| step type | requirements | statement |
0 | generalization | 1 | ⊢ |
1 | instantiation | 2, 3, 4 | ⊢ |
| : , : |
2 | theorem | | ⊢ |
| proveit.logic.booleans.conjunction.and_if_both |
3 | instantiation | 190, 5, 14 | ⊢ |
| : , : , : |
4 | instantiation | 6, 328, 20, 7, 22, 23, 8, 9* | ⊢ |
| : , : , : , : |
5 | instantiation | 244, 10, 11 | ⊢ |
| : , : , : |
6 | conjecture | | ⊢ |
| proveit.linear_algebra.tensors.norm_preserving_tensor_prod |
7 | instantiation | 31, 317, 318, 134, 46 | ⊢ |
| : , : , : |
8 | modus ponens | 12, 13 | ⊢ |
9 | instantiation | 211, 14 | ⊢ |
| : , : |
10 | instantiation | 15, 328, 16, 17, 18* | ⊢ |
| : , : , : |
11 | instantiation | 19, 328, 20, 21, 22, 23 | ⊢ |
| : , : , : , : |
12 | instantiation | 45, 317, 318, 46 | ⊢ |
| : , : , : , : |
13 | generalization | 24 | ⊢ |
14 | instantiation | 25, 328 | ⊢ |
| : |
15 | conjecture | | ⊢ |
| proveit.linear_algebra.tensors.tensor_prod_of_cart_exps_within_cart_exp |
16 | instantiation | 107, 26, 204, 33 | ⊢ |
| : , : , : , : |
17 | instantiation | 31, 317, 318, 260, 46 | ⊢ |
| : , : , : |
18 | instantiation | 27, 28, 297, 43, 29*, 43* | ⊢ |
| : , : |
19 | conjecture | | ⊢ |
| proveit.linear_algebra.tensors.tensor_prod_is_in_tensor_prod_space |
20 | instantiation | 107, 30, 204, 33 | ⊢ |
| : , : , : , : |
21 | instantiation | 31, 317, 318, 130, 46 | ⊢ |
| : , : , : |
22 | instantiation | 107, 32, 204, 33 | ⊢ |
| : , : , : , : |
23 | modus ponens | 34, 35 | ⊢ |
24 | instantiation | 253, 36, 37 | , ⊢ |
| : , : , : |
25 | axiom | | ⊢ |
| proveit.physics.quantum.QPE._psi_t_def |
26 | instantiation | 261, 38, 43 | ⊢ |
| : , : , : |
27 | conjecture | | ⊢ |
| proveit.numbers.exponentiation.exp_nat_pos_rev |
28 | instantiation | 149, 311, 278, 39, 279, 83, 325, 150 | ⊢ |
| : , : , : , : , : |
29 | instantiation | 211, 40 | ⊢ |
| : , : |
30 | instantiation | 261, 41, 43 | ⊢ |
| : , : , : |
31 | conjecture | | ⊢ |
| proveit.logic.booleans.conjunction.redundant_conjunction_general |
32 | instantiation | 261, 42, 43 | ⊢ |
| : , : , : |
33 | instantiation | 211, 44 | ⊢ |
| : , : |
34 | instantiation | 45, 317, 318, 46 | ⊢ |
| : , : , : , : |
35 | generalization | 47 | ⊢ |
36 | instantiation | 102, 134, 67, 68, 48*, 49* | , ⊢ |
| : , : , : , : |
37 | instantiation | 253, 50, 51 | ⊢ |
| : , : , : |
38 | instantiation | 56, 57 | ⊢ |
| : , : , : |
39 | instantiation | 290 | ⊢ |
| : , : |
40 | instantiation | 52, 320, 53, 54, 55 | ⊢ |
| : , : , : , : , : , : |
41 | instantiation | 56, 57 | ⊢ |
| : , : , : |
42 | instantiation | 56, 57 | ⊢ |
| : , : , : |
43 | instantiation | 253, 58, 59 | ⊢ |
| : , : , : |
44 | instantiation | 60, 61 | ⊢ |
| : , : |
45 | conjecture | | ⊢ |
| proveit.logic.booleans.conjunction.conjunction_from_quantification |
46 | instantiation | 178, 62, 63, 223, 64, 65*, 66* | ⊢ |
| : , : , : |
47 | instantiation | 129, 130, 67, 68 | , ⊢ |
| : , : , : , : |
48 | instantiation | 69, 70 | ⊢ |
| : |
49 | instantiation | 71, 130, 135, 97, 72, 73* | , ⊢ |
| : , : , : , : |
50 | instantiation | 235, 74 | ⊢ |
| : , : , : |
51 | instantiation | 261, 75, 76 | ⊢ |
| : , : , : |
52 | conjecture | | ⊢ |
| proveit.core_expr_types.tuples.shift_equivalence |
53 | instantiation | 77, 78, 83 | ⊢ |
| : , : |
54 | instantiation | 211, 79 | ⊢ |
| : , : |
55 | instantiation | 211, 80 | ⊢ |
| : , : |
56 | conjecture | | ⊢ |
| proveit.core_expr_types.tuples.range_len |
57 | instantiation | 81, 265, 82, 278, 83, 325 | ⊢ |
| : , : |
58 | instantiation | 235, 84 | ⊢ |
| : , : , : |
59 | instantiation | 107, 85, 86, 87 | ⊢ |
| : , : , : , : |
60 | conjecture | | ⊢ |
| proveit.core_expr_types.tuples.range_from1_len |
61 | instantiation | 326, 111, 328 | ⊢ |
| : , : , : |
62 | instantiation | 326, 309, 88 | ⊢ |
| : , : , : |
63 | conjecture | | ⊢ |
| proveit.numbers.number_sets.real_numbers.zero_is_real |
64 | instantiation | 89, 90 | ⊢ |
| : , : |
65 | instantiation | 253, 91, 92 | ⊢ |
| : , : , : |
66 | instantiation | 107, 93, 123, 94 | ⊢ |
| : , : , : , : |
67 | instantiation | 326, 306, 95 | ⊢ |
| : , : , : |
68 | instantiation | 96, 130, 135, 97 | , ⊢ |
| : , : , : , : |
69 | conjecture | | ⊢ |
| proveit.numbers.absolute_value.abs_non_neg_elim |
70 | instantiation | 98, 99 | ⊢ |
| : |
71 | conjecture | | ⊢ |
| proveit.linear_algebra.addition.norm_of_sum_of_orthogonal_pair |
72 | instantiation | 261, 100, 101 | , ⊢ |
| : , : , : |
73 | instantiation | 102, 134, 186, 136, 103* | , ⊢ |
| : , : , : , : |
74 | instantiation | 235, 104 | ⊢ |
| : , : , : |
75 | instantiation | 261, 105, 106 | ⊢ |
| : , : , : |
76 | instantiation | 107, 108, 109, 110 | ⊢ |
| : , : , : , : |
77 | conjecture | | ⊢ |
| proveit.numbers.addition.add_nat_closure_bin |
78 | instantiation | 326, 111, 112 | ⊢ |
| : , : , : |
79 | instantiation | 253, 113, 114 | ⊢ |
| : , : , : |
80 | instantiation | 253, 115, 116 | ⊢ |
| : , : , : |
81 | conjecture | | ⊢ |
| proveit.numbers.addition.add_nat_closure |
82 | instantiation | 283 | ⊢ |
| : , : , : |
83 | instantiation | 284, 117 | ⊢ |
| : |
84 | instantiation | 118, 201, 200, 153* | ⊢ |
| : , : |
85 | instantiation | 174, 325, 311, 119, 164, 203, 121, 200 | ⊢ |
| : , : , : , : , : , : |
86 | instantiation | 125, 278, 265, 279, 120, 203, 121, 200 | ⊢ |
| : , : , : , : |
87 | instantiation | 122, 200, 203, 123 | ⊢ |
| : , : , : |
88 | instantiation | 326, 312, 317 | ⊢ |
| : , : , : |
89 | conjecture | | ⊢ |
| proveit.numbers.ordering.relax_less |
90 | instantiation | 124, 328 | ⊢ |
| : |
91 | instantiation | 174, 325, 311, 278, 175, 279, 164, 201, 200 | ⊢ |
| : , : , : , : , : , : |
92 | instantiation | 125, 278, 311, 279, 175, 201, 200 | ⊢ |
| : , : , : , : |
93 | instantiation | 253, 126, 127 | ⊢ |
| : , : , : |
94 | instantiation | 211, 128 | ⊢ |
| : , : |
95 | instantiation | 326, 299, 132 | ⊢ |
| : , : , : |
96 | conjecture | | ⊢ |
| proveit.linear_algebra.addition.binary_closure |
97 | instantiation | 129, 130, 186, 136 | , ⊢ |
| : , : , : , : |
98 | conjecture | | ⊢ |
| proveit.numbers.number_sets.real_numbers.nonneg_if_in_real_nonneg |
99 | instantiation | 326, 131, 132 | ⊢ |
| : , : , : |
100 | instantiation | 133, 134, 186, 135, 136 | , ⊢ |
| : , : , : , : , : |
101 | instantiation | 253, 137, 138 | , ⊢ |
| : , : , : |
102 | conjecture | | ⊢ |
| proveit.linear_algebra.inner_products.scaled_norm |
103 | instantiation | 253, 139, 140 | , ⊢ |
| : , : , : |
104 | instantiation | 253, 141, 142 | ⊢ |
| : , : , : |
105 | instantiation | 143, 200, 144, 145 | ⊢ |
| : , : , : , : , : |
106 | instantiation | 253, 146, 147 | ⊢ |
| : , : , : |
107 | conjecture | | ⊢ |
| proveit.logic.equality.four_chain_transitivity |
108 | instantiation | 235, 148 | ⊢ |
| : , : , : |
109 | instantiation | 235, 148 | ⊢ |
| : , : , : |
110 | instantiation | 240, 200 | ⊢ |
| : |
111 | conjecture | | ⊢ |
| proveit.numbers.number_sets.natural_numbers.nat_pos_within_nat |
112 | instantiation | 149, 325, 278, 279, 150 | ⊢ |
| : , : , : , : , : |
113 | instantiation | 235, 153 | ⊢ |
| : , : , : |
114 | instantiation | 253, 151, 152 | ⊢ |
| : , : , : |
115 | instantiation | 235, 153 | ⊢ |
| : , : , : |
116 | instantiation | 156, 203 | ⊢ |
| : |
117 | instantiation | 294, 317, 154 | ⊢ |
| : |
118 | conjecture | | ⊢ |
| proveit.numbers.negation.distribute_neg_through_binary_sum |
119 | instantiation | 290 | ⊢ |
| : , : |
120 | instantiation | 283 | ⊢ |
| : , : , : |
121 | instantiation | 303, 200 | ⊢ |
| : |
122 | conjecture | | ⊢ |
| proveit.numbers.addition.subtraction.add_cancel_triple_32 |
123 | instantiation | 224 | ⊢ |
| : |
124 | conjecture | | ⊢ |
| proveit.numbers.number_sets.natural_numbers.natural_pos_is_pos |
125 | conjecture | | ⊢ |
| proveit.numbers.addition.elim_zero_any |
126 | instantiation | 174, 325, 311, 278, 175, 279, 203, 201, 200 | ⊢ |
| : , : , : , : , : , : |
127 | instantiation | 155, 203, 200, 204 | ⊢ |
| : , : , : |
128 | instantiation | 156, 200 | ⊢ |
| : |
129 | conjecture | | ⊢ |
| proveit.linear_algebra.scalar_multiplication.scalar_mult_closure |
130 | instantiation | 157, 260 | ⊢ |
| : |
131 | conjecture | | ⊢ |
| proveit.numbers.number_sets.real_numbers.real_pos_within_real_nonneg |
132 | instantiation | 158, 159, 206, 160 | ⊢ |
| : , : |
133 | conjecture | | ⊢ |
| proveit.linear_algebra.inner_products.inner_prod_scalar_mult_right |
134 | instantiation | 161, 260 | ⊢ |
| : |
135 | conjecture | | ⊢ |
| proveit.physics.quantum.algebra.ket_zero_in_qubit_space |
136 | conjecture | | ⊢ |
| proveit.physics.quantum.algebra.ket_one_in_qubit_space |
137 | instantiation | 235, 162 | ⊢ |
| : , : , : |
138 | instantiation | 163, 186, 164, 165* | , ⊢ |
| : , : |
139 | instantiation | 235, 166 | , ⊢ |
| : , : , : |
140 | instantiation | 218, 167 | ⊢ |
| : |
141 | instantiation | 253, 168, 169 | ⊢ |
| : , : , : |
142 | conjecture | | ⊢ |
| proveit.numbers.numerals.decimals.add_1_1 |
143 | conjecture | | ⊢ |
| proveit.numbers.division.mult_frac_cancel_denom_left |
144 | instantiation | 326, 171, 170 | ⊢ |
| : , : , : |
145 | instantiation | 326, 171, 184 | ⊢ |
| : , : , : |
146 | instantiation | 235, 172 | ⊢ |
| : , : , : |
147 | instantiation | 235, 173 | ⊢ |
| : , : , : |
148 | instantiation | 220, 200 | ⊢ |
| : |
149 | conjecture | | ⊢ |
| proveit.numbers.addition.add_nat_pos_from_nonneg |
150 | conjecture | | ⊢ |
| proveit.numbers.numerals.decimals.less_0_1 |
151 | instantiation | 174, 278, 311, 325, 279, 175, 201, 200, 203 | ⊢ |
| : , : , : , : , : , : |
152 | instantiation | 176, 203, 200, 204 | ⊢ |
| : , : , : |
153 | instantiation | 177, 203 | ⊢ |
| : |
154 | instantiation | 178, 222, 221, 223, 179, 180*, 181* | ⊢ |
| : , : , : |
155 | conjecture | | ⊢ |
| proveit.numbers.addition.subtraction.add_cancel_triple_12 |
156 | conjecture | | ⊢ |
| proveit.numbers.addition.elim_zero_left |
157 | conjecture | | ⊢ |
| proveit.linear_algebra.complex_vec_set_is_vec_space |
158 | conjecture | | ⊢ |
| proveit.numbers.division.div_real_pos_closure |
159 | instantiation | 326, 246, 182 | ⊢ |
| : , : , : |
160 | instantiation | 183, 184 | ⊢ |
| : |
161 | conjecture | | ⊢ |
| proveit.linear_algebra.inner_products.complex_vec_set_is_inner_prod_space |
162 | conjecture | | ⊢ |
| proveit.physics.quantum.algebra.ket_zero_and_one_have_zero_inner_prod |
163 | axiom | | ⊢ |
| proveit.linear_algebra.scalar_multiplication.scalar_mult_extends_number_mult |
164 | conjecture | | ⊢ |
| proveit.numbers.number_sets.complex_numbers.zero_is_complex |
165 | instantiation | 185, 186 | , ⊢ |
| : |
166 | instantiation | 187, 188, 189* | , ⊢ |
| : |
167 | instantiation | 190, 200, 236 | ⊢ |
| : , : , : |
168 | instantiation | 235, 191 | ⊢ |
| : , : , : |
169 | instantiation | 235, 192 | ⊢ |
| : , : , : |
170 | instantiation | 326, 193, 194 | ⊢ |
| : , : , : |
171 | conjecture | | ⊢ |
| proveit.numbers.number_sets.complex_numbers.real_nonzero_within_complex_nonzero |
172 | instantiation | 235, 195 | ⊢ |
| : , : , : |
173 | instantiation | 253, 196, 197 | ⊢ |
| : , : , : |
174 | conjecture | | ⊢ |
| proveit.numbers.addition.disassociation |
175 | instantiation | 290 | ⊢ |
| : , : |
176 | conjecture | | ⊢ |
| proveit.numbers.addition.subtraction.add_cancel_triple_31 |
177 | conjecture | | ⊢ |
| proveit.numbers.negation.double_negation |
178 | conjecture | | ⊢ |
| proveit.numbers.addition.weak_bound_via_left_term_bound |
179 | instantiation | 198, 328 | ⊢ |
| : |
180 | instantiation | 199, 200, 201 | ⊢ |
| : , : |
181 | instantiation | 202, 203, 204 | ⊢ |
| : , : |
182 | instantiation | 326, 259, 239 | ⊢ |
| : , : , : |
183 | conjecture | | ⊢ |
| proveit.numbers.number_sets.real_numbers.nonzero_if_in_real_nonzero |
184 | instantiation | 326, 205, 206 | ⊢ |
| : , : , : |
185 | conjecture | | ⊢ |
| proveit.numbers.multiplication.mult_zero_right |
186 | instantiation | 296, 207, 208 | , ⊢ |
| : , : |
187 | conjecture | | ⊢ |
| proveit.numbers.absolute_value.complex_unit_length |
188 | instantiation | 261, 209, 210 | , ⊢ |
| : , : , : |
189 | instantiation | 211, 212 | , ⊢ |
| : , : |
190 | theorem | | ⊢ |
| proveit.logic.equality.sub_left_side_into |
191 | instantiation | 253, 213, 215 | ⊢ |
| : , : , : |
192 | instantiation | 253, 214, 215 | ⊢ |
| : , : , : |
193 | conjecture | | ⊢ |
| proveit.numbers.number_sets.real_numbers.rational_nonzero_within_real_nonzero |
194 | instantiation | 326, 216, 217 | ⊢ |
| : , : , : |
195 | instantiation | 218, 241 | ⊢ |
| : |
196 | instantiation | 235, 219 | ⊢ |
| : , : , : |
197 | instantiation | 220, 241 | ⊢ |
| : |
198 | conjecture | | ⊢ |
| proveit.numbers.number_sets.natural_numbers.natural_pos_lower_bound |
199 | conjecture | | ⊢ |
| proveit.numbers.addition.commutation |
200 | instantiation | 326, 306, 221 | ⊢ |
| : , : , : |
201 | instantiation | 326, 306, 222 | ⊢ |
| : , : , : |
202 | conjecture | | ⊢ |
| proveit.numbers.addition.subtraction.add_cancel_basic |
203 | instantiation | 326, 306, 223 | ⊢ |
| : , : , : |
204 | instantiation | 224 | ⊢ |
| : |
205 | conjecture | | ⊢ |
| proveit.numbers.number_sets.real_numbers.real_pos_within_real_nonzero |
206 | instantiation | 225, 226 | ⊢ |
| : |
207 | instantiation | 326, 306, 227 | ⊢ |
| : , : , : |
208 | instantiation | 261, 228, 229 | , ⊢ |
| : , : , : |
209 | instantiation | 292, 282, 230 | , ⊢ |
| : , : |
210 | instantiation | 253, 231, 232 | , ⊢ |
| : , : , : |
211 | theorem | | ⊢ |
| proveit.logic.equality.equals_reversal |
212 | instantiation | 235, 233 | , ⊢ |
| : , : , : |
213 | instantiation | 235, 234 | ⊢ |
| : , : , : |
214 | instantiation | 235, 236 | ⊢ |
| : , : , : |
215 | instantiation | 237, 297 | ⊢ |
| : |
216 | conjecture | | ⊢ |
| proveit.numbers.number_sets.rational_numbers.nonzero_int_within_rational_nonzero |
217 | instantiation | 326, 238, 239 | ⊢ |
| : , : , : |
218 | conjecture | | ⊢ |
| proveit.numbers.multiplication.elim_one_left |
219 | instantiation | 240, 241 | ⊢ |
| : |
220 | conjecture | | ⊢ |
| proveit.numbers.division.frac_one_denom |
221 | instantiation | 326, 309, 242 | ⊢ |
| : , : , : |
222 | instantiation | 326, 309, 243 | ⊢ |
| : , : , : |
223 | instantiation | 244, 245, 328 | ⊢ |
| : , : , : |
224 | axiom | | ⊢ |
| proveit.logic.equality.equals_reflexivity |
225 | conjecture | | ⊢ |
| proveit.numbers.exponentiation.sqrt_real_pos_closure |
226 | instantiation | 326, 246, 247 | ⊢ |
| : , : , : |
227 | instantiation | 326, 299, 248 | ⊢ |
| : , : , : |
228 | instantiation | 287, 264, 249 | , ⊢ |
| : , : |
229 | instantiation | 253, 250, 251 | , ⊢ |
| : , : , : |
230 | instantiation | 292, 252, 291 | , ⊢ |
| : , : |
231 | instantiation | 277, 325, 311, 278, 271, 279, 264, 289, 281 | , ⊢ |
| : , : , : , : , : , : |
232 | instantiation | 277, 278, 311, 279, 270, 271, 297, 275, 289, 281 | , ⊢ |
| : , : , : , : , : , : |
233 | instantiation | 253, 254, 255 | , ⊢ |
| : , : , : |
234 | conjecture | | ⊢ |
| proveit.physics.quantum.algebra.ket_zero_norm |
235 | axiom | | ⊢ |
| proveit.logic.equality.substitution |
236 | conjecture | | ⊢ |
| proveit.physics.quantum.algebra.ket_one_norm |
237 | conjecture | | ⊢ |
| proveit.numbers.exponentiation.exponentiated_one |
238 | conjecture | | ⊢ |
| proveit.numbers.number_sets.integers.nat_pos_within_nonzero_int |
239 | conjecture | | ⊢ |
| proveit.numbers.numerals.decimals.posnat1 |
240 | conjecture | | ⊢ |
| proveit.numbers.multiplication.elim_one_right |
241 | instantiation | 256, 297 | ⊢ |
| : |
242 | instantiation | 326, 312, 321 | ⊢ |
| : , : , : |
243 | instantiation | 326, 312, 320 | ⊢ |
| : , : , : |
244 | theorem | | ⊢ |
| proveit.logic.sets.inclusion.unfold_subset_eq |
245 | instantiation | 257, 258 | ⊢ |
| : , : |
246 | conjecture | | ⊢ |
| proveit.numbers.number_sets.real_numbers.rational_pos_within_real_pos |
247 | instantiation | 326, 259, 260 | ⊢ |
| : , : , : |
248 | conjecture | | ⊢ |
| proveit.numbers.number_sets.real_numbers.e_is_real_pos |
249 | instantiation | 261, 262, 263 | , ⊢ |
| : , : , : |
250 | instantiation | 277, 325, 265, 278, 266, 279, 264, 288, 289, 281 | , ⊢ |
| : , : , : , : , : , : |
251 | instantiation | 277, 278, 311, 265, 279, 270, 266, 297, 275, 288, 289, 281 | , ⊢ |
| : , : , : , : , : , : |
252 | instantiation | 267, 302, 268 | , ⊢ |
| : , : |
253 | axiom | | ⊢ |
| proveit.logic.equality.equals_transitivity |
254 | instantiation | 269, 278, 311, 279, 270, 271, 297, 275, 288, 289, 281 | , ⊢ |
| : , : , : , : , : , : , : |
255 | instantiation | 272, 325, 273, 278, 274, 279, 288, 297, 275, 289, 281 | , ⊢ |
| : , : , : , : , : , : |
256 | conjecture | | ⊢ |
| proveit.numbers.exponentiation.sqrt_complex_closure |
257 | theorem | | ⊢ |
| proveit.logic.sets.inclusion.relax_proper_subset |
258 | conjecture | | ⊢ |
| proveit.numbers.number_sets.real_numbers.nat_pos_within_real |
259 | conjecture | | ⊢ |
| proveit.numbers.number_sets.rational_numbers.nat_pos_within_rational_pos |
260 | conjecture | | ⊢ |
| proveit.numbers.numerals.decimals.posnat2 |
261 | theorem | | ⊢ |
| proveit.logic.equality.sub_right_side_into |
262 | instantiation | 287, 276, 281 | , ⊢ |
| : , : |
263 | instantiation | 277, 278, 311, 325, 279, 280, 288, 289, 281 | , ⊢ |
| : , : , : , : , : , : |
264 | instantiation | 326, 306, 282 | ⊢ |
| : , : , : |
265 | conjecture | | ⊢ |
| proveit.numbers.numerals.decimals.nat3 |
266 | instantiation | 283 | ⊢ |
| : , : , : |
267 | conjecture | | ⊢ |
| proveit.numbers.exponentiation.exp_real_closure_nat_power |
268 | instantiation | 284, 285 | , ⊢ |
| : |
269 | conjecture | | ⊢ |
| proveit.numbers.multiplication.leftward_commutation |
270 | instantiation | 290 | ⊢ |
| : , : |
271 | instantiation | 290 | ⊢ |
| : , : |
272 | conjecture | | ⊢ |
| proveit.numbers.multiplication.association |
273 | conjecture | | ⊢ |
| proveit.numbers.numerals.decimals.nat4 |
274 | instantiation | 286 | ⊢ |
| : , : , : , : |
275 | instantiation | 326, 306, 293 | ⊢ |
| : , : , : |
276 | instantiation | 287, 288, 289 | , ⊢ |
| : , : |
277 | conjecture | | ⊢ |
| proveit.numbers.multiplication.disassociation |
278 | axiom | | ⊢ |
| proveit.numbers.number_sets.natural_numbers.zero_in_nats |
279 | conjecture | | ⊢ |
| proveit.core_expr_types.tuples.tuple_len_0_typical_eq |
280 | instantiation | 290 | ⊢ |
| : , : |
281 | instantiation | 326, 306, 291 | ⊢ |
| : , : , : |
282 | instantiation | 292, 302, 293 | ⊢ |
| : , : |
283 | conjecture | | ⊢ |
| proveit.numbers.numerals.decimals.tuple_len_3_typical_eq |
284 | conjecture | | ⊢ |
| proveit.numbers.negation.nat_closure |
285 | instantiation | 294, 313, 295 | , ⊢ |
| : |
286 | conjecture | | ⊢ |
| proveit.numbers.numerals.decimals.tuple_len_4_typical_eq |
287 | conjecture | | ⊢ |
| proveit.numbers.multiplication.mult_complex_closure_bin |
288 | conjecture | | ⊢ |
| proveit.numbers.number_sets.complex_numbers.i_is_complex |
289 | instantiation | 296, 297, 298 | , ⊢ |
| : , : |
290 | conjecture | | ⊢ |
| proveit.numbers.numerals.decimals.tuple_len_2_typical_eq |
291 | conjecture | | ⊢ |
| proveit.physics.quantum.QPE._phase_is_real |
292 | conjecture | | ⊢ |
| proveit.numbers.multiplication.mult_real_closure_bin |
293 | instantiation | 326, 299, 300 | ⊢ |
| : , : , : |
294 | conjecture | | ⊢ |
| proveit.numbers.number_sets.integers.nonpos_int_is_int_nonpos |
295 | instantiation | 301, 317, 318, 315 | , ⊢ |
| : , : , : |
296 | conjecture | | ⊢ |
| proveit.numbers.exponentiation.exp_complex_closure |
297 | instantiation | 326, 306, 302 | ⊢ |
| : , : , : |
298 | instantiation | 303, 304 | , ⊢ |
| : |
299 | conjecture | | ⊢ |
| proveit.numbers.number_sets.real_numbers.real_pos_within_real |
300 | conjecture | | ⊢ |
| proveit.numbers.number_sets.real_numbers.pi_is_real_pos |
301 | conjecture | | ⊢ |
| proveit.numbers.number_sets.integers.interval_upper_bound |
302 | instantiation | 326, 309, 305 | ⊢ |
| : , : , : |
303 | conjecture | | ⊢ |
| proveit.numbers.negation.complex_closure |
304 | instantiation | 326, 306, 307 | , ⊢ |
| : , : , : |
305 | instantiation | 326, 312, 308 | ⊢ |
| : , : , : |
306 | conjecture | | ⊢ |
| proveit.numbers.number_sets.complex_numbers.real_within_complex |
307 | instantiation | 326, 309, 310 | , ⊢ |
| : , : , : |
308 | instantiation | 326, 324, 311 | ⊢ |
| : , : , : |
309 | conjecture | | ⊢ |
| proveit.numbers.number_sets.real_numbers.rational_within_real |
310 | instantiation | 326, 312, 313 | , ⊢ |
| : , : , : |
311 | conjecture | | ⊢ |
| proveit.numbers.numerals.decimals.nat2 |
312 | conjecture | | ⊢ |
| proveit.numbers.number_sets.rational_numbers.int_within_rational |
313 | instantiation | 326, 314, 315 | , ⊢ |
| : , : , : |
314 | instantiation | 316, 317, 318 | ⊢ |
| : , : |
315 | assumption | | ⊢ |
316 | conjecture | | ⊢ |
| proveit.numbers.number_sets.integers.int_interval_within_int |
317 | instantiation | 319, 320, 321 | ⊢ |
| : , : |
318 | conjecture | | ⊢ |
| proveit.numbers.number_sets.integers.zero_is_int |
319 | conjecture | | ⊢ |
| proveit.numbers.addition.add_int_closure_bin |
320 | instantiation | 322, 323 | ⊢ |
| : |
321 | instantiation | 326, 324, 325 | ⊢ |
| : , : , : |
322 | conjecture | | ⊢ |
| proveit.numbers.negation.int_closure |
323 | instantiation | 326, 327, 328 | ⊢ |
| : , : , : |
324 | conjecture | | ⊢ |
| proveit.numbers.number_sets.integers.nat_within_int |
325 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.nat1 |
326 | theorem | | ⊢ |
| proveit.logic.sets.inclusion.superset_membership_from_proper_subset |
327 | conjecture | | ⊢ |
| proveit.numbers.number_sets.integers.nat_pos_within_int |
328 | assumption | | ⊢ |
*equality replacement requirements |