| step type | requirements | statement |
0 | generalization | 1 | ⊢ |
1 | instantiation | 331, 2, 3 | ⊢ |
| : , : , : |
2 | instantiation | 4, 5, 6 | ⊢ |
| : , : |
3 | instantiation | 7, 398, 8, 9, 10, 11 | ⊢ |
| : , : , : , : |
4 | theorem | | ⊢ |
| proveit.logic.equality.rhs_via_equality |
5 | instantiation | 306, 12, 13 | ⊢ |
| : , : , : |
6 | instantiation | 341, 14, 15*, 16*, 17* | ⊢ |
| : , : , : |
7 | axiom | | ⊢ |
| proveit.core_expr_types.operations.operands_substitution |
8 | instantiation | 338 | ⊢ |
| : , : |
9 | instantiation | 338 | ⊢ |
| : , : |
10 | instantiation | 107, 18 | ⊢ |
| : , : |
11 | instantiation | 341, 19 | ⊢ |
| : , : , : |
12 | instantiation | 306, 20, 21, 22* | ⊢ |
| : , : , : |
13 | modus ponens | 23, 152 | ⊢ |
14 | modus ponens | 24, 25 | ⊢ |
15 | instantiation | 101, 366 | ⊢ |
| : , : |
16 | instantiation | 101, 366 | ⊢ |
| : , : |
17 | instantiation | 331, 26, 27 | ⊢ |
| : , : , : |
18 | instantiation | 196, 28, 29, 30 | ⊢ |
| : , : , : , : |
19 | modus ponens | 31, 32 | ⊢ |
20 | instantiation | 306, 33, 34 | ⊢ |
| : , : , : |
21 | instantiation | 35, 400 | ⊢ |
| : |
22 | instantiation | 331, 36, 37 | ⊢ |
| : , : , : |
23 | instantiation | 38, 390, 398, 322, 210, 323, 39* | ⊢ |
| : , : , : , : , : , : , : , : |
24 | instantiation | 140, 390 | ⊢ |
| : , : , : , : , : , : , : |
25 | generalization | 40 | ⊢ |
26 | instantiation | 341, 41 | ⊢ |
| : , : , : |
27 | instantiation | 331, 42, 43 | ⊢ |
| : , : , : |
28 | instantiation | 315, 257, 227, 228, 44* | ⊢ |
| : , : |
29 | instantiation | 341, 45 | ⊢ |
| : , : , : |
30 | instantiation | 107, 46 | ⊢ |
| : , : |
31 | instantiation | 121, 390 | ⊢ |
| : , : , : , : , : , : |
32 | generalization | 47 | ⊢ |
33 | instantiation | 48, 356 | ⊢ |
| : |
34 | axiom | | ⊢ |
| proveit.physics.quantum.QPE._Psi_def |
35 | conjecture | | ⊢ |
| proveit.physics.quantum.QPE._psi_t_formula |
36 | instantiation | 341, 49 | ⊢ |
| : , : , : |
37 | instantiation | 331, 50, 51 | ⊢ |
| : , : , : |
38 | conjecture | | ⊢ |
| proveit.physics.quantum.algebra.qmult_distribution_over_summation |
39 | instantiation | 331, 52, 53 | ⊢ |
| : , : , : |
40 | instantiation | 54, 400, 366, 356, 55* | , ⊢ |
| : , : , : |
41 | instantiation | 331, 56, 57 | ⊢ |
| : , : , : |
42 | instantiation | 321, 403, 398, 322, 58, 323, 241, 60 | ⊢ |
| : , : , : , : , : , : |
43 | instantiation | 179, 322, 398, 403, 323, 59, 241, 60, 61* | ⊢ |
| : , : , : , : , : , : |
44 | instantiation | 331, 62, 63 | ⊢ |
| : , : , : |
45 | instantiation | 107, 64 | ⊢ |
| : , : |
46 | instantiation | 331, 65, 66 | ⊢ |
| : , : , : |
47 | instantiation | 138, 67 | ⊢ |
| : , : , : |
48 | axiom | | ⊢ |
| proveit.physics.quantum.QPE._alpha_m_def |
49 | instantiation | 196, 68, 69, 70 | ⊢ |
| : , : , : , : |
50 | instantiation | 331, 71, 72 | ⊢ |
| : , : , : |
51 | instantiation | 157, 158, 241, 73, 152, 74* | ⊢ |
| : , : , : |
52 | instantiation | 341, 75, 76*, 77* | ⊢ |
| : , : , : |
53 | modus ponens | 78, 79 | ⊢ |
54 | conjecture | | ⊢ |
| proveit.physics.quantum.QFT.invFT_on_matrix_elem |
55 | instantiation | 80, 226, 227, 228 | , ⊢ |
| : , : |
56 | instantiation | 341, 81 | ⊢ |
| : , : , : |
57 | instantiation | 331, 82, 83 | ⊢ |
| : , : , : |
58 | instantiation | 338 | ⊢ |
| : , : |
59 | instantiation | 338 | ⊢ |
| : , : |
60 | modus ponens | 84, 143 | ⊢ |
61 | instantiation | 85, 241, 390, 86*, 87* | ⊢ |
| : , : , : |
62 | instantiation | 341, 88 | ⊢ |
| : , : , : |
63 | instantiation | 290, 89 | ⊢ |
| : |
64 | instantiation | 90, 202, 361, 91* | ⊢ |
| : , : |
65 | instantiation | 341, 92 | ⊢ |
| : , : , : |
66 | instantiation | 184, 361, 93, 370, 316 | ⊢ |
| : , : , : |
67 | deduction | 94 | ⊢ |
68 | instantiation | 155, 241, 403, 322, 323, 95 | ⊢ |
| : , : , : , : , : , : |
69 | instantiation | 156, 403, 241, 95 | ⊢ |
| : , : , : , : , : |
70 | instantiation | 157, 392, 241, 151, 95 | ⊢ |
| : , : , : |
71 | instantiation | 331, 96, 97 | ⊢ |
| : , : , : |
72 | instantiation | 156, 403, 398, 241, 151, 152 | ⊢ |
| : , : , : , : , : |
73 | instantiation | 327 | ⊢ |
| : , : , : |
74 | instantiation | 175, 241, 98 | ⊢ |
| : , : |
75 | modus ponens | 99, 100 | ⊢ |
76 | instantiation | 101, 366 | ⊢ |
| : , : |
77 | instantiation | 101, 366 | ⊢ |
| : , : |
78 | instantiation | 102, 390 | ⊢ |
| : , : , : , : |
79 | generalization | 103 | ⊢ |
80 | conjecture | | ⊢ |
| proveit.numbers.division.neg_frac_neg_numerator |
81 | modus ponens | 104, 105 | ⊢ |
82 | instantiation | 341, 106 | ⊢ |
| : , : , : |
83 | instantiation | 107, 108 | ⊢ |
| : , : |
84 | instantiation | 109 | ⊢ |
| : , : , : |
85 | conjecture | | ⊢ |
| proveit.numbers.exponentiation.product_of_posnat_powers |
86 | instantiation | 360, 241 | ⊢ |
| : |
87 | conjecture | | ⊢ |
| proveit.numbers.numerals.decimals.add_1_1 |
88 | instantiation | 184, 361, 354, 232, 316, 110* | ⊢ |
| : , : , : |
89 | instantiation | 278, 361, 111 | ⊢ |
| : , : |
90 | conjecture | | ⊢ |
| proveit.numbers.multiplication.mult_neg_left |
91 | instantiation | 196, 112, 113, 127 | ⊢ |
| : , : , : , : |
92 | instantiation | 331, 114, 115 | ⊢ |
| : , : , : |
93 | instantiation | 116, 221 | ⊢ |
| : |
94 | instantiation | 343, 238, 181 | , ⊢ |
| : , : |
95 | instantiation | 190, 261, 244, 187 | ⊢ |
| : , : , : , : |
96 | instantiation | 155, 241, 403, 322, 323, 117 | ⊢ |
| : , : , : , : , : , : |
97 | instantiation | 150, 398, 392, 322, 206, 151, 323, 118 | ⊢ |
| : , : , : , : , : , : |
98 | instantiation | 280, 119, 172 | ⊢ |
| : , : , : |
99 | instantiation | 140, 390 | ⊢ |
| : , : , : , : , : , : , : |
100 | generalization | 120 | ⊢ |
101 | conjecture | | ⊢ |
| proveit.core_expr_types.conditionals.satisfied_condition_reduction |
102 | axiom | | ⊢ |
| proveit.linear_algebra.addition.scalar_sum_extends_number_sum |
103 | instantiation | 335, 238, 176 | , ⊢ |
| : , : |
104 | instantiation | 121, 390 | ⊢ |
| : , : , : , : , : , : |
105 | generalization | 122 | ⊢ |
106 | modus ponens | 123, 124 | ⊢ |
107 | theorem | | ⊢ |
| proveit.logic.equality.equals_reversal |
108 | instantiation | 125, 323, 241 | ⊢ |
| : , : |
109 | conjecture | | ⊢ |
| proveit.numbers.summation.summation_complex_closure |
110 | instantiation | 126, 344, 257, 127* | ⊢ |
| : , : |
111 | instantiation | 211, 344 | ⊢ |
| : |
112 | instantiation | 321, 322, 398, 403, 323, 234, 345, 344, 361 | ⊢ |
| : , : , : , : , : , : |
113 | instantiation | 331, 128, 129 | ⊢ |
| : , : , : |
114 | instantiation | 341, 282 | ⊢ |
| : , : , : |
115 | instantiation | 315, 257, 130, 281, 131* | ⊢ |
| : , : |
116 | conjecture | | ⊢ |
| proveit.numbers.negation.real_closure |
117 | instantiation | 280, 152, 132 | ⊢ |
| : , : , : |
118 | instantiation | 280, 133, 134 | ⊢ |
| : , : , : |
119 | instantiation | 207, 261, 262, 208, 187 | ⊢ |
| : , : , : , : |
120 | instantiation | 196, 135, 136, 137 | , ⊢ |
| : , : , : , : |
121 | axiom | | ⊢ |
| proveit.core_expr_types.lambda_maps.lambda_substitution |
122 | instantiation | 138, 139 | ⊢ |
| : , : , : |
123 | instantiation | 140, 390 | ⊢ |
| : , : , : , : , : , : , : |
124 | generalization | 141 | ⊢ |
125 | modus ponens | 142, 143 | ⊢ |
126 | conjecture | | ⊢ |
| proveit.numbers.multiplication.mult_neg_right |
127 | instantiation | 273, 344 | ⊢ |
| : |
128 | instantiation | 144, 322, 398, 323, 145, 345, 344, 361 | ⊢ |
| : , : , : , : , : , : , : |
129 | instantiation | 331, 146, 147 | ⊢ |
| : , : , : |
130 | instantiation | 278, 361, 202 | ⊢ |
| : , : |
131 | instantiation | 331, 148, 149 | ⊢ |
| : , : , : |
132 | instantiation | 150, 403, 392, 322, 151, 323, 152 | ⊢ |
| : , : , : , : , : , : |
133 | instantiation | 190, 261, 262, 153, 187 | ⊢ |
| : , : , : , : |
134 | instantiation | 209, 158, 154 | ⊢ |
| : , : , : |
135 | instantiation | 155, 238, 398, 322, 210, 323, 160 | , ⊢ |
| : , : , : , : , : , : |
136 | instantiation | 156, 398, 403, 238, 210, 160 | , ⊢ |
| : , : , : , : , : |
137 | instantiation | 157, 158, 238, 159, 160, 161* | , ⊢ |
| : , : , : |
138 | axiom | | ⊢ |
| proveit.core_expr_types.conditionals.conditional_substitution |
139 | deduction | 162 | ⊢ |
140 | conjecture | | ⊢ |
| proveit.core_expr_types.lambda_maps.general_lambda_substitution |
141 | instantiation | 331, 163, 164 | , ⊢ |
| : , : , : |
142 | instantiation | 165, 403, 390, 322 | ⊢ |
| : , : , : , : , : , : |
143 | generalization | 166 | ⊢ |
144 | conjecture | | ⊢ |
| proveit.numbers.multiplication.rightward_commutation |
145 | instantiation | 338 | ⊢ |
| : , : |
146 | instantiation | 179, 403, 398, 322, 167, 323, 344, 361, 345 | ⊢ |
| : , : , : , : , : , : |
147 | instantiation | 341, 168 | ⊢ |
| : , : , : |
148 | instantiation | 341, 169 | ⊢ |
| : , : , : |
149 | instantiation | 290, 170 | ⊢ |
| : |
150 | conjecture | | ⊢ |
| proveit.physics.quantum.algebra.qmult_disassociation |
151 | instantiation | 338 | ⊢ |
| : , : |
152 | instantiation | 280, 171, 172 | ⊢ |
| : , : , : |
153 | instantiation | 260, 261, 262, 173 | ⊢ |
| : , : , : |
154 | instantiation | 327 | ⊢ |
| : , : , : |
155 | conjecture | | ⊢ |
| proveit.physics.quantum.algebra.scalar_mult_absorption |
156 | conjecture | | ⊢ |
| proveit.physics.quantum.algebra.qmult_pulling_scalar_out_front |
157 | conjecture | | ⊢ |
| proveit.physics.quantum.algebra.scalar_mult_factorization |
158 | conjecture | | ⊢ |
| proveit.numbers.numerals.decimals.posnat3 |
159 | instantiation | 327 | ⊢ |
| : , : , : |
160 | instantiation | 280, 174, 192 | , ⊢ |
| : , : , : |
161 | instantiation | 175, 238, 176 | , ⊢ |
| : , : |
162 | instantiation | 321, 403, 398, 322, 177, 323, 238, 241, 181 | , ⊢ |
| : , : , : , : , : , : |
163 | instantiation | 178, 322, 403, 323, 238, 241, 181 | , ⊢ |
| : , : , : , : , : , : , : |
164 | instantiation | 179, 403, 398, 322, 180, 323, 241, 238, 181 | , ⊢ |
| : , : , : , : , : , : |
165 | conjecture | | ⊢ |
| proveit.numbers.multiplication.distribute_through_summation |
166 | instantiation | 335, 238, 181 | , ⊢ |
| : , : |
167 | instantiation | 338 | ⊢ |
| : , : |
168 | instantiation | 306, 182, 183 | ⊢ |
| : , : , : |
169 | instantiation | 184, 361, 221, 232, 316, 185* | ⊢ |
| : , : , : |
170 | instantiation | 278, 361, 186 | ⊢ |
| : , : |
171 | instantiation | 190, 261, 262, 208, 187 | ⊢ |
| : , : , : , : |
172 | instantiation | 209, 392, 210 | ⊢ |
| : , : , : |
173 | instantiation | 280, 188, 189 | ⊢ |
| : , : , : |
174 | instantiation | 190, 261, 262, 208, 239 | , ⊢ |
| : , : , : , : |
175 | axiom | | ⊢ |
| proveit.linear_algebra.scalar_multiplication.scalar_mult_extends_number_mult |
176 | instantiation | 280, 191, 192 | , ⊢ |
| : , : , : |
177 | instantiation | 338 | ⊢ |
| : , : |
178 | conjecture | | ⊢ |
| proveit.numbers.multiplication.leftward_commutation |
179 | conjecture | | ⊢ |
| proveit.numbers.multiplication.association |
180 | instantiation | 338 | ⊢ |
| : , : |
181 | instantiation | 278, 254, 193 | , ⊢ |
| : , : |
182 | instantiation | 306, 194, 195 | ⊢ |
| : , : , : |
183 | instantiation | 196, 197, 198, 199 | ⊢ |
| : , : , : , : |
184 | conjecture | | ⊢ |
| proveit.numbers.exponentiation.real_power_of_real_power |
185 | instantiation | 331, 200, 201 | ⊢ |
| : , : , : |
186 | instantiation | 211, 202 | ⊢ |
| : |
187 | modus ponens | 203, 204 | ⊢ |
188 | instantiation | 242, 261, 262, 205, 244 | ⊢ |
| : , : , : , : , : |
189 | instantiation | 209, 392, 206 | ⊢ |
| : , : , : |
190 | conjecture | | ⊢ |
| proveit.physics.quantum.algebra.qmult_op_ket_in_QmultCodomain |
191 | instantiation | 207, 261, 262, 208, 239 | , ⊢ |
| : , : , : , : |
192 | instantiation | 209, 392, 210 | ⊢ |
| : , : , : |
193 | instantiation | 211, 212 | , ⊢ |
| : |
194 | instantiation | 213, 257, 352, 214 | ⊢ |
| : , : , : , : , : |
195 | instantiation | 331, 215, 216 | ⊢ |
| : , : , : |
196 | conjecture | | ⊢ |
| proveit.logic.equality.four_chain_transitivity |
197 | instantiation | 341, 217 | ⊢ |
| : , : , : |
198 | instantiation | 341, 217 | ⊢ |
| : , : , : |
199 | instantiation | 273, 257 | ⊢ |
| : |
200 | instantiation | 321, 322, 398, 403, 323, 234, 345, 344, 218 | ⊢ |
| : , : , : , : , : , : |
201 | instantiation | 219, 398, 322, 234, 323, 345, 344, 257, 220* | ⊢ |
| : , : , : , : , : |
202 | instantiation | 401, 369, 221 | ⊢ |
| : , : , : |
203 | instantiation | 222, 390, 237 | ⊢ |
| : , : , : , : , : , : |
204 | generalization | 223 | ⊢ |
205 | instantiation | 260, 261, 262, 224 | ⊢ |
| : , : , : |
206 | instantiation | 338 | ⊢ |
| : , : |
207 | conjecture | | ⊢ |
| proveit.physics.quantum.algebra.qmult_op_ket_is_ket |
208 | instantiation | 260, 261, 262, 225 | ⊢ |
| : , : , : |
209 | axiom | | ⊢ |
| proveit.physics.quantum.algebra.multi_qmult_def |
210 | instantiation | 338 | ⊢ |
| : , : |
211 | conjecture | | ⊢ |
| proveit.numbers.negation.complex_closure |
212 | instantiation | 296, 226, 227, 228 | , ⊢ |
| : , : |
213 | conjecture | | ⊢ |
| proveit.numbers.division.mult_frac_cancel_numer_left |
214 | instantiation | 401, 358, 229 | ⊢ |
| : , : , : |
215 | instantiation | 341, 230 | ⊢ |
| : , : , : |
216 | instantiation | 341, 231 | ⊢ |
| : , : , : |
217 | instantiation | 272, 257 | ⊢ |
| : |
218 | instantiation | 401, 369, 232 | ⊢ |
| : , : , : |
219 | conjecture | | ⊢ |
| proveit.numbers.multiplication.mult_neg_any |
220 | instantiation | 233, 398, 322, 234, 323, 345, 344 | ⊢ |
| : , : , : , : |
221 | instantiation | 401, 380, 235 | ⊢ |
| : , : , : |
222 | conjecture | | ⊢ |
| proveit.linear_algebra.addition.summation_closure |
223 | instantiation | 236, 237, 238, 239 | ⊢ |
| : , : , : , : |
224 | instantiation | 240, 241, 261, 262, 243 | ⊢ |
| : , : , : , : |
225 | instantiation | 242, 261, 262, 243, 244 | ⊢ |
| : , : , : , : , : |
226 | instantiation | 306, 245, 246 | , ⊢ |
| : , : , : |
227 | instantiation | 401, 369, 247 | ⊢ |
| : , : , : |
228 | instantiation | 330, 301 | ⊢ |
| : |
229 | instantiation | 401, 367, 248 | ⊢ |
| : , : , : |
230 | instantiation | 331, 249, 250 | ⊢ |
| : , : , : |
231 | instantiation | 341, 251 | ⊢ |
| : , : , : |
232 | instantiation | 401, 380, 252 | ⊢ |
| : , : , : |
233 | conjecture | | ⊢ |
| proveit.numbers.multiplication.elim_one_any |
234 | instantiation | 338 | ⊢ |
| : , : |
235 | instantiation | 401, 373, 314 | ⊢ |
| : , : , : |
236 | conjecture | | ⊢ |
| proveit.linear_algebra.scalar_multiplication.scalar_mult_closure |
237 | instantiation | 253, 301 | ⊢ |
| : |
238 | instantiation | 278, 254, 255 | ⊢ |
| : , : |
239 | instantiation | 256, 400, 366 | ⊢ |
| : , : |
240 | conjecture | | ⊢ |
| proveit.physics.quantum.algebra.qmult_op_complex_closure |
241 | instantiation | 296, 257, 258, 259 | ⊢ |
| : , : |
242 | conjecture | | ⊢ |
| proveit.physics.quantum.algebra.qmult_op_op_is_op |
243 | instantiation | 260, 261, 262, 263 | ⊢ |
| : , : , : |
244 | instantiation | 264, 301, 265 | ⊢ |
| : , : , : |
245 | instantiation | 335, 309, 266 | , ⊢ |
| : , : |
246 | instantiation | 331, 267, 268 | , ⊢ |
| : , : , : |
247 | instantiation | 401, 380, 269 | ⊢ |
| : , : , : |
248 | instantiation | 401, 378, 270 | ⊢ |
| : , : , : |
249 | instantiation | 341, 271 | ⊢ |
| : , : , : |
250 | instantiation | 272, 361 | ⊢ |
| : |
251 | instantiation | 273, 361 | ⊢ |
| : |
252 | instantiation | 401, 389, 387 | ⊢ |
| : , : , : |
253 | conjecture | | ⊢ |
| proveit.linear_algebra.complex_vec_set_is_vec_space |
254 | instantiation | 401, 369, 274 | ⊢ |
| : , : , : |
255 | instantiation | 306, 275, 276 | ⊢ |
| : , : , : |
256 | conjecture | | ⊢ |
| proveit.physics.quantum.algebra.num_ket_in_register_space |
257 | instantiation | 401, 369, 277 | ⊢ |
| : , : , : |
258 | instantiation | 278, 361, 279 | ⊢ |
| : , : |
259 | instantiation | 280, 281, 282 | ⊢ |
| : , : , : |
260 | conjecture | | ⊢ |
| proveit.physics.quantum.algebra.qmult_op_is_linmap |
261 | instantiation | 283, 301 | ⊢ |
| : |
262 | conjecture | | ⊢ |
| proveit.linear_algebra.inner_products.complex_set_is_hilbert_space |
263 | instantiation | 284, 400, 356 | ⊢ |
| : , : |
264 | conjecture | | ⊢ |
| proveit.physics.quantum.algebra.qmult_matrix_is_linmap |
265 | instantiation | 362, 285, 286 | ⊢ |
| : , : , : |
266 | instantiation | 306, 287, 288 | , ⊢ |
| : , : , : |
267 | instantiation | 321, 403, 310, 322, 289, 323, 309, 336, 325, 305 | , ⊢ |
| : , : , : , : , : , : |
268 | instantiation | 321, 322, 398, 310, 323, 311, 289, 361, 326, 336, 325, 305 | , ⊢ |
| : , : , : , : , : , : |
269 | instantiation | 401, 389, 386 | ⊢ |
| : , : , : |
270 | instantiation | 401, 388, 390 | ⊢ |
| : , : , : |
271 | instantiation | 290, 361 | ⊢ |
| : |
272 | conjecture | | ⊢ |
| proveit.numbers.division.frac_one_denom |
273 | conjecture | | ⊢ |
| proveit.numbers.multiplication.elim_one_right |
274 | instantiation | 401, 349, 291 | ⊢ |
| : , : , : |
275 | instantiation | 335, 309, 292 | ⊢ |
| : , : |
276 | instantiation | 331, 293, 294 | ⊢ |
| : , : , : |
277 | instantiation | 401, 380, 295 | ⊢ |
| : , : , : |
278 | conjecture | | ⊢ |
| proveit.numbers.exponentiation.exp_complex_closure |
279 | instantiation | 296, 344, 361, 316 | ⊢ |
| : , : |
280 | theorem | | ⊢ |
| proveit.logic.equality.sub_left_side_into |
281 | instantiation | 297, 368, 298 | ⊢ |
| : , : |
282 | instantiation | 341, 299 | ⊢ |
| : , : , : |
283 | conjecture | | ⊢ |
| proveit.linear_algebra.inner_products.complex_vec_set_is_hilbert_space |
284 | conjecture | | ⊢ |
| proveit.physics.quantum.algebra.num_bra_is_lin_map |
285 | instantiation | 300, 301 | ⊢ |
| : |
286 | instantiation | 302, 400 | ⊢ |
| : |
287 | instantiation | 335, 303, 305 | , ⊢ |
| : , : |
288 | instantiation | 321, 322, 398, 403, 323, 304, 336, 325, 305 | , ⊢ |
| : , : , : , : , : , : |
289 | instantiation | 327 | ⊢ |
| : , : , : |
290 | conjecture | | ⊢ |
| proveit.numbers.multiplication.elim_one_left |
291 | conjecture | | ⊢ |
| proveit.numbers.number_sets.real_numbers.e_is_real_pos |
292 | instantiation | 306, 307, 308 | ⊢ |
| : , : , : |
293 | instantiation | 321, 403, 310, 322, 312, 323, 309, 336, 337, 325 | ⊢ |
| : , : , : , : , : , : |
294 | instantiation | 321, 322, 398, 310, 323, 311, 312, 361, 326, 336, 337, 325 | ⊢ |
| : , : , : , : , : , : |
295 | instantiation | 401, 389, 397 | ⊢ |
| : , : , : |
296 | conjecture | | ⊢ |
| proveit.numbers.division.div_complex_closure |
297 | conjecture | | ⊢ |
| proveit.numbers.exponentiation.exp_rational_non_zero__not_zero |
298 | instantiation | 401, 313, 314 | ⊢ |
| : , : , : |
299 | instantiation | 315, 344, 361, 316, 317* | ⊢ |
| : , : |
300 | conjecture | | ⊢ |
| proveit.linear_algebra.matrices.unitaries_are_matrices |
301 | instantiation | 318, 398, 395 | ⊢ |
| : , : |
302 | conjecture | | ⊢ |
| proveit.physics.quantum.QFT.invFT_is_unitary |
303 | instantiation | 335, 336, 325 | ⊢ |
| : , : |
304 | instantiation | 338 | ⊢ |
| : , : |
305 | instantiation | 401, 369, 319 | ⊢ |
| : , : , : |
306 | theorem | | ⊢ |
| proveit.logic.equality.sub_right_side_into |
307 | instantiation | 335, 320, 325 | ⊢ |
| : , : |
308 | instantiation | 321, 322, 398, 403, 323, 324, 336, 337, 325 | ⊢ |
| : , : , : , : , : , : |
309 | instantiation | 335, 361, 326 | ⊢ |
| : , : |
310 | conjecture | | ⊢ |
| proveit.numbers.numerals.decimals.nat3 |
311 | instantiation | 338 | ⊢ |
| : , : |
312 | instantiation | 327 | ⊢ |
| : , : , : |
313 | conjecture | | ⊢ |
| proveit.numbers.number_sets.rational_numbers.rational_pos_within_rational_nonzero |
314 | instantiation | 328, 374, 329 | ⊢ |
| : , : |
315 | conjecture | | ⊢ |
| proveit.numbers.division.div_as_mult |
316 | instantiation | 330, 392 | ⊢ |
| : |
317 | instantiation | 331, 332, 333 | ⊢ |
| : , : , : |
318 | conjecture | | ⊢ |
| proveit.numbers.exponentiation.exp_natpos_closure |
319 | instantiation | 401, 380, 334 | ⊢ |
| : , : , : |
320 | instantiation | 335, 336, 337 | ⊢ |
| : , : |
321 | conjecture | | ⊢ |
| proveit.numbers.multiplication.disassociation |
322 | axiom | | ⊢ |
| proveit.numbers.number_sets.natural_numbers.zero_in_nats |
323 | conjecture | | ⊢ |
| proveit.core_expr_types.tuples.tuple_len_0_typical_eq |
324 | instantiation | 338 | ⊢ |
| : , : |
325 | instantiation | 401, 369, 339 | ⊢ |
| : , : , : |
326 | instantiation | 401, 369, 340 | ⊢ |
| : , : , : |
327 | conjecture | | ⊢ |
| proveit.numbers.numerals.decimals.tuple_len_3_typical_eq |
328 | conjecture | | ⊢ |
| proveit.numbers.multiplication.mult_rational_pos_closure_bin |
329 | instantiation | 401, 391, 400 | ⊢ |
| : , : , : |
330 | conjecture | | ⊢ |
| proveit.numbers.number_sets.natural_numbers.nonzero_if_is_nat_pos |
331 | axiom | | ⊢ |
| proveit.logic.equality.equals_transitivity |
332 | instantiation | 341, 342 | ⊢ |
| : , : , : |
333 | instantiation | 343, 344, 345 | ⊢ |
| : , : |
334 | instantiation | 401, 389, 346 | ⊢ |
| : , : , : |
335 | conjecture | | ⊢ |
| proveit.numbers.multiplication.mult_complex_closure_bin |
336 | conjecture | | ⊢ |
| proveit.numbers.number_sets.complex_numbers.i_is_complex |
337 | instantiation | 401, 369, 347 | ⊢ |
| : , : , : |
338 | conjecture | | ⊢ |
| proveit.numbers.numerals.decimals.tuple_len_2_typical_eq |
339 | instantiation | 401, 380, 348 | ⊢ |
| : , : , : |
340 | instantiation | 401, 349, 350 | ⊢ |
| : , : , : |
341 | axiom | | ⊢ |
| proveit.logic.equality.substitution |
342 | instantiation | 351, 352, 390, 353* | ⊢ |
| : , : |
343 | conjecture | | ⊢ |
| proveit.numbers.multiplication.commutation |
344 | instantiation | 401, 369, 354 | ⊢ |
| : , : , : |
345 | instantiation | 401, 369, 355 | ⊢ |
| : , : , : |
346 | instantiation | 401, 365, 356 | ⊢ |
| : , : , : |
347 | conjecture | | ⊢ |
| proveit.physics.quantum.QPE._phase_is_real |
348 | instantiation | 401, 389, 357 | ⊢ |
| : , : , : |
349 | conjecture | | ⊢ |
| proveit.numbers.number_sets.real_numbers.real_pos_within_real |
350 | conjecture | | ⊢ |
| proveit.numbers.number_sets.real_numbers.pi_is_real_pos |
351 | conjecture | | ⊢ |
| proveit.numbers.exponentiation.neg_power_as_div |
352 | instantiation | 401, 358, 359 | ⊢ |
| : , : , : |
353 | instantiation | 360, 361 | ⊢ |
| : |
354 | instantiation | 362, 363, 400 | ⊢ |
| : , : , : |
355 | instantiation | 401, 380, 364 | ⊢ |
| : , : , : |
356 | assumption | | ⊢ |
357 | instantiation | 401, 365, 366 | ⊢ |
| : , : , : |
358 | conjecture | | ⊢ |
| proveit.numbers.number_sets.complex_numbers.real_nonzero_within_complex_nonzero |
359 | instantiation | 401, 367, 368 | ⊢ |
| : , : , : |
360 | conjecture | | ⊢ |
| proveit.numbers.exponentiation.complex_x_to_first_power_is_x |
361 | instantiation | 401, 369, 370 | ⊢ |
| : , : , : |
362 | theorem | | ⊢ |
| proveit.logic.sets.inclusion.unfold_subset_eq |
363 | instantiation | 371, 372 | ⊢ |
| : , : |
364 | instantiation | 401, 373, 374 | ⊢ |
| : , : , : |
365 | instantiation | 375, 376, 377 | ⊢ |
| : , : |
366 | assumption | | ⊢ |
367 | conjecture | | ⊢ |
| proveit.numbers.number_sets.real_numbers.rational_nonzero_within_real_nonzero |
368 | instantiation | 401, 378, 379 | ⊢ |
| : , : , : |
369 | conjecture | | ⊢ |
| proveit.numbers.number_sets.complex_numbers.real_within_complex |
370 | instantiation | 401, 380, 381 | ⊢ |
| : , : , : |
371 | theorem | | ⊢ |
| proveit.logic.sets.inclusion.relax_proper_subset |
372 | conjecture | | ⊢ |
| proveit.numbers.number_sets.real_numbers.nat_pos_within_real |
373 | conjecture | | ⊢ |
| proveit.numbers.number_sets.rational_numbers.rational_pos_within_rational |
374 | instantiation | 382, 383, 384 | ⊢ |
| : , : |
375 | conjecture | | ⊢ |
| proveit.numbers.number_sets.integers.int_interval_within_int |
376 | conjecture | | ⊢ |
| proveit.numbers.number_sets.integers.zero_is_int |
377 | instantiation | 385, 386, 387 | ⊢ |
| : , : |
378 | conjecture | | ⊢ |
| proveit.numbers.number_sets.rational_numbers.nonzero_int_within_rational_nonzero |
379 | instantiation | 401, 388, 392 | ⊢ |
| : , : , : |
380 | conjecture | | ⊢ |
| proveit.numbers.number_sets.real_numbers.rational_within_real |
381 | instantiation | 401, 389, 394 | ⊢ |
| : , : , : |
382 | conjecture | | ⊢ |
| proveit.numbers.division.div_rational_pos_closure |
383 | instantiation | 401, 391, 390 | ⊢ |
| : , : , : |
384 | instantiation | 401, 391, 392 | ⊢ |
| : , : , : |
385 | conjecture | | ⊢ |
| proveit.numbers.addition.add_int_closure_bin |
386 | instantiation | 393, 394, 395 | ⊢ |
| : , : |
387 | instantiation | 396, 397 | ⊢ |
| : |
388 | conjecture | | ⊢ |
| proveit.numbers.number_sets.integers.nat_pos_within_nonzero_int |
389 | conjecture | | ⊢ |
| proveit.numbers.number_sets.rational_numbers.int_within_rational |
390 | conjecture | | ⊢ |
| proveit.numbers.numerals.decimals.posnat1 |
391 | conjecture | | ⊢ |
| proveit.numbers.number_sets.rational_numbers.nat_pos_within_rational_pos |
392 | conjecture | | ⊢ |
| proveit.numbers.numerals.decimals.posnat2 |
393 | conjecture | | ⊢ |
| proveit.numbers.exponentiation.exp_int_closure |
394 | instantiation | 401, 402, 398 | ⊢ |
| : , : , : |
395 | instantiation | 401, 399, 400 | ⊢ |
| : , : , : |
396 | conjecture | | ⊢ |
| proveit.numbers.negation.int_closure |
397 | instantiation | 401, 402, 403 | ⊢ |
| : , : , : |
398 | conjecture | | ⊢ |
| proveit.numbers.numerals.decimals.nat2 |
399 | conjecture | | ⊢ |
| proveit.numbers.number_sets.natural_numbers.nat_pos_within_nat |
400 | axiom | | ⊢ |
| proveit.physics.quantum.QPE._t_in_natural_pos |
401 | theorem | | ⊢ |
| proveit.logic.sets.inclusion.superset_membership_from_proper_subset |
402 | conjecture | | ⊢ |
| proveit.numbers.number_sets.integers.nat_within_int |
403 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.nat1 |
*equality replacement requirements |