 219, 450, 308, 424, 146 | ⊢ |
| : , : , : , : , : , : , : |
126 | instantiation | 242, 459, 243, 361, 219, 362, 146, 450, 308, 424 | ⊢ |
| : , : , : , : , : , : |
127 | instantiation | 264, 147 | ⊢ |
| : |
128 | instantiation | 315, 412, 148, 450, 308, 424, 366, 149* | ⊢ |
| : , : |
129 | instantiation | 408, 150, 151 | ⊢ |
| : , : , : |
130 | instantiation | 292, 152, 153 | ⊢ |
| : , : , : |
131 | theorem | | ⊢ |
| proveit.numbers.number_sets.real_numbers.e_is_real_pos |
132 | instantiation | 264, 154 | ⊢ |
| : |
133 | instantiation | 315, 155, 219, 450, 308, 424, 189*, 190* | ⊢ |
| : , : |
134 | instantiation | 242, 459, 466, 361, 169, 362, 450, 308, 309 | ⊢ |
| : , : , : , : , : , : |
135 | theorem | | ⊢ |
| proveit.numbers.division.frac_cancel_left |
136 | instantiation | 464, 456, 157 | ⊢ |
| : , : , : |
137 | theorem | | ⊢ |
| proveit.trigonometry.sine_pos_interval |
138 | instantiation | 156, 234, 338, 157, 158 | ⊢ |
| : , : , : |
139 | instantiation | 159, 425 | ⊢ |
| : , : |
140 | theorem | | ⊢ |
| proveit.logic.booleans.in_bool_if_true |
141 | instantiation | 160, 161 | ⊢ |
| : |
142 | theorem | | ⊢ |
| proveit.numbers.multiplication.mult_not_eq_zero |
143 | instantiation | 464, 350, 275 | ⊢ |
| : , : , : |
144 | instantiation | 416, 162 | ⊢ |
| : , : , : |
145 | instantiation | 408, 163, 164 | ⊢ |
| : , : , : |
146 | theorem | | ⊢ |
| proveit.numbers.number_sets.complex_numbers.i_is_complex |
147 | instantiation | 173, 165 | ⊢ |
| : |
148 | instantiation | 166 | ⊢ |
| : , : , : , : |
149 | instantiation | 408, 167, 168 | ⊢ |
| : , : , : |
150 | instantiation | 222, 361, 459, 466, 362, 169, 366, 450, 308, 309 | ⊢ |
| : , : , : , : , : , : , : |
151 | instantiation | 242, 459, 243, 361, 170, 362, 450, 366, 308, 309 | ⊢ |
| : , : , : , : , : , : |
152 | instantiation | 464, 456, 171 | ⊢ |
| : , : , : |
153 | instantiation | 285, 361, 466, 459, 362, 172, 366, 308, 309 | ⊢ |
| : , : , : , : , : , : |
154 | instantiation | 173, 174 | ⊢ |
| : |
155 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.posnat3 |
156 | theorem | | ⊢ |
| proveit.numbers.number_sets.real_numbers.in_IntervalOO |
157 | instantiation | 464, 369, 195 | ⊢ |
| : , : , : |
158 | instantiation | 175, 176, 177 | ⊢ |
| : , : |
159 | theorem | | ⊢ |
| proveit.logic.equality.unfold_not_equals |
160 | theorem | | ⊢ |
| proveit.physics.quantum.QPE._delta_b_is_zero_or_non_int |
161 | instantiation | 178, 459, 361, 362 | ⊢ |
| : , : , : , : , : |
162 | instantiation | 179, 450, 308, 397, 428, 249, 180* | ⊢ |
| : , : , : |
163 | instantiation | 408, 181, 182 | ⊢ |
| : , : , : |
164 | instantiation | 408, 183, 184 | ⊢ |
| : , : , : |
165 | instantiation | 292, 185, 186 | ⊢ |
| : , : , : |
166 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.tuple_len_4_typical_eq |
167 | instantiation | 430, 243, 187, 188, 189, 190, 317 | ⊢ |
| : , : , : , : |
168 | instantiation | 222, 361, 243, 362, 191, 450, 308, 309, 366 | ⊢ |
| : , : , : , : , : , : , : |
169 | instantiation | 447 | ⊢ |
| : , : |
170 | instantiation | 270 | ⊢ |
| : , : , : |
171 | instantiation | 319, 192, 339 | ⊢ |
| : , : |
172 | instantiation | 447 | ⊢ |
| : , : |
173 | theorem | | ⊢ |
| proveit.numbers.negation.complex_closure |
174 | instantiation | 292, 193, 194 | ⊢ |
| : , : , : |
175 | theorem | | ⊢ |
| proveit.logic.booleans.conjunction.and_if_both |
176 | instantiation | 318, 195 | ⊢ |
| : |
177 | instantiation | 196, 197, 198 | ⊢ |
| : , : , : |
178 | theorem | | ⊢ |
| proveit.logic.sets.enumeration.in_enumerated_set |
179 | theorem | | ⊢ |
| proveit.numbers.exponentiation.real_power_of_product |
180 | instantiation | 199, 325, 436, 359* | ⊢ |
| : , : |
181 | instantiation | 408, 200, 201 | ⊢ |
| : , : , : |
182 | instantiation | 408, 202, 203 | ⊢ |
| : , : , : |
183 | instantiation | 307, 361, 243, 362, 245, 308, 424, 246 | ⊢ |
| : , : , : , : |
184 | instantiation | 408, 204, 205 | ⊢ |
| : , : , : |
185 | instantiation | 464, 456, 206 | ⊢ |
| : , : , : |
186 | instantiation | 408, 207, 208 | ⊢ |
| : , : , : |
187 | instantiation | 270 | ⊢ |
| : , : , : |
188 | instantiation | 270 | ⊢ |
| : , : , : |
189 | instantiation | 344, 209 | ⊢ |
| : |
190 | instantiation | 344, 259 | ⊢ |
| : |
191 | instantiation | 270 | ⊢ |
| : , : , : |
192 | instantiation | 319, 398, 338 | ⊢ |
| : , : |
193 | instantiation | 464, 456, 210 | ⊢ |
| : , : , : |
194 | instantiation | 285, 361, 466, 459, 362, 227, 450, 308, 424 | ⊢ |
| : , : , : , : , : , : |
195 | instantiation | 211, 368, 370 | ⊢ |
| : , : |
196 | axiom | | ⊢ |
| proveit.numbers.ordering.transitivity_less_less |
197 | instantiation | 292, 212, 255 | ⊢ |
| : , : , : |
198 | instantiation | 302, 290, 213, 214, 215*, 216* | ⊢ |
| : , : , : |
199 | theorem | | ⊢ |
| proveit.numbers.exponentiation.neg_power_as_div |
200 | instantiation | 285, 361, 243, 459, 362, 219, 450, 308, 424, 217 | ⊢ |
| : , : , : , : , : , : |
201 | instantiation | 285, 243, 466, 361, 219, 218, 362, 450, 308, 424, 289, 246 | ⊢ |
| : , : , : , : , : , : |
202 | instantiation | 222, 361, 243, 459, 362, 219, 450, 308, 424, 289, 246 | ⊢ |
| : , : , : , : , : , : , : |
203 | instantiation | 408, 220, 221 | ⊢ |
| : , : , : |
204 | instantiation | 222, 459, 361, 362, 308, 424, 246 | ⊢ |
| : , : , : , : , : , : , : |
205 | instantiation | 242, 361, 466, 459, 362, 223, 308, 246, 424, 224* | ⊢ |
| : , : , : , : , : , : |
206 | instantiation | 319, 252, 225 | ⊢ |
| : , : |
207 | instantiation | 285, 459, 466, 361, 228, 362, 226, 424, 366 | ⊢ |
| : , : , : , : , : , : |
208 | instantiation | 285, 361, 466, 362, 227, 228, 450, 308, 424, 366 | ⊢ |
| : , : , : , : , : , : |
209 | instantiation | 229, 466 | ⊢ |
| : |
210 | instantiation | 319, 252, 443 | ⊢ |
| : , : |
211 | theorem | | ⊢ |
| proveit.numbers.multiplication.mult_real_pos_closure_bin |
212 | instantiation | 230, 231, 232 | ⊢ |
| : , : , : |
213 | instantiation | 319, 320, 234 | ⊢ |
| : , : |
214 | instantiation | 233, 320, 234, 338, 284, 235 | ⊢ |
| : , : , : |
215 | instantiation | 408, 236, 237 | ⊢ |
| : , : , : |
216 | instantiation | 238, 239, 240* | ⊢ |
| : , : |
217 | instantiation | 241, 289, 246 | ⊢ |
| : , : |
218 | instantiation | 447 | ⊢ |
| : , : |
219 | instantiation | 270 | ⊢ |
| : , : , : |
220 | instantiation | 242, 361, 466, 243, 362, 244, 245, 289, 450, 308, 424, 246 | ⊢ |
| : , : , : , : , : , : |
221 | instantiation | 416, 247 | ⊢ |
| : , : , : |
222 | theorem | | ⊢ |
| proveit.numbers.multiplication.leftward_commutation |
223 | instantiation | 447 | ⊢ |
| : , : |
224 | instantiation | 248, 308, 427, 397, 249, 250*, 251* | ⊢ |
| : , : , : |
225 | instantiation | 319, 443, 398 | ⊢ |
| : , : |
226 | instantiation | 464, 456, 252 | ⊢ |
| : , : , : |
227 | instantiation | 447 | ⊢ |
| : , : |
228 | instantiation | 447 | ⊢ |
| : , : |
229 | theorem | | ⊢ |
| proveit.numbers.number_sets.natural_numbers.natural_lower_bound |
230 | theorem | | ⊢ |
| proveit.numbers.ordering.transitivity_less_less_eq |
231 | instantiation | 253, 254, 255 | ⊢ |
| : , : , : |
232 | instantiation | 256, 338, 257, 403, 258, 259, 260*, 261* | ⊢ |
| : , : , : |
233 | theorem | | ⊢ |
| proveit.numbers.multiplication.strong_bound_via_right_factor_bound |
234 | theorem | | ⊢ |
| proveit.numbers.number_sets.real_numbers.zero_is_real |
235 | instantiation | 262, 380 | ⊢ |
| : |
236 | instantiation | 416, 263 | ⊢ |
| : , : , : |
237 | instantiation | 264, 265 | ⊢ |
| : |
238 | theorem | | ⊢ |
| proveit.logic.equality.equals_reversal |
239 | instantiation | 266, 361, 466, 459, 362, 267, 289, 308 | ⊢ |
| : , : , : , : , : , : |
240 | instantiation | 408, 268, 269 | ⊢ |
| : , : , : |
241 | theorem | | ⊢ |
| proveit.numbers.multiplication.mult_complex_closure_bin |
242 | theorem | | ⊢ |
| proveit.numbers.multiplication.association |
243 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.nat3 |
244 | instantiation | 447 | ⊢ |
| : , : |
245 | instantiation | 270 | ⊢ |
| : , : , : |
246 | instantiation | 271, 308, 364 | ⊢ |
| : , : |
247 | instantiation | 292, 272, 273 | ⊢ |
| : , : , : |
248 | theorem | | ⊢ |
| proveit.numbers.exponentiation.product_of_real_powers |
249 | instantiation | 274, 275 | ⊢ |
| : |
250 | instantiation | 396, 308 | ⊢ |
| : |
251 | instantiation | 408, 276, 277 | ⊢ |
| : , : , : |
252 | instantiation | 319, 457, 338 | ⊢ |
| : , : |
253 | theorem | | ⊢ |
| proveit.logic.equality.sub_left_side_into |
254 | instantiation | 278, 459, 368, 370, 279, 280* | ⊢ |
| : , : , : , : , : , : |
255 | instantiation | 416, 281 | ⊢ |
| : , : , : |
256 | theorem | | ⊢ |
| proveit.numbers.multiplication.weak_bound_via_right_factor_bound |
257 | instantiation | 319, 398, 339 | ⊢ |
| : , : |
258 | instantiation | 292, 282, 283 | ⊢ |
| : , : , : |
259 | instantiation | 377, 284 | ⊢ |
| : , : |
260 | instantiation | 285, 459, 466, 361, 286, 362, 308, 366, 309 | ⊢ |
| : , : , : , : , : , : |
261 | instantiation | 287, 308, 289 | ⊢ |
| : , : |
262 | theorem | | ⊢ |
| proveit.numbers.number_sets.rational_numbers.positive_if_in_rational_pos |
263 | instantiation | 288, 289 | ⊢ |
| : |
264 | theorem | | ⊢ |
| proveit.numbers.addition.elim_zero_left |
265 | instantiation | 464, 456, 290 | ⊢ |
| : , : , : |
266 | theorem | | ⊢ |
| proveit.numbers.multiplication.distribute_through_sum |
267 | instantiation | 447 | ⊢ |
| : , : |
268 | instantiation | 416, 291 | ⊢ |
| : , : , : |
269 | instantiation | 448, 308 | ⊢ |
| : |
270 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.tuple_len_3_typical_eq |
271 | theorem | | ⊢ |
| proveit.numbers.exponentiation.exp_complex_closure |
272 | instantiation | 292, 293, 294 | ⊢ |
| : , : , : |
273 | instantiation | 295, 296, 297, 298 | ⊢ |
| : , : , : , : |
274 | theorem | | ⊢ |
| proveit.numbers.number_sets.real_numbers.nonzero_if_in_real_nonzero |
275 | instantiation | 464, 299, 368 | ⊢ |
| : , : , : |
276 | instantiation | 416, 300 | ⊢ |
| : , : , : |
277 | instantiation | 301, 308 | ⊢ |
| : |
278 | theorem | | ⊢ |
| proveit.numbers.multiplication.strong_bound_via_factor_bound |
279 | instantiation | 302, 397, 457, 303, 304, 305*, 306* | ⊢ |
| : , : , : |
280 | instantiation | 307, 459, 308, 309 | ⊢ |
| : , : , : , : |
281 | instantiation | 408, 310, 311 | ⊢ |
| : , : , : |
282 | instantiation | 312, 313, 314 | ⊢ |
| : , : |
283 | instantiation | 315, 446, 316, 366, 424, 317* | ⊢ |
| : , : |
284 | instantiation | 318, 368 | ⊢ |
| : |
285 | theorem | | ⊢ |
| proveit.numbers.multiplication.disassociation |
286 | instantiation | 447 | ⊢ |
| : , : |
287 | theorem | | ⊢ |
| proveit.numbers.multiplication.commutation |
288 | theorem | | ⊢ |
| proveit.numbers.multiplication.mult_zero_right |
289 | instantiation | 464, 456, 403 | ⊢ |
| : , : , : |
290 | instantiation | 319, 320, 338 | ⊢ |
| : , : |
291 | instantiation | 321, 455, 463, 322* | ⊢ |
| : , : , : , : |
292 | theorem | | ⊢ |
| proveit.logic.equality.sub_right_side_into |
293 | instantiation | 323, 372, 324, 325 | ⊢ |
| : , : , : , : , : |
294 | instantiation | 408, 326, 327 | ⊢ |
| : , : , : |
295 | theorem | | ⊢ |
| proveit.logic.equality.four_chain_transitivity |
296 | instantiation | 416, 328 | ⊢ |
| : , : , : |
297 | instantiation | 416, 328 | ⊢ |
| : , : , : |
298 | instantiation | 449, 372 | ⊢ |
| : |
299 | theorem | | ⊢ |
| proveit.numbers.number_sets.real_numbers.real_pos_within_real_nonzero |
300 | instantiation | 329, 372, 367 | ⊢ |
| : , : |
301 | theorem | | ⊢ |
| proveit.numbers.exponentiation.exp_zero_eq_one |
302 | theorem | | ⊢ |
| proveit.numbers.addition.strong_bound_via_left_term_bound |
303 | instantiation | 464, 460, 330 | ⊢ |
| : , : , : |
304 | instantiation | 331, 457, 398, 427, 332, 333 | ⊢ |
| : , : , : |
305 | instantiation | 334, 372, 450, 335 | ⊢ |
| : , : , : |
306 | instantiation | 408, 336, 337 | ⊢ |
| : , : , : |
307 | theorem | | ⊢ |
| proveit.numbers.multiplication.elim_one_any |
308 | instantiation | 464, 456, 338 | ⊢ |
| : , : , : |
309 | instantiation | 464, 456, 339 | ⊢ |
| : , : , : |
310 | instantiation | 416, 340 | ⊢ |
| : , : , : |
311 | instantiation | 341, 424 | ⊢ |
| : |
312 | theorem | | ⊢ |
| proveit.numbers.absolute_value.weak_upper_bound |
313 | instantiation | 342, 375, 403, 376 | ⊢ |
| : , : , : |
314 | instantiation | 377, 343 | ⊢ |
| : , : |
315 | theorem | | ⊢ |
| proveit.numbers.absolute_value.abs_prod |
316 | instantiation | 447 | ⊢ |
| : , : |
317 | instantiation | 344, 345 | ⊢ |
| : |
318 | theorem | | ⊢ |
| proveit.numbers.number_sets.real_numbers.positive_if_in_real_pos |
319 | theorem | | ⊢ |
| proveit.numbers.multiplication.mult_real_closure_bin |
320 | instantiation | 464, 460, 346 | ⊢ |
| : , : , : |
321 | theorem | | ⊢ |
| proveit.numbers.addition.rational_pair_addition |
322 | instantiation | 408, 347, 348 | ⊢ |
| : , : , : |
323 | theorem | | ⊢ |
| proveit.numbers.division.mult_frac_cancel_denom_left |
324 | instantiation | 464, 350, 349 | ⊢ |
| : , : , : |
325 | instantiation | 464, 350, 351 | ⊢ |
| : , : , : |
326 | instantiation | 416, 352 | ⊢ |
| : , : , : |
327 | instantiation | 416, 353 | ⊢ |
| : , : , : |
328 | instantiation | 417, 372 | ⊢ |
| : |
329 | theorem | | ⊢ |
| proveit.numbers.addition.subtraction.add_cancel_basic |
330 | instantiation | 464, 462, 354 | ⊢ |
| : , : , : |
331 | theorem | | ⊢ |
| proveit.numbers.ordering.less_eq_add_right_strong |
332 | instantiation | 355, 457, 427, 356, 357, 358, 359* | ⊢ |
| : , : , : |
333 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.less_0_1 |
334 | theorem | | ⊢ |
| proveit.numbers.addition.subtraction.subtract_from_add |
335 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.add_1_1 |
336 | instantiation | 360, 361, 466, 459, 362, 363, 366, 372, 364 | ⊢ |
| : , : , : , : , : , : |
337 | instantiation | 365, 372, 366, 367 | ⊢ |
| : , : , : |
338 | instantiation | 464, 369, 368 | ⊢ |
| : , : , : |
339 | instantiation | 464, 369, 370 | ⊢ |
| : , : , : |
340 | instantiation | 371, 372, 424, 373* | ⊢ |
| : , : |
341 | theorem | | ⊢ |
| proveit.numbers.absolute_value.abs_even |
342 | theorem | | ⊢ |
| proveit.numbers.number_sets.real_numbers.interval_co_lower_bound |
343 | instantiation | 374, 375, 403, 376 | ⊢ |
| : , : , : |
344 | theorem | | ⊢ |
| proveit.numbers.absolute_value.abs_non_neg_elim |
345 | instantiation | 377, 378 | ⊢ |
| : , : |
346 | instantiation | 464, 379, 380 | ⊢ |
| : , : , : |
347 | instantiation | 430, 466, 381, 382, 383, 384 | ⊢ |
| : , : , : , : |
348 | instantiation | 385, 386, 387 | ⊢ |
| : |
349 | instantiation | 464, 389, 388 | ⊢ |
| : , : , : |
350 | theorem | | ⊢ |
| proveit.numbers.number_sets.complex_numbers.real_nonzero_within_complex_nonzero |
351 | instantiation | 464, 389, 390 | ⊢ |
| : , : , : |
352 | instantiation | 416, 433 | ⊢ |
| : , : , : |
353 | instantiation | 408, 391, 392 | ⊢ |
| : , : , : |
354 | instantiation | 464, 465, 393 | ⊢ |
| : , : , : |
355 | theorem | | ⊢ |
| proveit.numbers.exponentiation.exp_monotonicity_large_base_less_eq |
356 | instantiation | 421, 422, 395 | ⊢ |
| : , : , : |
357 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.less_1_2 |
358 | instantiation | 394, 395 | ⊢ |
| : |
359 | instantiation | 396, 450 | ⊢ |
| : |
360 | theorem | | ⊢ |
| proveit.numbers.addition.disassociation |
361 | axiom | | ⊢ |
| proveit.numbers.number_sets.natural_numbers.zero_in_nats |
362 | theorem | | ⊢ |
| proveit.core_expr_types.tuples.tuple_len_0_typical_eq |
363 | instantiation | 447 | ⊢ |
| : , : |
364 | instantiation | 464, 456, 397 | ⊢ |
| : , : , : |
365 | theorem | | ⊢ |
| proveit.numbers.addition.subtraction.add_cancel_triple_23 |
366 | instantiation | 464, 456, 398 | ⊢ |
| : , : , : |
367 | instantiation | 399 | ⊢ |
| : |
368 | theorem | | ⊢ |
| proveit.numbers.number_sets.real_numbers.pi_is_real_pos |
369 | theorem | | ⊢ |
| proveit.numbers.number_sets.real_numbers.real_pos_within_real |
370 | instantiation | 400, 401 | ⊢ |
| : |
371 | theorem | | ⊢ |
| proveit.numbers.multiplication.mult_neg_left |
372 | instantiation | 464, 456, 427 | ⊢ |
| : , : , : |
373 | instantiation | 448, 424 | ⊢ |
| : |
374 | theorem | | ⊢ |
| proveit.numbers.number_sets.real_numbers.interval_co_upper_bound |
375 | instantiation | 402, 403 | ⊢ |
| : |
376 | theorem | | ⊢ |
| proveit.physics.quantum.QPE._scaled_delta_b_round_in_interval |
377 | theorem | | ⊢ |
| proveit.numbers.ordering.relax_less |
378 | instantiation | 404, 439 | ⊢ |
| : |
379 | theorem | | ⊢ |
| proveit.numbers.number_sets.rational_numbers.rational_pos_within_rational |
380 | instantiation | 405, 406, 407 | ⊢ |
| : , : |
381 | instantiation | 447 | ⊢ |
| : , : |
382 | instantiation | 447 | ⊢ |
| : , : |
383 | instantiation | 408, 409, 410 | ⊢ |
| : , : , : |
384 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.mult_2_2 |
385 | theorem | | ⊢ |
| proveit.numbers.division.frac_cancel_complete |
386 | instantiation | 464, 456, 411 | ⊢ |
| : , : , : |
387 | instantiation | 445, 412 | ⊢ |
| : |
388 | instantiation | 464, 414, 413 | ⊢ |
| : , : , : |
389 | theorem | | ⊢ |
| proveit.numbers.number_sets.real_numbers.rational_nonzero_within_real_nonzero |
390 | instantiation | 464, 414, 415 | ⊢ |
| : , : , : |
391 | instantiation | 416, 434 | ⊢ |
| : , : , : |
392 | instantiation | 417, 450 | ⊢ |
| : |
393 | instantiation | 418, 419, 459 | ⊢ |
| : , : |
394 | theorem | | ⊢ |
| proveit.numbers.number_sets.natural_numbers.natural_pos_lower_bound |
395 | axiom | | ⊢ |
| proveit.physics.quantum.QPE._t_in_natural_pos |
396 | theorem | | ⊢ |
| proveit.numbers.exponentiation.complex_x_to_first_power_is_x |
397 | instantiation | 464, 460, 420 | ⊢ |
| : , : , : |
398 | instantiation | 421, 422, 439 | ⊢ |
| : , : , : |
399 | axiom | | ⊢ |
| proveit.logic.equality.equals_reflexivity |
400 | theorem | | ⊢ |
| proveit.numbers.absolute_value.abs_nonzero_closure |
401 | instantiation | 423, 424, 425 | ⊢ |
| : |
402 | theorem | | ⊢ |
| proveit.numbers.negation.real_closure |
403 | instantiation | 426, 427, 457, 428 | ⊢ |
| : , : |
404 | theorem | | ⊢ |
| proveit.numbers.number_sets.natural_numbers.natural_pos_is_pos |
405 | theorem | | ⊢ |
| proveit.numbers.division.div_rational_pos_closure |
406 | instantiation | 464, 429, 436 | ⊢ |
| : , : , : |
407 | instantiation | 464, 429, 446 | ⊢ |
| : , : , : |
408 | axiom | | ⊢ |
| proveit.logic.equality.equals_transitivity |
409 | instantiation | 430, 466, 431, 432, 433, 434 | ⊢ |
| : , : , : , : |
410 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.add_2_2 |
411 | instantiation | 464, 460, 435 | ⊢ |
| : , : , : |
412 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.posnat4 |
413 | instantiation | 464, 437, 436 | ⊢ |
| : , : , : |
414 | theorem | | ⊢ |
| proveit.numbers.number_sets.rational_numbers.nonzero_int_within_rational_nonzero |
415 | instantiation | 464, 437, 446 | ⊢ |
| : , : , : |
416 | axiom | | ⊢ |
| proveit.logic.equality.substitution |
417 | theorem | | ⊢ |
| proveit.numbers.division.frac_one_denom |
418 | theorem | | ⊢ |
| proveit.numbers.addition.add_nat_closure_bin |
419 | instantiation | 464, 438, 439 | ⊢ |
| : , : , : |
420 | instantiation | 464, 462, 440 | ⊢ |
| : , : , : |
421 | theorem | | ⊢ |
| proveit.logic.sets.inclusion.unfold_subset_eq |
422 | instantiation | 441, 442 | ⊢ |
| : , : |
423 | theorem | | ⊢ |
| proveit.numbers.number_sets.complex_numbers.nonzero_complex_is_complex_nonzero |
424 | instantiation | 464, 456, 443 | ⊢ |
| : , : , : |
425 | assumption | | ⊢ |
426 | theorem | | ⊢ |
| proveit.numbers.division.div_real_closure |
427 | instantiation | 464, 460, 444 | ⊢ |
| : , : , : |
428 | instantiation | 445, 446 | ⊢ |
| : |
429 | theorem | | ⊢ |
| proveit.numbers.number_sets.rational_numbers.nat_pos_within_rational_pos |
430 | axiom | | ⊢ |
| proveit.core_expr_types.operations.operands_substitution |
431 | instantiation | 447 | ⊢ |
| : , : |
432 | instantiation | 447 | ⊢ |
| : , : |
433 | instantiation | 448, 450 | ⊢ |
| : |
434 | instantiation | 449, 450 | ⊢ |
| : |
435 | instantiation | 464, 462, 451 | ⊢ |
| : , : , : |
436 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.posnat1 |
437 | theorem | | ⊢ |
| proveit.numbers.number_sets.integers.nat_pos_within_nonzero_int |
438 | theorem | | ⊢ |
| proveit.numbers.number_sets.natural_numbers.nat_pos_within_nat |
439 | theorem | | ⊢ |
| proveit.physics.quantum.QPE._two_pow_t_is_nat_pos |
440 | instantiation | 452, 455 | ⊢ |
| : |
441 | theorem | | ⊢ |
| proveit.logic.sets.inclusion.relax_proper_subset |
442 | theorem | | ⊢ |
| proveit.numbers.number_sets.real_numbers.nat_pos_within_real |
443 | instantiation | 453, 454 | ⊢ |
| : |
444 | instantiation | 464, 462, 455 | ⊢ |
| : , : , : |
445 | theorem | | ⊢ |
| proveit.numbers.number_sets.natural_numbers.nonzero_if_is_nat_pos |
446 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.posnat2 |
447 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.tuple_len_2_typical_eq |
448 | theorem | | ⊢ |
| proveit.numbers.multiplication.elim_one_left |
449 | theorem | | ⊢ |
| proveit.numbers.multiplication.elim_one_right |
450 | instantiation | 464, 456, 457 | ⊢ |
| : , : , : |
451 | instantiation | 464, 465, 458 | ⊢ |
| : , : , : |
452 | theorem | | ⊢ |
| proveit.numbers.negation.int_closure |
453 | theorem | | ⊢ |
| proveit.physics.quantum.QPE._delta_b_is_real |
454 | theorem | | ⊢ |
| proveit.physics.quantum.QPE._best_round_is_int |
455 | instantiation | 464, 465, 459 | ⊢ |
| : , : , : |
456 | theorem | | ⊢ |
| proveit.numbers.number_sets.complex_numbers.real_within_complex |
457 | instantiation | 464, 460, 461 | ⊢ |
| : , : , : |
458 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.nat4 |
459 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.nat1 |
460 | theorem | | ⊢ |
| proveit.numbers.number_sets.real_numbers.rational_within_real |
461 | instantiation | 464, 462, 463 | ⊢ |
| : , : , : |
462 | theorem | | ⊢ |
| proveit.numbers.number_sets.rational_numbers.int_within_rational |
463 | instantiation | 464, 465, 466 | ⊢ |
| : , : , : |
464 | theorem | | ⊢ |
| proveit.logic.sets.inclusion.superset_membership_from_proper_subset |
465 | theorem | | ⊢ |
| proveit.numbers.number_sets.integers.nat_within_int |
466 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.nat2 |
*equality replacement requirements |