| step type | requirements | statement |
0 | generalization | 1 | ⊢ |
1 | instantiation | 2, 3, 4 | ⊢ |
| : , : |
2 | theorem | | ⊢ |
| proveit.logic.booleans.implication.iff_intro |
3 | deduction | 5 | ⊢ |
4 | deduction | 6 | ⊢ |
5 | instantiation | 85, 7, 8 | , ⊢ |
| : , : |
6 | instantiation | 9, 10, 11, 26, 12, 13 | , ⊢ |
| : , : , : |
7 | instantiation | 381, 14, 15 | , ⊢ |
| : , : , : |
8 | instantiation | 283, 24 | ⊢ |
| : , : |
9 | theorem | | ⊢ |
| proveit.logic.booleans.disjunction.singular_constructive_dilemma |
10 | instantiation | 16, 18 | ⊢ |
| : , : |
11 | instantiation | 17, 18 | ⊢ |
| : , : |
12 | deduction | 19 | , ⊢ |
13 | deduction | 20 | , ⊢ |
14 | instantiation | 21, 388, 35, 22, 23 | ⊢ |
| : , : , : |
15 | instantiation | 373, 24 | ⊢ |
| : , : |
16 | axiom | | ⊢ |
| proveit.logic.booleans.disjunction.left_in_bool |
17 | axiom | | ⊢ |
| proveit.logic.booleans.disjunction.right_in_bool |
18 | instantiation | 25, 26 | ⊢ |
| : |
19 | instantiation | 85, 27, 260 | , , ⊢ |
| : , : |
20 | instantiation | 85, 28, 260 | , , ⊢ |
| : , : |
21 | theorem | | ⊢ |
| proveit.logic.sets.unification.union_inclusion |
22 | instantiation | 30, 372, 83, 400, 29 | ⊢ |
| : , : , : , : |
23 | instantiation | 30, 372, 113, 400, 31 | ⊢ |
| : , : , : , : |
24 | assumption | | ⊢ |
25 | theorem | | ⊢ |
| proveit.logic.booleans.in_bool_if_true |
26 | instantiation | 32, 328, 132 | ⊢ |
| : , : |
27 | instantiation | 34, 388, 35, 33 | , , ⊢ |
| : , : , : |
28 | instantiation | 34, 388, 35, 36 | , , ⊢ |
| : , : , : |
29 | instantiation | 40, 319, 37, 38, 52, 39 | ⊢ |
| : , : |
30 | theorem | | ⊢ |
| proveit.numbers.number_sets.integers.interval_subset_eq |
31 | instantiation | 40, 319, 41, 42, 43, 44 | ⊢ |
| : , : |
32 | theorem | | ⊢ |
| proveit.numbers.ordering.less_or_greater_eq |
33 | instantiation | 110, 45, 46 | , , ⊢ |
| : , : |
34 | theorem | | ⊢ |
| proveit.logic.sets.unification.membership_folding |
35 | instantiation | 323 | ⊢ |
| : , : |
36 | instantiation | 114, 47, 48 | , , ⊢ |
| : , : |
37 | instantiation | 335 | ⊢ |
| : , : , : |
38 | instantiation | 57, 154, 49 | ⊢ |
| : , : |
39 | instantiation | 325, 50 | ⊢ |
| : , : |
40 | theorem | | ⊢ |
| proveit.logic.booleans.conjunction.and_if_all |
41 | instantiation | 335 | ⊢ |
| : , : , : |
42 | instantiation | 51, 52, 53 | ⊢ |
| : , : , : |
43 | instantiation | 131, 377, 350, 54, 55, 56* | ⊢ |
| : , : , : |
44 | instantiation | 57, 151, 58 | ⊢ |
| : , : |
45 | instantiation | 63, 372, 83, 351, 59 | , , ⊢ |
| : , : , : |
46 | instantiation | 61, 60 | , , ⊢ |
| : , : |
47 | instantiation | 61, 62 | , , ⊢ |
| : , : |
48 | instantiation | 63, 113, 400, 351, 64 | , , ⊢ |
| : , : , : |
49 | instantiation | 303 | ⊢ |
| : |
50 | instantiation | 149, 156, 65 | ⊢ |
| : , : , : |
51 | theorem | | ⊢ |
| proveit.numbers.ordering.transitivity_less_eq_less_eq |
52 | instantiation | 131, 66, 350, 75, 76, 67*, 68* | ⊢ |
| : , : , : |
53 | instantiation | 131, 172, 69, 70, 71, 72*, 73* | ⊢ |
| : , : , : |
54 | instantiation | 327, 75, 377 | ⊢ |
| : , : |
55 | instantiation | 74, 350, 75, 377, 76, 77 | ⊢ |
| : , : , : |
56 | instantiation | 314, 78, 277, 79 | ⊢ |
| : , : , : , : |
57 | theorem | | ⊢ |
| proveit.numbers.ordering.relax_equal_to_less_eq |
58 | instantiation | 303 | ⊢ |
| : |
59 | instantiation | 85, 155, 80 | , , ⊢ |
| : , : |
60 | instantiation | 82, 113, 400, 351, 81 | , , ⊢ |
| : , : , : |
61 | theorem | | ⊢ |
| proveit.logic.sets.membership.unfold_not_in_set |
62 | instantiation | 82, 372, 83, 351, 84 | , , ⊢ |
| : , : , : |
63 | theorem | | ⊢ |
| proveit.numbers.number_sets.integers.in_interval |
64 | instantiation | 85, 86, 152 | , , ⊢ |
| : , : |
65 | instantiation | 187, 405 | ⊢ |
| : |
66 | instantiation | 87, 319, 88, 89, 377, 206 | ⊢ |
| : , : |
67 | instantiation | 314, 90, 91, 92 | ⊢ |
| : , : , : , : |
68 | instantiation | 331, 93 | ⊢ |
| : , : |
69 | instantiation | 229, 391, 132 | ⊢ |
| : , : |
70 | instantiation | 327, 207, 391 | ⊢ |
| : , : |
71 | instantiation | 94, 95, 96, 407, 97, 98 | ⊢ |
| : , : , : |
72 | instantiation | 331, 99 | ⊢ |
| : , : |
73 | instantiation | 314, 100, 101, 102 | ⊢ |
| : , : , : , : |
74 | theorem | | ⊢ |
| proveit.numbers.ordering.less_eq_add_right |
75 | instantiation | 408, 397, 103 | ⊢ |
| : , : , : |
76 | instantiation | 188, 396, 395, 385 | ⊢ |
| : , : , : |
77 | instantiation | 166, 402 | ⊢ |
| : |
78 | instantiation | 272, 104, 105 | ⊢ |
| : , : , : |
79 | instantiation | 331, 297 | ⊢ |
| : , : |
80 | instantiation | 131, 309, 377, 106, 107, 108*, 109* | , , ⊢ |
| : , : , : |
81 | instantiation | 110, 111, 112 | , , ⊢ |
| : , : |
82 | theorem | | ⊢ |
| proveit.numbers.number_sets.integers.int_not_in_interval |
83 | instantiation | 406, 113 | ⊢ |
| : |
84 | instantiation | 114, 115, 116 | , , ⊢ |
| : , : |
85 | theorem | | ⊢ |
| proveit.logic.booleans.conjunction.and_if_both |
86 | instantiation | 131, 350, 377, 117, 118, 119*, 120* | , , ⊢ |
| : , : , : |
87 | theorem | | ⊢ |
| proveit.numbers.addition.add_real_closure |
88 | instantiation | 335 | ⊢ |
| : , : , : |
89 | instantiation | 408, 397, 121 | ⊢ |
| : , : , : |
90 | instantiation | 272, 122, 123 | ⊢ |
| : , : , : |
91 | instantiation | 303 | ⊢ |
| : |
92 | instantiation | 331, 124 | ⊢ |
| : , : |
93 | instantiation | 314, 184, 125, 126 | ⊢ |
| : , : , : , : |
94 | theorem | | ⊢ |
| proveit.numbers.ordering.less_add_right_weak_int |
95 | instantiation | 408, 409, 127 | ⊢ |
| : , : , : |
96 | instantiation | 408, 409, 128 | ⊢ |
| : , : , : |
97 | instantiation | 129, 391, 132, 350, 294, 130 | ⊢ |
| : , : , : |
98 | instantiation | 131, 343, 132, 203, 133, 134*, 135* | ⊢ |
| : , : , : |
99 | instantiation | 314, 184, 185, 136 | ⊢ |
| : , : , : , : |
100 | instantiation | 299, 300, 410, 402, 302, 138, 175, 380, 137 | ⊢ |
| : , : , : , : , : , : |
101 | instantiation | 299, 410, 300, 138, 254, 302, 175, 380, 322, 341 | ⊢ |
| : , : , : , : , : , : |
102 | instantiation | 314, 139, 140, 141 | ⊢ |
| : , : , : , : |
103 | instantiation | 408, 403, 395 | ⊢ |
| : , : , : |
104 | instantiation | 333, 142 | ⊢ |
| : , : , : |
105 | instantiation | 272, 143, 144 | ⊢ |
| : , : , : |
106 | instantiation | 381, 382, 145 | , , ⊢ |
| : , : , : |
107 | instantiation | 157, 145 | , , ⊢ |
| : |
108 | instantiation | 272, 146, 147 | ⊢ |
| : , : , : |
109 | instantiation | 331, 148 | , ⊢ |
| : , : |
110 | theorem | | ⊢ |
| proveit.logic.booleans.disjunction.or_if_only_left |
111 | instantiation | 149, 326, 150 | , ⊢ |
| : , : , : |
112 | instantiation | 153, 328, 151, 152 | ⊢ |
| : , : |
113 | instantiation | 399, 371, 396 | ⊢ |
| : , : |
114 | theorem | | ⊢ |
| proveit.logic.booleans.disjunction.or_if_only_right |
115 | instantiation | 153, 154, 328, 155 | ⊢ |
| : , : |
116 | instantiation | 311, 156, 296 | , ⊢ |
| : , : , : |
117 | instantiation | 327, 328, 206 | , ⊢ |
| : , : |
118 | instantiation | 157, 158 | , , ⊢ |
| : |
119 | instantiation | 340, 366, 337 | ⊢ |
| : , : |
120 | instantiation | 272, 159, 160 | , ⊢ |
| : , : , : |
121 | instantiation | 408, 403, 386 | ⊢ |
| : , : , : |
122 | instantiation | 333, 244 | ⊢ |
| : , : , : |
123 | instantiation | 272, 161, 162 | ⊢ |
| : , : , : |
124 | instantiation | 333, 271 | ⊢ |
| : , : , : |
125 | instantiation | 340, 322, 341 | ⊢ |
| : , : |
126 | instantiation | 331, 163 | ⊢ |
| : , : |
127 | instantiation | 164, 410, 300 | ⊢ |
| : , : |
128 | instantiation | 164, 410, 165 | ⊢ |
| : , : |
129 | theorem | | ⊢ |
| proveit.numbers.multiplication.strong_bound_via_right_factor_bound |
130 | instantiation | 187, 388 | ⊢ |
| : |
131 | theorem | | ⊢ |
| proveit.numbers.addition.weak_bound_via_left_term_bound |
132 | theorem | | ⊢ |
| proveit.numbers.number_sets.real_numbers.zero_is_real |
133 | instantiation | 166, 319 | ⊢ |
| : |
134 | instantiation | 278, 167, 168 | ⊢ |
| : , : , : |
135 | instantiation | 282, 380, 366, 169, 170 | ⊢ |
| : , : , : |
136 | instantiation | 331, 171 | ⊢ |
| : , : |
137 | instantiation | 408, 390, 172 | ⊢ |
| : , : , : |
138 | instantiation | 323 | ⊢ |
| : , : |
139 | instantiation | 173, 402, 175, 380, 322, 341 | ⊢ |
| : , : , : , : , : , : , : |
140 | instantiation | 247, 300, 410, 302, 174, 257, 175, 322, 380, 341, 176* | ⊢ |
| : , : , : , : , : , : |
141 | instantiation | 247, 402, 410, 300, 257, 302, 337, 380, 341, 258* | ⊢ |
| : , : , : , : , : , : |
142 | instantiation | 272, 177, 178 | ⊢ |
| : , : , : |
143 | instantiation | 299, 300, 410, 402, 302, 179, 336, 341, 366 | ⊢ |
| : , : , : , : , : , : |
144 | instantiation | 195, 366, 336, 183 | ⊢ |
| : , : , : |
145 | instantiation | 180, 181 | , , ⊢ |
| : |
146 | instantiation | 299, 402, 410, 300, 289, 302, 366, 292, 341 | ⊢ |
| : , : , : , : , : , : |
147 | instantiation | 182, 366, 292, 183 | ⊢ |
| : , : , : |
148 | instantiation | 314, 184, 185, 186 | , ⊢ |
| : , : , : , : |
149 | axiom | | ⊢ |
| proveit.numbers.ordering.transitivity_less_less |
150 | instantiation | 187, 217 | ⊢ |
| : |
151 | instantiation | 381, 382, 405 | ⊢ |
| : , : , : |
152 | instantiation | 188, 372, 400, 362 | ⊢ |
| : , : , : |
153 | theorem | | ⊢ |
| proveit.numbers.ordering.not_less_from_less_eq |
154 | instantiation | 408, 397, 189 | ⊢ |
| : , : , : |
155 | instantiation | 329, 372, 400, 362 | ⊢ |
| : , : , : |
156 | instantiation | 190, 191 | ⊢ |
| : |
157 | theorem | | ⊢ |
| proveit.numbers.number_sets.natural_numbers.natural_pos_lower_bound |
158 | instantiation | 293, 192, 193 | , , ⊢ |
| : |
159 | instantiation | 299, 300, 410, 402, 302, 194, 292, 322, 337 | , ⊢ |
| : , : , : , : , : , : |
160 | instantiation | 195, 337, 292, 197 | , ⊢ |
| : , : , : |
161 | instantiation | 299, 402, 319, 300, 320, 302, 337, 321, 366, 322 | ⊢ |
| : , : , : , : , : , : |
162 | instantiation | 275, 300, 410, 302, 196, 337, 321, 366, 197 | ⊢ |
| : , : , : , : , : , : , : , : |
163 | instantiation | 272, 198, 199 | ⊢ |
| : , : , : |
164 | theorem | | ⊢ |
| proveit.numbers.multiplication.mult_nat_closure_bin |
165 | instantiation | 200, 371, 201 | ⊢ |
| : |
166 | theorem | | ⊢ |
| proveit.numbers.number_sets.natural_numbers.natural_lower_bound |
167 | instantiation | 202, 341 | ⊢ |
| : |
168 | instantiation | 340, 341, 252 | ⊢ |
| : , : |
169 | instantiation | 408, 390, 203 | ⊢ |
| : , : , : |
170 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.add_2_1 |
171 | instantiation | 272, 204, 205 | ⊢ |
| : , : , : |
172 | instantiation | 327, 206, 343 | ⊢ |
| : , : |
173 | theorem | | ⊢ |
| proveit.numbers.addition.leftward_commutation |
174 | instantiation | 323 | ⊢ |
| : , : |
175 | instantiation | 408, 390, 207 | ⊢ |
| : , : , : |
176 | instantiation | 272, 208, 209, 210* | ⊢ |
| : , : , : |
177 | instantiation | 333, 243 | ⊢ |
| : , : , : |
178 | instantiation | 272, 211, 212 | ⊢ |
| : , : , : |
179 | instantiation | 323 | ⊢ |
| : , : |
180 | theorem | | ⊢ |
| proveit.numbers.negation.nat_pos_closure |
181 | instantiation | 213, 214, 215 | , , ⊢ |
| : |
182 | theorem | | ⊢ |
| proveit.numbers.addition.subtraction.add_cancel_triple_13 |
183 | instantiation | 303 | ⊢ |
| : |
184 | instantiation | 286, 337, 366 | ⊢ |
| : , : |
185 | instantiation | 303 | ⊢ |
| : |
186 | instantiation | 331, 216 | , ⊢ |
| : , : |
187 | theorem | | ⊢ |
| proveit.numbers.number_sets.natural_numbers.natural_pos_is_pos |
188 | theorem | | ⊢ |
| proveit.numbers.number_sets.integers.interval_upper_bound |
189 | instantiation | 408, 403, 372 | ⊢ |
| : , : , : |
190 | theorem | | ⊢ |
| proveit.numbers.number_sets.integers.negative_if_in_neg_int |
191 | instantiation | 268, 217 | ⊢ |
| : |
192 | instantiation | 399, 351, 218 | , ⊢ |
| : , : |
193 | instantiation | 219, 220 | , ⊢ |
| : , : |
194 | instantiation | 323 | ⊢ |
| : , : |
195 | theorem | | ⊢ |
| proveit.numbers.addition.subtraction.add_cancel_triple_32 |
196 | instantiation | 323 | ⊢ |
| : , : |
197 | instantiation | 303 | ⊢ |
| : |
198 | instantiation | 272, 221, 222 | ⊢ |
| : , : , : |
199 | instantiation | 272, 223, 224 | ⊢ |
| : , : , : |
200 | theorem | | ⊢ |
| proveit.numbers.number_sets.integers.nonneg_int_is_natural |
201 | instantiation | 325, 294 | ⊢ |
| : , : |
202 | theorem | | ⊢ |
| proveit.numbers.addition.elim_zero_right |
203 | instantiation | 408, 397, 225 | ⊢ |
| : , : , : |
204 | instantiation | 333, 226 | ⊢ |
| : , : , : |
205 | instantiation | 272, 227, 228 | ⊢ |
| : , : , : |
206 | instantiation | 353, 350 | ⊢ |
| : |
207 | instantiation | 229, 391, 350 | ⊢ |
| : , : |
208 | instantiation | 333, 230 | ⊢ |
| : , : , : |
209 | instantiation | 331, 231 | ⊢ |
| : , : |
210 | instantiation | 272, 232, 233 | ⊢ |
| : , : , : |
211 | instantiation | 299, 300, 410, 402, 302, 301, 336, 306, 366 | ⊢ |
| : , : , : , : , : , : |
212 | instantiation | 247, 402, 410, 300, 248, 302, 336, 306, 366, 249* | ⊢ |
| : , : , : , : , : , : |
213 | theorem | | ⊢ |
| proveit.numbers.number_sets.integers.neg_int_is_int_neg |
214 | instantiation | 399, 371, 351 | , ⊢ |
| : , : |
215 | instantiation | 234, 328, 350, 310, 235, 236* | , , ⊢ |
| : , : , : |
216 | instantiation | 272, 237, 238 | , ⊢ |
| : , : , : |
217 | instantiation | 239, 269, 346 | ⊢ |
| : , : |
218 | instantiation | 408, 240, 241 | ⊢ |
| : , : , : |
219 | theorem | | ⊢ |
| proveit.numbers.addition.subtraction.pos_difference |
220 | instantiation | 278, 260, 242 | , ⊢ |
| : , : , : |
221 | instantiation | 333, 243 | ⊢ |
| : , : , : |
222 | instantiation | 333, 244 | ⊢ |
| : , : , : |
223 | instantiation | 272, 245, 246 | ⊢ |
| : , : , : |
224 | instantiation | 247, 300, 410, 402, 302, 248, 306, 366, 322, 249* | ⊢ |
| : , : , : , : , : , : |
225 | instantiation | 408, 403, 250 | ⊢ |
| : , : , : |
226 | instantiation | 251, 380 | ⊢ |
| : |
227 | instantiation | 299, 402, 410, 300, 254, 302, 252, 322, 341 | ⊢ |
| : , : , : , : , : , : |
228 | instantiation | 253, 300, 410, 302, 254, 322, 341 | ⊢ |
| : , : , : , : |
229 | theorem | | ⊢ |
| proveit.numbers.multiplication.mult_real_closure_bin |
230 | instantiation | 331, 255 | ⊢ |
| : , : |
231 | instantiation | 256, 300, 410, 402, 302, 257, 380, 341, 337 | ⊢ |
| : , : , : , : , : , : |
232 | instantiation | 333, 258 | ⊢ |
| : , : , : |
233 | instantiation | 259, 337 | ⊢ |
| : |
234 | theorem | | ⊢ |
| proveit.numbers.addition.strong_bound_via_left_term_bound |
235 | instantiation | 278, 260, 261 | , ⊢ |
| : , : , : |
236 | instantiation | 262, 292, 263 | ⊢ |
| : , : |
237 | instantiation | 333, 264 | , ⊢ |
| : , : , : |
238 | instantiation | 314, 265, 266, 267 | , ⊢ |
| : , : , : , : |
239 | theorem | | ⊢ |
| proveit.numbers.addition.add_nat_pos_closure_bin |
240 | theorem | | ⊢ |
| proveit.numbers.number_sets.integers.neg_int_within_int |
241 | instantiation | 268, 269 | ⊢ |
| : |
242 | instantiation | 284, 362, 270* | , ⊢ |
| : |
243 | instantiation | 333, 297 | ⊢ |
| : , : , : |
244 | instantiation | 333, 271 | ⊢ |
| : , : , : |
245 | instantiation | 272, 273, 274 | ⊢ |
| : , : , : |
246 | instantiation | 275, 300, 402, 410, 302, 276, 336, 306, 366, 322, 277 | ⊢ |
| : , : , : , : , : , : , : , : |
247 | theorem | | ⊢ |
| proveit.numbers.addition.association |
248 | instantiation | 323 | ⊢ |
| : , : |
249 | instantiation | 278, 279, 280 | ⊢ |
| : , : , : |
250 | instantiation | 408, 409, 319 | ⊢ |
| : , : , : |
251 | theorem | | ⊢ |
| proveit.numbers.multiplication.mult_zero_right |
252 | theorem | | ⊢ |
| proveit.numbers.number_sets.complex_numbers.zero_is_complex |
253 | theorem | | ⊢ |
| proveit.numbers.addition.elim_zero_any |
254 | instantiation | 323 | ⊢ |
| : , : |
255 | instantiation | 281, 337 | ⊢ |
| : |
256 | theorem | | ⊢ |
| proveit.numbers.multiplication.distribute_through_sum |
257 | instantiation | 323 | ⊢ |
| : , : |
258 | instantiation | 282, 366, 380, 305 | ⊢ |
| : , : , : |
259 | theorem | | ⊢ |
| proveit.numbers.multiplication.elim_one_left |
260 | instantiation | 283, 374 | ⊢ |
| : , : |
261 | instantiation | 284, 362, 285* | , ⊢ |
| : |
262 | theorem | | ⊢ |
| proveit.numbers.addition.subtraction.add_cancel_reverse |
263 | instantiation | 303 | ⊢ |
| : |
264 | instantiation | 286, 337, 292 | , ⊢ |
| : , : |
265 | instantiation | 299, 300, 410, 402, 302, 288, 322, 290, 287 | , ⊢ |
| : , : , : , : , : , : |
266 | instantiation | 299, 410, 300, 288, 289, 302, 322, 290, 292, 341 | , ⊢ |
| : , : , : , : , : , : |
267 | instantiation | 291, 402, 300, 302, 322, 292, 341 | , ⊢ |
| : , : , : , : , : , : , : , : |
268 | theorem | | ⊢ |
| proveit.numbers.negation.int_neg_closure |
269 | instantiation | 293, 371, 294 | ⊢ |
| : |
270 | instantiation | 295, 296 | ⊢ |
| : |
271 | instantiation | 333, 297 | ⊢ |
| : , : , : |
272 | axiom | | ⊢ |
| proveit.logic.equality.equals_transitivity |
273 | instantiation | 299, 300, 410, 402, 302, 301, 336, 306, 298 | ⊢ |
| : , : , : , : , : , : |
274 | instantiation | 299, 410, 319, 300, 301, 320, 302, 336, 306, 321, 366, 322 | ⊢ |
| : , : , : , : , : , : |
275 | theorem | | ⊢ |
| proveit.numbers.addition.subtraction.add_cancel_general |
276 | instantiation | 323 | ⊢ |
| : , : |
277 | instantiation | 303 | ⊢ |
| : |
278 | theorem | | ⊢ |
| proveit.logic.equality.sub_right_side_into |
279 | instantiation | 304, 366, 380, 305 | ⊢ |
| : , : , : |
280 | instantiation | 340, 366, 306 | ⊢ |
| : , : |
281 | theorem | | ⊢ |
| proveit.numbers.negation.mult_neg_one_left |
282 | theorem | | ⊢ |
| proveit.numbers.addition.subtraction.subtract_from_add |
283 | theorem | | ⊢ |
| proveit.logic.booleans.conjunction.right_from_and |
284 | theorem | | ⊢ |
| proveit.physics.quantum.QPE._modabs_in_full_domain_simp |
285 | instantiation | 307, 308 | ⊢ |
| : |
286 | theorem | | ⊢ |
| proveit.numbers.negation.distribute_neg_through_binary_sum |
287 | instantiation | 408, 390, 309 | ⊢ |
| : , : , : |
288 | instantiation | 323 | ⊢ |
| : , : |
289 | instantiation | 323 | ⊢ |
| : , : |
290 | instantiation | 408, 390, 310 | ⊢ |
| : , : , : |
291 | theorem | | ⊢ |
| proveit.numbers.addition.subtraction.add_cancel_general_rev |
292 | instantiation | 408, 390, 328 | ⊢ |
| : , : , : |
293 | theorem | | ⊢ |
| proveit.numbers.number_sets.integers.pos_int_is_natural_pos |
294 | instantiation | 311, 312, 313 | ⊢ |
| : , : , : |
295 | theorem | | ⊢ |
| proveit.numbers.absolute_value.abs_non_neg_elim |
296 | assumption | | ⊢ |
297 | instantiation | 314, 315, 316, 317 | ⊢ |
| : , : , : , : |
298 | instantiation | 318, 319, 320, 321, 366, 322 | ⊢ |
| : , : |
299 | theorem | | ⊢ |
| proveit.numbers.addition.disassociation |
300 | axiom | | ⊢ |
| proveit.numbers.number_sets.natural_numbers.zero_in_nats |
301 | instantiation | 323 | ⊢ |
| : , : |
302 | theorem | | ⊢ |
| proveit.core_expr_types.tuples.tuple_len_0_typical_eq |
303 | axiom | | ⊢ |
| proveit.logic.equality.equals_reflexivity |
304 | theorem | | ⊢ |
| proveit.numbers.addition.subtraction.subtract_from_add_reversed |
305 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.add_1_1 |
306 | instantiation | 408, 390, 324 | ⊢ |
| : , : , : |
307 | theorem | | ⊢ |
| proveit.numbers.absolute_value.abs_neg_elim |
308 | instantiation | 325, 326 | ⊢ |
| : , : |
309 | instantiation | 327, 328, 343 | ⊢ |
| : , : |
310 | instantiation | 353, 328 | ⊢ |
| : |
311 | theorem | | ⊢ |
| proveit.numbers.ordering.transitivity_less_less_eq |
312 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.less_0_1 |
313 | instantiation | 329, 396, 395, 385 | ⊢ |
| : , : , : |
314 | theorem | | ⊢ |
| proveit.logic.equality.four_chain_transitivity |
315 | instantiation | 333, 330 | ⊢ |
| : , : , : |
316 | instantiation | 331, 332 | ⊢ |
| : , : |
317 | instantiation | 333, 334 | ⊢ |
| : , : , : |
318 | theorem | | ⊢ |
| proveit.numbers.addition.add_complex_closure |
319 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.nat3 |
320 | instantiation | 335 | ⊢ |
| : , : , : |
321 | instantiation | 352, 336 | ⊢ |
| : |
322 | instantiation | 352, 337 | ⊢ |
| : |
323 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.tuple_len_2_typical_eq |
324 | instantiation | 408, 397, 338 | ⊢ |
| : , : , : |
325 | theorem | | ⊢ |
| proveit.numbers.ordering.relax_less |
326 | assumption | | ⊢ |
327 | theorem | | ⊢ |
| proveit.numbers.addition.add_real_closure_bin |
328 | instantiation | 408, 397, 339 | ⊢ |
| : , : , : |
329 | theorem | | ⊢ |
| proveit.numbers.number_sets.integers.interval_lower_bound |
330 | instantiation | 340, 359, 341 | ⊢ |
| : , : |
331 | theorem | | ⊢ |
| proveit.logic.equality.equals_reversal |
332 | instantiation | 342, 380, 343, 370, 368 | ⊢ |
| : , : , : |
333 | axiom | | ⊢ |
| proveit.logic.equality.substitution |
334 | instantiation | 344, 345, 346 | ⊢ |
| : , : |
335 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.tuple_len_3_typical_eq |
336 | instantiation | 347, 348, 349 | ⊢ |
| : , : |
337 | instantiation | 408, 390, 350 | ⊢ |
| : , : , : |
338 | instantiation | 408, 403, 401 | ⊢ |
| : , : , : |
339 | instantiation | 408, 403, 351 | ⊢ |
| : , : , : |
340 | theorem | | ⊢ |
| proveit.numbers.addition.commutation |
341 | instantiation | 352, 366 | ⊢ |
| : |
342 | theorem | | ⊢ |
| proveit.numbers.exponentiation.product_of_real_powers |
343 | instantiation | 353, 377 | ⊢ |
| : |
344 | theorem | | ⊢ |
| proveit.numbers.exponentiation.neg_power_as_div |
345 | instantiation | 408, 354, 355 | ⊢ |
| : , : , : |
346 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.posnat1 |
347 | theorem | | ⊢ |
| proveit.numbers.multiplication.mult_complex_closure_bin |
348 | instantiation | 356, 366, 357, 358 | ⊢ |
| : , : |
349 | instantiation | 365, 380, 359 | ⊢ |
| : , : |
350 | instantiation | 408, 397, 360 | ⊢ |
| : , : , : |
351 | instantiation | 408, 361, 362 | ⊢ |
| : , : , : |
352 | theorem | | ⊢ |
| proveit.numbers.negation.complex_closure |
353 | theorem | | ⊢ |
| proveit.numbers.negation.real_closure |
354 | theorem | | ⊢ |
| proveit.numbers.number_sets.complex_numbers.real_nonzero_within_complex_nonzero |
355 | instantiation | 408, 363, 364 | ⊢ |
| : , : , : |
356 | theorem | | ⊢ |
| proveit.numbers.division.div_complex_closure |
357 | instantiation | 365, 380, 366 | ⊢ |
| : , : |
358 | instantiation | 367, 368, 369 | ⊢ |
| : , : , : |
359 | instantiation | 408, 390, 370 | ⊢ |
| : , : , : |
360 | instantiation | 408, 403, 371 | ⊢ |
| : , : , : |
361 | instantiation | 394, 372, 400 | ⊢ |
| : , : |
362 | instantiation | 373, 374 | ⊢ |
| : , : |
363 | theorem | | ⊢ |
| proveit.numbers.number_sets.real_numbers.rational_nonzero_within_real_nonzero |
364 | instantiation | 408, 375, 376 | ⊢ |
| : , : , : |
365 | theorem | | ⊢ |
| proveit.numbers.exponentiation.exp_complex_closure |
366 | instantiation | 408, 390, 377 | ⊢ |
| : , : , : |
367 | theorem | | ⊢ |
| proveit.logic.equality.sub_left_side_into |
368 | instantiation | 378, 388 | ⊢ |
| : |
369 | instantiation | 379, 380 | ⊢ |
| : |
370 | instantiation | 381, 382, 383 | ⊢ |
| : , : , : |
371 | instantiation | 408, 384, 385 | ⊢ |
| : , : , : |
372 | instantiation | 399, 386, 396 | ⊢ |
| : , : |
373 | theorem | | ⊢ |
| proveit.logic.booleans.conjunction.left_from_and |
374 | assumption | | ⊢ |
375 | theorem | | ⊢ |
| proveit.numbers.number_sets.rational_numbers.nonzero_int_within_rational_nonzero |
376 | instantiation | 408, 387, 388 | ⊢ |
| : , : , : |
377 | instantiation | 408, 397, 389 | ⊢ |
| : , : , : |
378 | theorem | | ⊢ |
| proveit.numbers.number_sets.natural_numbers.nonzero_if_is_nat_pos |
379 | theorem | | ⊢ |
| proveit.numbers.exponentiation.complex_x_to_first_power_is_x |
380 | instantiation | 408, 390, 391 | ⊢ |
| : , : , : |
381 | theorem | | ⊢ |
| proveit.logic.sets.inclusion.unfold_subset_eq |
382 | instantiation | 392, 393 | ⊢ |
| : , : |
383 | axiom | | ⊢ |
| proveit.physics.quantum.QPE._t_in_natural_pos |
384 | instantiation | 394, 396, 395 | ⊢ |
| : , : |
385 | assumption | | ⊢ |
386 | instantiation | 406, 400 | ⊢ |
| : |
387 | theorem | | ⊢ |
| proveit.numbers.number_sets.integers.nat_pos_within_nonzero_int |
388 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.posnat2 |
389 | instantiation | 408, 403, 396 | ⊢ |
| : , : , : |
390 | theorem | | ⊢ |
| proveit.numbers.number_sets.complex_numbers.real_within_complex |
391 | instantiation | 408, 397, 398 | ⊢ |
| : , : , : |
392 | theorem | | ⊢ |
| proveit.logic.sets.inclusion.relax_proper_subset |
393 | theorem | | ⊢ |
| proveit.numbers.number_sets.real_numbers.nat_pos_within_real |
394 | theorem | | ⊢ |
| proveit.numbers.number_sets.integers.int_interval_within_int |
395 | instantiation | 399, 400, 401 | ⊢ |
| : , : |
396 | instantiation | 408, 409, 402 | ⊢ |
| : , : , : |
397 | theorem | | ⊢ |
| proveit.numbers.number_sets.real_numbers.rational_within_real |
398 | instantiation | 408, 403, 407 | ⊢ |
| : , : , : |
399 | theorem | | ⊢ |
| proveit.numbers.addition.add_int_closure_bin |
400 | instantiation | 408, 404, 405 | ⊢ |
| : , : , : |
401 | instantiation | 406, 407 | ⊢ |
| : |
402 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.nat1 |
403 | theorem | | ⊢ |
| proveit.numbers.number_sets.rational_numbers.int_within_rational |
404 | theorem | | ⊢ |
| proveit.numbers.number_sets.integers.nat_pos_within_int |
405 | theorem | | ⊢ |
| proveit.physics.quantum.QPE._two_pow_t_minus_one_is_nat_pos |
406 | theorem | | ⊢ |
| proveit.numbers.negation.int_closure |
407 | instantiation | 408, 409, 410 | ⊢ |
| : , : , : |
408 | theorem | | ⊢ |
| proveit.logic.sets.inclusion.superset_membership_from_proper_subset |
409 | theorem | | ⊢ |
| proveit.numbers.number_sets.integers.nat_within_int |
410 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.nat2 |
*equality replacement requirements |