| step type | requirements | statement |
0 | instantiation | 1, 2 | , ⊢ |
| : , : |
1 | reference | 385 | ⊢ |
2 | instantiation | 471, 3, 4 | , ⊢ |
| : , : , : |
3 | instantiation | 471, 5, 6, 7* | , ⊢ |
| : , : , : |
4 | instantiation | 529, 8, 9 | ⊢ |
| : , : , : |
5 | instantiation | 351, 10, 11 | , ⊢ |
| : , : , : |
6 | instantiation | 41, 597 | ⊢ |
| : |
7 | instantiation | 529, 12, 13 | ⊢ |
| : , : , : |
8 | instantiation | 385, 14 | ⊢ |
| : , : |
9 | instantiation | 385, 15 | ⊢ |
| : , : |
10 | instantiation | 471, 16, 17 | ⊢ |
| : , : , : |
11 | assumption | | ⊢ |
12 | instantiation | 18, 598, 122, 538, 95, 45, 540, 410, 46, 47, 19, 49 | ⊢ |
| : , : , : , : , : , : , : , : , : , : |
13 | instantiation | 381, 207, 538, 122, 540, 95, 45, 410, 46, 47, 204, 49 | ⊢ |
| : , : , : , : , : , : , : , : , : , : |
14 | instantiation | 20, 610, 21, 22, 23, 24 | ⊢ |
| : , : , : , : |
15 | instantiation | 25, 89, 26, 27, 28, 29, 30* | ⊢ |
| : , : , : , : |
16 | instantiation | 31, 32 | ⊢ |
| : , : , : |
17 | instantiation | 529, 33, 34 | ⊢ |
| : , : , : |
18 | theorem | | ⊢ |
| proveit.linear_algebra.tensors.tensor_prod_disassociation |
19 | instantiation | 378, 410, 207, 204 | ⊢ |
| : , : , : , : |
20 | axiom | | ⊢ |
| proveit.core_expr_types.operations.operands_substitution |
21 | instantiation | 552 | ⊢ |
| : , : |
22 | instantiation | 552 | ⊢ |
| : , : |
23 | instantiation | 385, 361 | ⊢ |
| : , : |
24 | instantiation | 542, 35 | ⊢ |
| : , : , : |
25 | theorem | | ⊢ |
| proveit.logic.equality.sub_in_right_operands_via_tuple |
26 | instantiation | 209, 36, 37, 40 | ⊢ |
| : , : , : , : |
27 | instantiation | 209, 38, 39, 40 | ⊢ |
| : , : , : , : |
28 | instantiation | 41, 119, 42 | ⊢ |
| : |
29 | instantiation | 43, 44, 218* | ⊢ |
| : , : , : |
30 | instantiation | 381, 131, 538, 122, 540, 95, 45, 410, 46, 47, 48, 49 | ⊢ |
| : , : , : , : , : , : , : , : , : , : |
31 | theorem | | ⊢ |
| proveit.linear_algebra.scalar_multiplication.scalar_mult_eq |
32 | instantiation | 73, 50, 51 | ⊢ |
| : , : |
33 | instantiation | 542, 52 | ⊢ |
| : , : , : |
34 | instantiation | 385, 53 | ⊢ |
| : , : |
35 | instantiation | 385, 70 | ⊢ |
| : , : |
36 | instantiation | 471, 54, 55 | ⊢ |
| : , : , : |
37 | instantiation | 500 | ⊢ |
| : |
38 | instantiation | 56, 607, 57, 58, 59, 60, 122, 88*, 95* | ⊢ |
| : , : , : , : |
39 | instantiation | 385, 61 | ⊢ |
| : , : |
40 | instantiation | 385, 62 | ⊢ |
| : , : |
41 | axiom | | ⊢ |
| proveit.physics.quantum.QPE._psi_t_def |
42 | instantiation | 529, 63, 64 | ⊢ |
| : , : , : |
43 | theorem | | ⊢ |
| proveit.core_expr_types.tuples.partition_front |
44 | instantiation | 65, 538, 118 | ⊢ |
| : , : |
45 | instantiation | 209, 66, 334, 69 | ⊢ |
| : , : , : , : |
46 | instantiation | 67, 546, 562, 410, 99 | ⊢ |
| : , : , : |
47 | instantiation | 209, 68, 334, 69 | ⊢ |
| : , : , : , : |
48 | instantiation | 471, 204, 70 | ⊢ |
| : , : , : |
49 | modus ponens | 71, 72 | ⊢ |
50 | instantiation | 73, 74, 75 | ⊢ |
| : , : |
51 | instantiation | 542, 76, 77*, 78*, 79* | ⊢ |
| : , : , : |
52 | instantiation | 529, 80, 81 | ⊢ |
| : , : , : |
53 | instantiation | 209, 82, 83, 84 | ⊢ |
| : , : , : , : |
54 | instantiation | 121, 85 | ⊢ |
| : , : , : |
55 | instantiation | 529, 86, 87 | ⊢ |
| : , : , : |
56 | theorem | | ⊢ |
| proveit.core_expr_types.tuples.general_len |
57 | instantiation | 552 | ⊢ |
| : , : |
58 | instantiation | 552 | ⊢ |
| : , : |
59 | instantiation | 552 | ⊢ |
| : , : |
60 | instantiation | 351, 598, 88 | ⊢ |
| : , : , : |
61 | instantiation | 417, 550, 551 | ⊢ |
| : , : |
62 | instantiation | 125, 89 | ⊢ |
| : , : |
63 | instantiation | 542, 90 | ⊢ |
| : , : , : |
64 | instantiation | 529, 91, 92 | ⊢ |
| : , : , : |
65 | theorem | | ⊢ |
| proveit.numbers.addition.add_nat_closure_bin |
66 | instantiation | 471, 93, 95 | ⊢ |
| : , : , : |
67 | theorem | | ⊢ |
| proveit.logic.booleans.conjunction.redundant_conjunction_general |
68 | instantiation | 471, 94, 95 | ⊢ |
| : , : , : |
69 | instantiation | 385, 96 | ⊢ |
| : , : |
70 | instantiation | 542, 97 | ⊢ |
| : , : , : |
71 | instantiation | 98, 546, 562, 99 | ⊢ |
| : , : , : , : |
72 | generalization | 100 | ⊢ |
73 | theorem | | ⊢ |
| proveit.logic.equality.rhs_via_equality |
74 | instantiation | 471, 101, 102 | ⊢ |
| : , : , : |
75 | instantiation | 542, 103, 104*, 105*, 106* | ⊢ |
| : , : , : |
76 | modus ponens | 107, 108 | ⊢ |
77 | instantiation | 241, 548 | ⊢ |
| : , : |
78 | instantiation | 241, 548 | ⊢ |
| : , : |
79 | instantiation | 385, 109 | ⊢ |
| : , : |
80 | instantiation | 542, 110 | ⊢ |
| : , : , : |
81 | modus ponens | 111, 112 | ⊢ |
82 | instantiation | 529, 113, 114, 115* | ⊢ |
| : , : , : |
83 | instantiation | 542, 116 | ⊢ |
| : , : , : |
84 | instantiation | 500 | ⊢ |
| : |
85 | instantiation | 163, 475, 117, 538, 118, 598 | ⊢ |
| : , : |
86 | instantiation | 542, 218 | ⊢ |
| : , : , : |
87 | instantiation | 270, 538, 610, 540, 539, 550, 551 | ⊢ |
| : , : , : , : |
88 | instantiation | 266, 551, 233 | ⊢ |
| : , : , : |
89 | instantiation | 608, 596, 119 | ⊢ |
| : , : , : |
90 | instantiation | 217, 550, 551 | ⊢ |
| : , : |
91 | instantiation | 480, 538, 610, 598, 540, 120, 332, 503, 551 | ⊢ |
| : , : , : , : , : , : |
92 | instantiation | 232, 551, 332, 233 | ⊢ |
| : , : , : |
93 | instantiation | 121, 122 | ⊢ |
| : , : , : |
94 | instantiation | 121, 122 | ⊢ |
| : , : , : |
95 | instantiation | 529, 123, 124 | ⊢ |
| : , : , : |
96 | instantiation | 125, 585 | ⊢ |
| : , : |
97 | instantiation | 385, 126 | ⊢ |
| : , : |
98 | theorem | | ⊢ |
| proveit.logic.booleans.conjunction.conjunction_from_quantification |
99 | instantiation | 299, 127, 183, 564, 128, 129*, 130* | ⊢ |
| : , : , : |
100 | instantiation | 378, 410, 131, 132 | , ⊢ |
| : , : , : , : |
101 | instantiation | 133, 562, 563, 138, 134, 135, 136* | ⊢ |
| : , : , : , : , : |
102 | instantiation | 137, 573, 138, 370, 139*, 140*, 141* | ⊢ |
| : , : , : , : , : |
103 | modus ponens | 142, 143 | ⊢ |
104 | instantiation | 241, 548 | ⊢ |
| : , : |
105 | instantiation | 241, 548 | ⊢ |
| : , : |
106 | instantiation | 209, 144, 145, 146 | ⊢ |
| : , : , : , : |
107 | instantiation | 284, 605 | ⊢ |
| : , : , : , : , : , : , : |
108 | generalization | 147 | ⊢ |
109 | modus ponens | 148, 149 | ⊢ |
110 | instantiation | 385, 150 | ⊢ |
| : , : |
111 | instantiation | 151, 538, 610, 598, 152, 540, 153 | ⊢ |
| : , : , : , : , : , : , : , : |
112 | instantiation | 575, 154, 158 | ⊢ |
| : , : , : |
113 | instantiation | 381, 207, 538, 598, 540, 410, 411, 204, 155 | ⊢ |
| : , : , : , : , : , : , : , : , : , : |
114 | instantiation | 542, 156 | ⊢ |
| : , : , : |
115 | instantiation | 157, 379, 158, 207, 208, 159* | ⊢ |
| : , : , : , : , : |
116 | instantiation | 385, 160 | ⊢ |
| : , : |
117 | instantiation | 496 | ⊢ |
| : , : , : |
118 | instantiation | 608, 596, 161 | ⊢ |
| : , : , : |
119 | instantiation | 162, 597, 605 | ⊢ |
| : , : |
120 | instantiation | 552 | ⊢ |
| : , : |
121 | theorem | | ⊢ |
| proveit.core_expr_types.tuples.range_len |
122 | instantiation | 163, 475, 164, 538, 165, 598 | ⊢ |
| : , : |
123 | instantiation | 542, 166 | ⊢ |
| : , : , : |
124 | instantiation | 209, 167, 168, 169 | ⊢ |
| : , : , : , : |
125 | theorem | | ⊢ |
| proveit.core_expr_types.tuples.range_from1_len |
126 | instantiation | 542, 170 | ⊢ |
| : , : , : |
127 | instantiation | 608, 594, 171 | ⊢ |
| : , : , : |
128 | instantiation | 172, 173 | ⊢ |
| : , : |
129 | instantiation | 529, 174, 175 | ⊢ |
| : , : , : |
130 | instantiation | 209, 176, 233, 177 | ⊢ |
| : , : , : , : |
131 | instantiation | 383, 551, 390, 391 | ⊢ |
| : , : |
132 | instantiation | 247, 410, 248, 178 | , ⊢ |
| : , : , : , : |
133 | theorem | | ⊢ |
| proveit.linear_algebra.addition.vec_sum_split_after |
134 | instantiation | 179, 180 | ⊢ |
| : , : |
135 | instantiation | 181, 182, 183, 470, 184, 185*, 186* | ⊢ |
| : , : , : |
136 | instantiation | 529, 187, 188 | ⊢ |
| : , : , : |
137 | theorem | | ⊢ |
| proveit.linear_algebra.addition.vec_sum_index_shift |
138 | instantiation | 572, 369, 574 | ⊢ |
| : , : |
139 | instantiation | 333, 452, 189 | ⊢ |
| : , : |
140 | instantiation | 529, 190, 191 | ⊢ |
| : , : , : |
141 | instantiation | 262, 452 | ⊢ |
| : |
142 | instantiation | 284, 605 | ⊢ |
| : , : , : , : , : , : , : |
143 | generalization | 192 | ⊢ |
144 | instantiation | 542, 193, 194*, 195* | ⊢ |
| : , : , : |
145 | instantiation | 385, 196 | ⊢ |
| : , : |
146 | instantiation | 542, 197 | ⊢ |
| : , : , : |
147 | instantiation | 198, 597, 548 | , ⊢ |
| : , : |
148 | instantiation | 317, 598, 605, 538, 379, 540 | ⊢ |
| : , : , : , : , : , : , : , : , : , : , : |
149 | generalization | 199 | ⊢ |
150 | instantiation | 381, 315, 538, 598, 540, 410, 411, 413, 205 | ⊢ |
| : , : , : , : , : , : , : , : , : , : |
151 | theorem | | ⊢ |
| proveit.linear_algebra.tensors.tensor_prod_factorization_from_add |
152 | instantiation | 434, 200 | ⊢ |
| : |
153 | instantiation | 552 | ⊢ |
| : , : |
154 | instantiation | 201, 607, 202, 435 | ⊢ |
| : , : , : |
155 | instantiation | 378, 411, 208, 205 | ⊢ |
| : , : , : , : |
156 | instantiation | 381, 208, 598, 538, 540, 410, 411, 204, 205 | ⊢ |
| : , : , : , : , : , : , : , : , : , : |
157 | theorem | | ⊢ |
| proveit.linear_algebra.scalar_multiplication.doubly_scaled_as_singly_scaled |
158 | instantiation | 408, 607, 409, 410, 411, 203, 204, 205 | ⊢ |
| : , : , : , : |
159 | instantiation | 206, 207, 208 | ⊢ |
| : , : |
160 | instantiation | 209, 210, 211, 212 | ⊢ |
| : , : , : , : |
161 | instantiation | 213, 214 | ⊢ |
| : |
162 | theorem | | ⊢ |
| proveit.numbers.addition.add_nat_pos_closure_bin |
163 | theorem | | ⊢ |
| proveit.numbers.addition.add_nat_closure |
164 | instantiation | 496 | ⊢ |
| : , : , : |
165 | instantiation | 215, 216 | ⊢ |
| : |
166 | instantiation | 217, 332, 551, 218* | ⊢ |
| : , : |
167 | instantiation | 480, 598, 610, 219, 269, 550, 503, 551 | ⊢ |
| : , : , : , : , : , : |
168 | instantiation | 270, 538, 475, 540, 220, 550, 503, 551 | ⊢ |
| : , : , : , : |
169 | instantiation | 232, 551, 550, 233 | ⊢ |
| : , : , : |
170 | instantiation | 542, 221 | ⊢ |
| : , : , : |
171 | instantiation | 608, 603, 546 | ⊢ |
| : , : , : |
172 | theorem | | ⊢ |
| proveit.numbers.ordering.relax_less |
173 | instantiation | 227, 597 | ⊢ |
| : |
174 | instantiation | 480, 598, 610, 538, 265, 540, 269, 332, 551 | ⊢ |
| : , : , : , : , : , : |
175 | instantiation | 270, 538, 610, 540, 265, 332, 551 | ⊢ |
| : , : , : , : |
176 | instantiation | 529, 222, 223 | ⊢ |
| : , : , : |
177 | instantiation | 385, 224 | ⊢ |
| : , : |
178 | instantiation | 378, 410, 225, 413 | , ⊢ |
| : , : , : , : |
179 | theorem | | ⊢ |
| proveit.numbers.addition.subtraction.nonneg_difference |
180 | instantiation | 331, 435 | ⊢ |
| : |
181 | theorem | | ⊢ |
| proveit.numbers.addition.strong_bound_via_left_term_bound |
182 | instantiation | 608, 594, 226 | ⊢ |
| : , : , : |
183 | theorem | | ⊢ |
| proveit.numbers.number_sets.real_numbers.zero_is_real |
184 | instantiation | 227, 435 | ⊢ |
| : |
185 | instantiation | 529, 228, 229 | ⊢ |
| : , : , : |
186 | instantiation | 529, 230, 231 | ⊢ |
| : , : , : |
187 | instantiation | 480, 538, 610, 598, 540, 271, 452, 503, 551 | ⊢ |
| : , : , : , : , : , : |
188 | instantiation | 232, 551, 452, 233 | ⊢ |
| : , : , : |
189 | instantiation | 500 | ⊢ |
| : |
190 | instantiation | 480, 538, 610, 598, 540, 234, 277, 503, 278 | ⊢ |
| : , : , : , : , : , : |
191 | instantiation | 529, 235, 236 | ⊢ |
| : , : , : |
192 | instantiation | 471, 237, 238 | , ⊢ |
| : , : , : |
193 | modus ponens | 239, 240 | ⊢ |
194 | instantiation | 241, 548 | ⊢ |
| : , : |
195 | instantiation | 241, 548 | ⊢ |
| : , : |
196 | modus ponens | 242, 243 | ⊢ |
197 | instantiation | 385, 244 | ⊢ |
| : , : |
198 | theorem | | ⊢ |
| proveit.physics.quantum.algebra.prepend_num_ket_with_zero_ket |
199 | instantiation | 408, 607, 409, 410, 411, 245, 248, 291 | , ⊢ |
| : , : , : , : |
200 | instantiation | 246, 607, 435 | ⊢ |
| : , : |
201 | theorem | | ⊢ |
| proveit.linear_algebra.tensors.tensor_prod_of_cart_exps_within_cart_exp |
202 | instantiation | 552 | ⊢ |
| : , : |
203 | instantiation | 552 | ⊢ |
| : , : |
204 | instantiation | 247, 410, 248, 249 | ⊢ |
| : , : , : , : |
205 | modus ponens | 250, 251 | ⊢ |
206 | axiom | | ⊢ |
| proveit.linear_algebra.scalar_multiplication.scalar_mult_extends_number_mult |
207 | instantiation | 383, 551, 252, 253 | ⊢ |
| : , : |
208 | instantiation | 383, 551, 254, 255 | ⊢ |
| : , : |
209 | theorem | | ⊢ |
| proveit.logic.equality.four_chain_transitivity |
210 | instantiation | 529, 256, 257 | ⊢ |
| : , : , : |
211 | instantiation | 500 | ⊢ |
| : |
212 | instantiation | 385, 258 | ⊢ |
| : , : |
213 | theorem | | ⊢ |
| proveit.numbers.negation.nat_pos_closure |
214 | instantiation | 259, 597 | ⊢ |
| : |
215 | theorem | | ⊢ |
| proveit.numbers.negation.nat_closure |
216 | instantiation | 260, 546, 261 | ⊢ |
| : |
217 | theorem | | ⊢ |
| proveit.numbers.negation.distribute_neg_through_binary_sum |
218 | instantiation | 262, 550 | ⊢ |
| : |
219 | instantiation | 552 | ⊢ |
| : , : |
220 | instantiation | 496 | ⊢ |
| : , : , : |
221 | instantiation | 263, 475, 598, 538, 264, 540, 570, 495, 508, 452, 509 | ⊢ |
| : , : , : , : , : , : , : |
222 | instantiation | 480, 598, 610, 538, 265, 540, 550, 332, 551 | ⊢ |
| : , : , : , : , : , : |
223 | instantiation | 266, 550, 551, 334 | ⊢ |
| : , : , : |
224 | instantiation | 267, 551 | ⊢ |
| : |
225 | instantiation | 468, 415, 268 | , ⊢ |
| : , : |
226 | instantiation | 608, 603, 563 | ⊢ |
| : , : , : |
227 | theorem | | ⊢ |
| proveit.numbers.number_sets.natural_numbers.natural_pos_is_pos |
228 | instantiation | 480, 598, 610, 538, 271, 540, 269, 452, 503 | ⊢ |
| : , : , : , : , : , : |
229 | instantiation | 270, 538, 610, 540, 271, 452, 503 | ⊢ |
| : , : , : , : |
230 | instantiation | 480, 598, 610, 538, 271, 540, 452, 503 | ⊢ |
| : , : , : , : , : , : |
231 | instantiation | 275, 538, 610, 598, 540, 272, 452, 503, 273* | ⊢ |
| : , : , : , : , : , : |
232 | theorem | | ⊢ |
| proveit.numbers.addition.subtraction.add_cancel_triple_32 |
233 | instantiation | 500 | ⊢ |
| : |
234 | instantiation | 552 | ⊢ |
| : , : |
235 | instantiation | 274, 598, 538, 540, 277, 503, 278 | ⊢ |
| : , : , : , : , : , : , : |
236 | instantiation | 275, 538, 610, 598, 540, 276, 277, 278, 503, 279* | ⊢ |
| : , : , : , : , : , : |
237 | instantiation | 351, 280, 281 | , ⊢ |
| : , : , : |
238 | instantiation | 529, 282, 283 | , ⊢ |
| : , : , : |
239 | instantiation | 284, 605 | ⊢ |
| : , : , : , : , : , : , : |
240 | generalization | 285 | ⊢ |
241 | theorem | | ⊢ |
| proveit.core_expr_types.conditionals.satisfied_condition_reduction |
242 | instantiation | 286, 605, 379, 315 | ⊢ |
| : , : , : , : , : , : , : , : |
243 | modus ponens | 287, 288 | ⊢ |
244 | modus ponens | 289, 290 | ⊢ |
245 | instantiation | 552 | ⊢ |
| : , : |
246 | theorem | | ⊢ |
| proveit.numbers.multiplication.mult_nat_pos_closure_bin |
247 | theorem | | ⊢ |
| proveit.linear_algebra.addition.binary_closure |
248 | theorem | | ⊢ |
| proveit.physics.quantum.algebra.ket_zero_in_qubit_space |
249 | instantiation | 378, 410, 315, 413 | ⊢ |
| : , : , : , : |
250 | instantiation | 316, 605, 411 | ⊢ |
| : , : , : , : , : , : |
251 | generalization | 291 | ⊢ |
252 | instantiation | 468, 570, 292 | ⊢ |
| : , : |
253 | instantiation | 351, 391, 389 | ⊢ |
| : , : , : |
254 | instantiation | 468, 570, 354 | ⊢ |
| : , : |
255 | instantiation | 351, 395, 393 | ⊢ |
| : , : , : |
256 | instantiation | 542, 293 | ⊢ |
| : , : , : |
257 | instantiation | 514, 551, 294, 295, 296* | ⊢ |
| : , : |
258 | instantiation | 529, 297, 298 | ⊢ |
| : , : , : |
259 | theorem | | ⊢ |
| proveit.numbers.negation.int_neg_closure |
260 | theorem | | ⊢ |
| proveit.numbers.number_sets.integers.nonpos_int_is_int_nonpos |
261 | instantiation | 299, 365, 565, 564, 300, 301*, 302* | ⊢ |
| : , : , : |
262 | theorem | | ⊢ |
| proveit.numbers.negation.double_negation |
263 | theorem | | ⊢ |
| proveit.numbers.multiplication.leftward_commutation |
264 | instantiation | 496 | ⊢ |
| : , : , : |
265 | instantiation | 552 | ⊢ |
| : , : |
266 | theorem | | ⊢ |
| proveit.numbers.addition.subtraction.add_cancel_triple_12 |
267 | theorem | | ⊢ |
| proveit.numbers.addition.elim_zero_left |
268 | instantiation | 471, 303, 304 | , ⊢ |
| : , : , : |
269 | theorem | | ⊢ |
| proveit.numbers.number_sets.complex_numbers.zero_is_complex |
270 | theorem | | ⊢ |
| proveit.numbers.addition.elim_zero_any |
271 | instantiation | 552 | ⊢ |
| : , : |
272 | instantiation | 552 | ⊢ |
| : , : |
273 | instantiation | 385, 305, 403* | ⊢ |
| : , : |
274 | theorem | | ⊢ |
| proveit.numbers.addition.leftward_commutation |
275 | theorem | | ⊢ |
| proveit.numbers.addition.association |
276 | instantiation | 552 | ⊢ |
| : , : |
277 | instantiation | 608, 581, 306 | ⊢ |
| : , : , : |
278 | instantiation | 608, 581, 307 | ⊢ |
| : , : , : |
279 | instantiation | 529, 308, 309, 310* | ⊢ |
| : , : , : |
280 | instantiation | 542, 311 | , ⊢ |
| : , : , : |
281 | instantiation | 312, 454, 416, 350 | , ⊢ |
| : , : , : |
282 | instantiation | 385, 313 | , ⊢ |
| : , : |
283 | instantiation | 314, 597, 548 | , ⊢ |
| : , : |
284 | theorem | | ⊢ |
| proveit.core_expr_types.lambda_maps.general_lambda_substitution |
285 | instantiation | 544, 382, 315 | , ⊢ |
| : , : |
286 | theorem | | ⊢ |
| proveit.linear_algebra.scalar_multiplication.distribution_over_vec_sum_with_scalar_mult |
287 | instantiation | 316, 605, 379 | ⊢ |
| : , : , : , : , : , : |
288 | generalization | 352 | ⊢ |
289 | instantiation | 317, 598, 605, 538, 379, 540 | ⊢ |
| : , : , : , : , : , : , : , : , : , : , : |
290 | generalization | 318 | ⊢ |
291 | instantiation | 378, 411, 382, 414 | , ⊢ |
| : , : , : , : |
292 | instantiation | 549, 319, 320 | ⊢ |
| : , : |
293 | instantiation | 529, 321, 322 | ⊢ |
| : , : , : |
294 | instantiation | 507, 390, 394 | ⊢ |
| : , : |
295 | instantiation | 323, 610, 324, 325, 326 | ⊢ |
| : , : |
296 | instantiation | 529, 327, 328 | ⊢ |
| : , : , : |
297 | instantiation | 542, 329 | ⊢ |
| : , : , : |
298 | instantiation | 542, 330 | ⊢ |
| : , : , : |
299 | theorem | | ⊢ |
| proveit.numbers.addition.weak_bound_via_left_term_bound |
300 | instantiation | 331, 597 | ⊢ |
| : |
301 | instantiation | 417, 551, 332 | ⊢ |
| : , : |
302 | instantiation | 333, 550, 334 | ⊢ |
| : , : |
303 | instantiation | 507, 474, 335 | , ⊢ |
| : , : |
304 | instantiation | 529, 336, 337 | , ⊢ |
| : , : , : |
305 | instantiation | 537, 538, 610, 598, 540, 338, 551, 452, 344* | ⊢ |
| : , : , : , : , : , : |
306 | instantiation | 608, 594, 339 | ⊢ |
| : , : , : |
307 | instantiation | 608, 594, 340 | ⊢ |
| : , : , : |
308 | instantiation | 542, 341 | ⊢ |
| : , : , : |
309 | instantiation | 385, 342 | ⊢ |
| : , : |
310 | instantiation | 529, 343, 344 | ⊢ |
| : , : , : |
311 | instantiation | 537, 345, 610, 538, 346, 347, 540, 570, 495, 508, 509, 494, 452 | , ⊢ |
| : , : , : , : , : , : |
312 | theorem | | ⊢ |
| proveit.numbers.exponentiation.product_of_complex_powers |
313 | instantiation | 348, 349 | , ⊢ |
| : , : , : |
314 | theorem | | ⊢ |
| proveit.physics.quantum.algebra.prepend_num_ket_with_one_ket |
315 | instantiation | 468, 415, 350 | ⊢ |
| : , : |
316 | theorem | | ⊢ |
| proveit.linear_algebra.addition.summation_closure |
317 | theorem | | ⊢ |
| proveit.linear_algebra.tensors.tensor_prod_distribution_over_summation_with_scalar_mult |
318 | instantiation | 351, 352, 353 | , ⊢ |
| : , : , : |
319 | instantiation | 383, 536, 570, 515 | ⊢ |
| : , : |
320 | instantiation | 518, 354 | ⊢ |
| : |
321 | instantiation | 542, 478 | ⊢ |
| : , : , : |
322 | instantiation | 529, 355, 356 | ⊢ |
| : , : , : |
323 | theorem | | ⊢ |
| proveit.numbers.multiplication.mult_not_eq_zero |
324 | instantiation | 552 | ⊢ |
| : , : |
325 | instantiation | 357, 390, 391 | ⊢ |
| : |
326 | instantiation | 357, 394, 395 | ⊢ |
| : |
327 | instantiation | 542, 358 | ⊢ |
| : , : , : |
328 | instantiation | 529, 359, 360 | ⊢ |
| : , : , : |
329 | instantiation | 529, 361, 362 | ⊢ |
| : , : , : |
330 | instantiation | 529, 363, 364 | ⊢ |
| : , : , : |
331 | theorem | | ⊢ |
| proveit.numbers.number_sets.natural_numbers.natural_pos_lower_bound |
332 | instantiation | 608, 581, 365 | ⊢ |
| : , : , : |
333 | theorem | | ⊢ |
| proveit.numbers.addition.subtraction.add_cancel_basic |
334 | instantiation | 500 | ⊢ |
| : |
335 | instantiation | 471, 366, 367 | , ⊢ |
| : , : , : |
336 | instantiation | 502, 598, 475, 538, 368, 540, 474, 508, 430, 509 | , ⊢ |
| : , : , : , : , : , : |
337 | instantiation | 502, 538, 610, 475, 540, 476, 368, 570, 495, 508, 430, 509 | , ⊢ |
| : , : , : , : , : , : |
338 | instantiation | 552 | ⊢ |
| : , : |
339 | instantiation | 608, 603, 369 | ⊢ |
| : , : , : |
340 | instantiation | 608, 603, 370 | ⊢ |
| : , : , : |
341 | instantiation | 385, 371 | ⊢ |
| : , : |
342 | instantiation | 537, 538, 610, 598, 540, 372, 570, 503, 452 | ⊢ |
| : , : , : , : , : , : |
343 | instantiation | 542, 373 | ⊢ |
| : , : , : |
344 | instantiation | 449, 452 | ⊢ |
| : |
345 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.nat4 |
346 | instantiation | 374 | ⊢ |
| : , : , : , : |
347 | instantiation | 552 | ⊢ |
| : , : |
348 | theorem | | ⊢ |
| proveit.physics.quantum.algebra.num_ket_eq |
349 | instantiation | 385, 375 | , ⊢ |
| : , : |
350 | instantiation | 471, 376, 377 | ⊢ |
| : , : , : |
351 | theorem | | ⊢ |
| proveit.logic.equality.sub_left_side_into |
352 | instantiation | 378, 379, 382, 380 | , ⊢ |
| : , : , : , : |
353 | instantiation | 381, 382, 598, 538, 540, 410, 411, 413, 414 | , ⊢ |
| : , : , : , : , : , : , : , : , : , : |
354 | instantiation | 383, 550, 570, 515 | ⊢ |
| : , : |
355 | instantiation | 542, 384 | ⊢ |
| : , : , : |
356 | instantiation | 385, 386 | ⊢ |
| : , : |
357 | theorem | | ⊢ |
| proveit.numbers.number_sets.complex_numbers.nonzero_complex_is_complex_nonzero |
358 | instantiation | 387, 390, 394, 466, 391, 395, 445*, 448* | ⊢ |
| : , : , : |
359 | instantiation | 502, 598, 610, 538, 388, 540, 551, 446, 450 | ⊢ |
| : , : , : , : , : , : |
360 | instantiation | 519, 538, 610, 540, 388, 446, 450 | ⊢ |
| : , : , : , : |
361 | instantiation | 542, 389 | ⊢ |
| : , : , : |
362 | instantiation | 514, 551, 390, 391, 392* | ⊢ |
| : , : |
363 | instantiation | 542, 393 | ⊢ |
| : , : , : |
364 | instantiation | 514, 551, 394, 395, 396* | ⊢ |
| : , : |
365 | instantiation | 608, 594, 397 | ⊢ |
| : , : , : |
366 | instantiation | 507, 398, 509 | , ⊢ |
| : , : |
367 | instantiation | 502, 538, 610, 598, 540, 399, 508, 430, 509 | , ⊢ |
| : , : , : , : , : , : |
368 | instantiation | 496 | ⊢ |
| : , : , : |
369 | instantiation | 400, 604, 573 | ⊢ |
| : , : |
370 | instantiation | 586, 573 | ⊢ |
| : |
371 | instantiation | 401, 452 | ⊢ |
| : |
372 | instantiation | 552 | ⊢ |
| : , : |
373 | instantiation | 402, 551, 570, 403 | ⊢ |
| : , : , : |
374 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.tuple_len_4_typical_eq |
375 | instantiation | 417, 494, 452 | , ⊢ |
| : , : |
376 | instantiation | 507, 474, 404 | ⊢ |
| : , : |
377 | instantiation | 529, 405, 406 | ⊢ |
| : , : , : |
378 | theorem | | ⊢ |
| proveit.linear_algebra.scalar_multiplication.scalar_mult_closure |
379 | instantiation | 407, 607, 409, 410, 411 | ⊢ |
| : , : , : |
380 | instantiation | 408, 607, 409, 410, 411, 412, 413, 414 | , ⊢ |
| : , : , : , : |
381 | theorem | | ⊢ |
| proveit.linear_algebra.tensors.factor_scalar_from_tensor_prod |
382 | instantiation | 468, 415, 416 | , ⊢ |
| : , : |
383 | theorem | | ⊢ |
| proveit.numbers.division.div_complex_closure |
384 | instantiation | 417, 499, 554 | ⊢ |
| : , : |
385 | theorem | | ⊢ |
| proveit.logic.equality.equals_reversal |
386 | instantiation | 418, 570, 419, 420 | ⊢ |
| : , : , : |
387 | theorem | | ⊢ |
| proveit.numbers.exponentiation.real_power_of_product |
388 | instantiation | 552 | ⊢ |
| : , : |
389 | instantiation | 542, 421 | ⊢ |
| : , : , : |
390 | instantiation | 422, 570 | ⊢ |
| : |
391 | instantiation | 426, 580, 423 | ⊢ |
| : , : |
392 | instantiation | 529, 424, 425 | ⊢ |
| : , : , : |
393 | instantiation | 542, 498 | ⊢ |
| : , : , : |
394 | instantiation | 468, 570, 499 | ⊢ |
| : , : |
395 | instantiation | 426, 580, 427 | ⊢ |
| : , : |
396 | instantiation | 529, 428, 429 | ⊢ |
| : , : , : |
397 | instantiation | 608, 603, 560 | ⊢ |
| : , : , : |
398 | instantiation | 507, 508, 430 | , ⊢ |
| : , : |
399 | instantiation | 552 | ⊢ |
| : , : |
400 | theorem | | ⊢ |
| proveit.numbers.multiplication.mult_int_closure_bin |
401 | theorem | | ⊢ |
| proveit.numbers.negation.mult_neg_one_left |
402 | theorem | | ⊢ |
| proveit.numbers.addition.subtraction.subtract_from_add |
403 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.add_1_1 |
404 | instantiation | 471, 431, 432 | ⊢ |
| : , : , : |
405 | instantiation | 502, 598, 475, 538, 433, 540, 474, 508, 509, 452 | ⊢ |
| : , : , : , : , : , : |
406 | instantiation | 502, 538, 610, 475, 540, 476, 433, 570, 495, 508, 509, 452 | ⊢ |
| : , : , : , : , : , : |
407 | theorem | | ⊢ |
| proveit.linear_algebra.tensors.tensor_prod_of_vec_spaces_is_vec_space |
408 | theorem | | ⊢ |
| proveit.linear_algebra.tensors.tensor_prod_is_in_tensor_prod_space |
409 | instantiation | 552 | ⊢ |
| : , : |
410 | instantiation | 434, 607 | ⊢ |
| : |
411 | instantiation | 434, 435 | ⊢ |
| : |
412 | instantiation | 552 | ⊢ |
| : , : |
413 | theorem | | ⊢ |
| proveit.physics.quantum.algebra.ket_one_in_qubit_space |
414 | instantiation | 436, 597, 548 | , ⊢ |
| : , : |
415 | instantiation | 608, 581, 437 | ⊢ |
| : , : , : |
416 | instantiation | 471, 438, 439 | , ⊢ |
| : , : , : |
417 | theorem | | ⊢ |
| proveit.numbers.addition.commutation |
418 | theorem | | ⊢ |
| proveit.numbers.exponentiation.product_of_pos_powers |
419 | instantiation | 608, 440, 591 | ⊢ |
| : , : , : |
420 | instantiation | 608, 440, 545 | ⊢ |
| : , : , : |
421 | instantiation | 529, 441, 442 | ⊢ |
| : , : , : |
422 | theorem | | ⊢ |
| proveit.numbers.exponentiation.sqrt_complex_closure |
423 | instantiation | 443, 444, 580 | ⊢ |
| : , : |
424 | instantiation | 542, 445 | ⊢ |
| : , : , : |
425 | instantiation | 449, 446 | ⊢ |
| : |
426 | theorem | | ⊢ |
| proveit.numbers.exponentiation.exp_rational_non_zero__not_zero |
427 | instantiation | 608, 447, 545 | ⊢ |
| : , : , : |
428 | instantiation | 542, 448 | ⊢ |
| : , : , : |
429 | instantiation | 449, 450 | ⊢ |
| : |
430 | instantiation | 468, 570, 451 | , ⊢ |
| : , : |
431 | instantiation | 507, 492, 452 | ⊢ |
| : , : |
432 | instantiation | 502, 538, 610, 598, 540, 493, 508, 509, 452 | ⊢ |
| : , : , : , : , : , : |
433 | instantiation | 496 | ⊢ |
| : , : , : |
434 | theorem | | ⊢ |
| proveit.linear_algebra.complex_vec_set_is_vec_space |
435 | instantiation | 453, 610, 585 | ⊢ |
| : , : |
436 | theorem | | ⊢ |
| proveit.physics.quantum.algebra.num_ket_in_register_space |
437 | instantiation | 608, 524, 454 | ⊢ |
| : , : , : |
438 | instantiation | 507, 474, 455 | , ⊢ |
| : , : |
439 | instantiation | 529, 456, 457 | , ⊢ |
| : , : , : |
440 | theorem | | ⊢ |
| proveit.numbers.number_sets.real_numbers.rational_pos_within_real_pos |
441 | instantiation | 529, 458, 459 | ⊢ |
| : , : , : |
442 | instantiation | 529, 460, 461 | ⊢ |
| : , : , : |
443 | theorem | | ⊢ |
| proveit.numbers.division.div_rational_nonzero_closure |
444 | instantiation | 608, 592, 462 | ⊢ |
| : , : , : |
445 | instantiation | 465, 570, 566, 466, 515, 463* | ⊢ |
| : , : , : |
446 | instantiation | 468, 570, 464 | ⊢ |
| : , : |
447 | theorem | | ⊢ |
| proveit.numbers.number_sets.rational_numbers.rational_pos_within_rational_nonzero |
448 | instantiation | 465, 570, 517, 466, 515, 467* | ⊢ |
| : , : , : |
449 | theorem | | ⊢ |
| proveit.numbers.multiplication.elim_one_left |
450 | instantiation | 468, 570, 482 | ⊢ |
| : , : |
451 | instantiation | 518, 469 | , ⊢ |
| : |
452 | instantiation | 608, 581, 470 | ⊢ |
| : , : , : |
453 | theorem | | ⊢ |
| proveit.numbers.exponentiation.exp_natpos_closure |
454 | theorem | | ⊢ |
| proveit.numbers.number_sets.real_numbers.e_is_real_pos |
455 | instantiation | 471, 472, 473 | , ⊢ |
| : , : , : |
456 | instantiation | 502, 598, 475, 538, 477, 540, 474, 508, 509, 494 | , ⊢ |
| : , : , : , : , : , : |
457 | instantiation | 502, 538, 610, 475, 540, 476, 477, 570, 495, 508, 509, 494 | , ⊢ |
| : , : , : , : , : , : |
458 | instantiation | 542, 478 | ⊢ |
| : , : , : |
459 | instantiation | 542, 479 | ⊢ |
| : , : , : |
460 | instantiation | 480, 538, 610, 598, 540, 481, 499, 554, 482 | ⊢ |
| : , : , : , : , : , : |
461 | instantiation | 483, 499, 554, 484 | ⊢ |
| : , : , : |
462 | instantiation | 608, 602, 605 | ⊢ |
| : , : , : |
463 | instantiation | 485, 554, 551, 541* | ⊢ |
| : , : |
464 | instantiation | 608, 581, 486 | ⊢ |
| : , : , : |
465 | theorem | | ⊢ |
| proveit.numbers.exponentiation.real_power_of_real_power |
466 | instantiation | 608, 594, 487 | ⊢ |
| : , : , : |
467 | instantiation | 529, 488, 489 | ⊢ |
| : , : , : |
468 | theorem | | ⊢ |
| proveit.numbers.exponentiation.exp_complex_closure |
469 | instantiation | 608, 581, 490 | , ⊢ |
| : , : , : |
470 | instantiation | 608, 594, 491 | ⊢ |
| : , : , : |
471 | theorem | | ⊢ |
| proveit.logic.equality.sub_right_side_into |
472 | instantiation | 507, 492, 494 | , ⊢ |
| : , : |
473 | instantiation | 502, 538, 610, 598, 540, 493, 508, 509, 494 | , ⊢ |
| : , : , : , : , : , : |
474 | instantiation | 507, 570, 495 | ⊢ |
| : , : |
475 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.nat3 |
476 | instantiation | 552 | ⊢ |
| : , : |
477 | instantiation | 496 | ⊢ |
| : , : , : |
478 | instantiation | 514, 536, 570, 515, 497* | ⊢ |
| : , : |
479 | instantiation | 542, 498 | ⊢ |
| : , : , : |
480 | theorem | | ⊢ |
| proveit.numbers.addition.disassociation |
481 | instantiation | 552 | ⊢ |
| : , : |
482 | instantiation | 518, 499 | ⊢ |
| : |
483 | theorem | | ⊢ |
| proveit.numbers.addition.subtraction.add_cancel_triple_13 |
484 | instantiation | 500 | ⊢ |
| : |
485 | theorem | | ⊢ |
| proveit.numbers.negation.pos_times_neg |
486 | instantiation | 501, 566 | ⊢ |
| : |
487 | instantiation | 608, 603, 574 | ⊢ |
| : , : , : |
488 | instantiation | 502, 538, 610, 598, 540, 520, 554, 550, 503 | ⊢ |
| : , : , : , : , : , : |
489 | instantiation | 504, 610, 538, 520, 540, 554, 550, 551, 505* | ⊢ |
| : , : , : , : , : |
490 | instantiation | 608, 594, 506 | , ⊢ |
| : , : , : |
491 | instantiation | 608, 603, 573 | ⊢ |
| : , : , : |
492 | instantiation | 507, 508, 509 | ⊢ |
| : , : |
493 | instantiation | 552 | ⊢ |
| : , : |
494 | instantiation | 608, 581, 510 | , ⊢ |
| : , : , : |
495 | instantiation | 608, 581, 511 | ⊢ |
| : , : , : |
496 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.tuple_len_3_typical_eq |
497 | instantiation | 529, 512, 513 | ⊢ |
| : , : , : |
498 | instantiation | 514, 550, 570, 515, 516* | ⊢ |
| : , : |
499 | instantiation | 608, 581, 517 | ⊢ |
| : , : , : |
500 | axiom | | ⊢ |
| proveit.logic.equality.equals_reflexivity |
501 | theorem | | ⊢ |
| proveit.numbers.negation.real_closure |
502 | theorem | | ⊢ |
| proveit.numbers.multiplication.disassociation |
503 | instantiation | 518, 551 | ⊢ |
| : |
504 | theorem | | ⊢ |
| proveit.numbers.multiplication.mult_neg_any |
505 | instantiation | 519, 610, 538, 520, 540, 554, 550 | ⊢ |
| : , : , : , : |
506 | instantiation | 608, 603, 521 | , ⊢ |
| : , : , : |
507 | theorem | | ⊢ |
| proveit.numbers.multiplication.mult_complex_closure_bin |
508 | theorem | | ⊢ |
| proveit.numbers.number_sets.complex_numbers.i_is_complex |
509 | instantiation | 608, 581, 522 | ⊢ |
| : , : , : |
510 | instantiation | 608, 594, 523 | , ⊢ |
| : , : , : |
511 | instantiation | 608, 524, 525 | ⊢ |
| : , : , : |
512 | instantiation | 542, 543 | ⊢ |
| : , : , : |
513 | instantiation | 529, 526, 527 | ⊢ |
| : , : , : |
514 | theorem | | ⊢ |
| proveit.numbers.division.div_as_mult |
515 | instantiation | 528, 607 | ⊢ |
| : |
516 | instantiation | 529, 530, 531 | ⊢ |
| : , : , : |
517 | instantiation | 608, 594, 532 | ⊢ |
| : , : , : |
518 | theorem | | ⊢ |
| proveit.numbers.negation.complex_closure |
519 | theorem | | ⊢ |
| proveit.numbers.multiplication.elim_one_any |
520 | instantiation | 552 | ⊢ |
| : , : |
521 | instantiation | 608, 533, 534 | , ⊢ |
| : , : , : |
522 | theorem | | ⊢ |
| proveit.physics.quantum.QPE._phase_is_real |
523 | instantiation | 608, 603, 535 | , ⊢ |
| : , : , : |
524 | theorem | | ⊢ |
| proveit.numbers.number_sets.real_numbers.real_pos_within_real |
525 | theorem | | ⊢ |
| proveit.numbers.number_sets.real_numbers.pi_is_real_pos |
526 | instantiation | 544, 536, 554 | ⊢ |
| : , : |
527 | instantiation | 537, 598, 610, 538, 539, 540, 554, 550, 551, 541* | ⊢ |
| : , : , : , : , : , : |
528 | theorem | | ⊢ |
| proveit.numbers.number_sets.natural_numbers.nonzero_if_is_nat_pos |
529 | axiom | | ⊢ |
| proveit.logic.equality.equals_transitivity |
530 | instantiation | 542, 543 | ⊢ |
| : , : , : |
531 | instantiation | 544, 550, 554 | ⊢ |
| : , : |
532 | instantiation | 608, 590, 545 | ⊢ |
| : , : , : |
533 | instantiation | 561, 546, 562 | ⊢ |
| : , : |
534 | assumption | | ⊢ |
535 | instantiation | 608, 547, 548 | , ⊢ |
| : , : , : |
536 | instantiation | 549, 550, 551 | ⊢ |
| : , : |
537 | theorem | | ⊢ |
| proveit.numbers.multiplication.distribute_through_sum |
538 | axiom | | ⊢ |
| proveit.numbers.number_sets.natural_numbers.zero_in_nats |
539 | instantiation | 552 | ⊢ |
| : , : |
540 | theorem | | ⊢ |
| proveit.core_expr_types.tuples.tuple_len_0_typical_eq |
541 | instantiation | 553, 554 | ⊢ |
| : |
542 | axiom | | ⊢ |
| proveit.logic.equality.substitution |
543 | instantiation | 555, 556, 605, 557* | ⊢ |
| : , : |
544 | theorem | | ⊢ |
| proveit.numbers.multiplication.commutation |
545 | instantiation | 558, 591, 559 | ⊢ |
| : , : |
546 | instantiation | 572, 560, 589 | ⊢ |
| : , : |
547 | instantiation | 561, 562, 563 | ⊢ |
| : , : |
548 | assumption | | ⊢ |
549 | theorem | | ⊢ |
| proveit.numbers.addition.add_complex_closure_bin |
550 | instantiation | 608, 581, 564 | ⊢ |
| : , : , : |
551 | instantiation | 608, 581, 565 | ⊢ |
| : , : , : |
552 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.tuple_len_2_typical_eq |
553 | theorem | | ⊢ |
| proveit.numbers.multiplication.elim_one_right |
554 | instantiation | 608, 581, 566 | ⊢ |
| : , : , : |
555 | theorem | | ⊢ |
| proveit.numbers.exponentiation.neg_power_as_div |
556 | instantiation | 608, 567, 568 | ⊢ |
| : , : , : |
557 | instantiation | 569, 570 | ⊢ |
| : |
558 | theorem | | ⊢ |
| proveit.numbers.multiplication.mult_rational_pos_closure_bin |
559 | instantiation | 608, 606, 597 | ⊢ |
| : , : , : |
560 | instantiation | 586, 571 | ⊢ |
| : |
561 | theorem | | ⊢ |
| proveit.numbers.number_sets.integers.int_interval_within_int |
562 | theorem | | ⊢ |
| proveit.numbers.number_sets.integers.zero_is_int |
563 | instantiation | 572, 573, 574 | ⊢ |
| : , : |
564 | instantiation | 575, 576, 597 | ⊢ |
| : , : , : |
565 | instantiation | 608, 594, 577 | ⊢ |
| : , : , : |
566 | instantiation | 608, 594, 578 | ⊢ |
| : , : , : |
567 | theorem | | ⊢ |
| proveit.numbers.number_sets.complex_numbers.real_nonzero_within_complex_nonzero |
568 | instantiation | 608, 579, 580 | ⊢ |
| : , : , : |
569 | theorem | | ⊢ |
| proveit.numbers.exponentiation.complex_x_to_first_power_is_x |
570 | instantiation | 608, 581, 582 | ⊢ |
| : , : , : |
571 | instantiation | 608, 583, 597 | ⊢ |
| : , : , : |
572 | theorem | | ⊢ |
| proveit.numbers.addition.add_int_closure_bin |
573 | instantiation | 584, 604, 585 | ⊢ |
| : , : |
574 | instantiation | 586, 589 | ⊢ |
| : |
575 | theorem | | ⊢ |
| proveit.logic.sets.inclusion.unfold_subset_eq |
576 | instantiation | 587, 588 | ⊢ |
| : , : |
577 | instantiation | 608, 603, 589 | ⊢ |
| : , : , : |
578 | instantiation | 608, 590, 591 | ⊢ |
| : , : , : |
579 | theorem | | ⊢ |
| proveit.numbers.number_sets.real_numbers.rational_nonzero_within_real_nonzero |
580 | instantiation | 608, 592, 593 | ⊢ |
| : , : , : |
581 | theorem | | ⊢ |
| proveit.numbers.number_sets.complex_numbers.real_within_complex |
582 | instantiation | 608, 594, 595 | ⊢ |
| : , : , : |
583 | theorem | | ⊢ |
| proveit.numbers.number_sets.integers.nat_pos_within_int |
584 | theorem | | ⊢ |
| proveit.numbers.exponentiation.exp_int_closure |
585 | instantiation | 608, 596, 597 | ⊢ |
| : , : , : |
586 | theorem | | ⊢ |
| proveit.numbers.negation.int_closure |
587 | theorem | | ⊢ |
| proveit.logic.sets.inclusion.relax_proper_subset |
588 | theorem | | ⊢ |
| proveit.numbers.number_sets.real_numbers.nat_pos_within_real |
589 | instantiation | 608, 609, 598 | ⊢ |
| : , : , : |
590 | theorem | | ⊢ |
| proveit.numbers.number_sets.rational_numbers.rational_pos_within_rational |
591 | instantiation | 599, 600, 601 | ⊢ |
| : , : |
592 | theorem | | ⊢ |
| proveit.numbers.number_sets.rational_numbers.nonzero_int_within_rational_nonzero |
593 | instantiation | 608, 602, 607 | ⊢ |
| : , : , : |
594 | theorem | | ⊢ |
| proveit.numbers.number_sets.real_numbers.rational_within_real |
595 | instantiation | 608, 603, 604 | ⊢ |
| : , : , : |
596 | theorem | | ⊢ |
| proveit.numbers.number_sets.natural_numbers.nat_pos_within_nat |
597 | assumption | | ⊢ |
598 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.nat1 |
599 | theorem | | ⊢ |
| proveit.numbers.division.div_rational_pos_closure |
600 | instantiation | 608, 606, 605 | ⊢ |
| : , : , : |
601 | instantiation | 608, 606, 607 | ⊢ |
| : , : , : |
602 | theorem | | ⊢ |
| proveit.numbers.number_sets.integers.nat_pos_within_nonzero_int |
603 | theorem | | ⊢ |
| proveit.numbers.number_sets.rational_numbers.int_within_rational |
604 | instantiation | 608, 609, 610 | ⊢ |
| : , : , : |
605 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.posnat1 |
606 | theorem | | ⊢ |
| proveit.numbers.number_sets.rational_numbers.nat_pos_within_rational_pos |
607 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.posnat2 |
608 | theorem | | ⊢ |
| proveit.logic.sets.inclusion.superset_membership_from_proper_subset |
609 | theorem | | ⊢ |
| proveit.numbers.number_sets.integers.nat_within_int |
610 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.nat2 |
*equality replacement requirements |