| step type | requirements | statement |
0 | instantiation | 1, 2, 3 | , ⊢ |
| : , : , : |
1 | reference | 12 | ⊢ |
2 | instantiation | 4, 5 | , ⊢ |
| : , : |
3 | instantiation | 196, 6 | ⊢ |
| : , : , : |
4 | theorem | | ⊢ |
| proveit.logic.equality.not_equals_symmetry |
5 | instantiation | 7, 8, 9, 10* | , ⊢ |
| : |
6 | instantiation | 196, 11 | ⊢ |
| : , : , : |
7 | theorem | | ⊢ |
| proveit.numbers.exponentiation.unit_complex_polar_num_neq_one |
8 | instantiation | 125, 47, 39 | ⊢ |
| : , : , : |
9 | instantiation | 12, 13, 14 | , ⊢ |
| : , : , : |
10 | instantiation | 32, 15 | ⊢ |
| : , : |
11 | instantiation | 196, 16 | ⊢ |
| : , : , : |
12 | theorem | | ⊢ |
| proveit.logic.equality.sub_left_side_into |
13 | instantiation | 17, 18, 207, 19 | , ⊢ |
| : , : |
14 | instantiation | 128, 20, 21, 22 | ⊢ |
| : , : , : , : |
15 | instantiation | 196, 23 | ⊢ |
| : , : , : |
16 | instantiation | 185, 24, 25 | ⊢ |
| : , : , : |
17 | theorem | | ⊢ |
| proveit.physics.quantum.QPE._non_int_delta_b_diff |
18 | instantiation | 26, 143, 230, 144 | ⊢ |
| : , : , : , : , : |
19 | assumption | | ⊢ |
20 | instantiation | 62, 27, 28, 29, 30* | ⊢ |
| : , : |
21 | instantiation | 31, 86, 107 | ⊢ |
| : , : |
22 | instantiation | 32, 33 | ⊢ |
| : , : |
23 | instantiation | 185, 34, 35 | ⊢ |
| : , : , : |
24 | instantiation | 196, 36 | ⊢ |
| : , : , : |
25 | instantiation | 37, 143, 232, 144, 145, 179, 146, 147, 121* | ⊢ |
| : , : , : , : , : |
26 | theorem | | ⊢ |
| proveit.logic.sets.enumeration.in_enumerated_set |
27 | instantiation | 125, 38, 39 | ⊢ |
| : , : , : |
28 | instantiation | 233, 211, 55 | ⊢ |
| : , : , : |
29 | instantiation | 40, 232, 48, 153, 41 | ⊢ |
| : , : |
30 | instantiation | 185, 42, 43 | ⊢ |
| : , : , : |
31 | theorem | | ⊢ |
| proveit.numbers.addition.commutation |
32 | theorem | | ⊢ |
| proveit.logic.equality.equals_reversal |
33 | instantiation | 196, 44 | ⊢ |
| : , : , : |
34 | instantiation | 97, 143, 232, 230, 144, 48, 205, 165, 45, 101 | ⊢ |
| : , : , : , : , : , : , : |
35 | instantiation | 98, 230, 92, 143, 79, 144, 45, 205, 165, 101 | ⊢ |
| : , : , : , : , : , : |
36 | instantiation | 196, 46 | ⊢ |
| : , : , : |
37 | theorem | | ⊢ |
| proveit.numbers.multiplication.mult_neg_any |
38 | instantiation | 233, 211, 47 | ⊢ |
| : , : , : |
39 | instantiation | 141, 143, 232, 230, 144, 48, 205, 165, 101 | ⊢ |
| : , : , : , : , : , : |
40 | theorem | | ⊢ |
| proveit.numbers.multiplication.mult_not_eq_zero |
41 | instantiation | 233, 170, 137 | ⊢ |
| : , : , : |
42 | instantiation | 196, 49 | ⊢ |
| : , : , : |
43 | instantiation | 185, 50, 51 | ⊢ |
| : , : , : |
44 | instantiation | 196, 52 | ⊢ |
| : , : , : |
45 | theorem | | ⊢ |
| proveit.numbers.number_sets.complex_numbers.i_is_complex |
46 | instantiation | 53, 179, 108, 54* | ⊢ |
| : , : |
47 | instantiation | 175, 55, 115 | ⊢ |
| : , : |
48 | instantiation | 166 | ⊢ |
| : , : |
49 | instantiation | 56, 205, 165, 132, 124, 117, 57* | ⊢ |
| : , : , : |
50 | instantiation | 185, 58, 59 | ⊢ |
| : , : , : |
51 | instantiation | 185, 60, 61 | ⊢ |
| : , : , : |
52 | instantiation | 62, 146, 63, 64, 65* | ⊢ |
| : , : |
53 | theorem | | ⊢ |
| proveit.numbers.multiplication.mult_neg_left |
54 | instantiation | 195, 108 | ⊢ |
| : |
55 | instantiation | 175, 212, 181 | ⊢ |
| : , : |
56 | theorem | | ⊢ |
| proveit.numbers.exponentiation.real_power_of_product |
57 | instantiation | 66, 153, 203, 67* | ⊢ |
| : , : |
58 | instantiation | 185, 68, 69 | ⊢ |
| : , : , : |
59 | instantiation | 185, 70, 71 | ⊢ |
| : , : , : |
60 | instantiation | 142, 143, 92, 144, 94, 165, 101, 100 | ⊢ |
| : , : , : , : |
61 | instantiation | 185, 72, 73 | ⊢ |
| : , : , : |
62 | theorem | | ⊢ |
| proveit.numbers.division.div_as_mult |
63 | instantiation | 233, 211, 74 | ⊢ |
| : , : , : |
64 | instantiation | 150, 89 | ⊢ |
| : |
65 | instantiation | 75, 205, 122, 132, 124, 76* | ⊢ |
| : , : , : |
66 | theorem | | ⊢ |
| proveit.numbers.exponentiation.neg_power_as_div |
67 | instantiation | 138, 205 | ⊢ |
| : |
68 | instantiation | 141, 143, 92, 230, 144, 79, 205, 165, 101, 77 | ⊢ |
| : , : , : , : , : , : |
69 | instantiation | 141, 92, 232, 143, 79, 78, 144, 205, 165, 101, 95, 100 | ⊢ |
| : , : , : , : , : , : |
70 | instantiation | 97, 143, 92, 230, 144, 79, 205, 165, 101, 95, 100 | ⊢ |
| : , : , : , : , : , : , : |
71 | instantiation | 185, 80, 81 | ⊢ |
| : , : , : |
72 | instantiation | 185, 82, 83 | ⊢ |
| : , : , : |
73 | instantiation | 84, 230, 232, 143, 85, 144, 179, 86, 107, 87*, 88* | ⊢ |
| : , : , : , : , : , : |
74 | instantiation | 148, 149, 89 | ⊢ |
| : , : , : |
75 | theorem | | ⊢ |
| proveit.numbers.exponentiation.real_power_of_real_power |
76 | instantiation | 104, 108, 179, 90* | ⊢ |
| : , : |
77 | instantiation | 91, 95, 100 | ⊢ |
| : , : |
78 | instantiation | 166 | ⊢ |
| : , : |
79 | instantiation | 109 | ⊢ |
| : , : , : |
80 | instantiation | 98, 143, 232, 92, 144, 93, 94, 95, 205, 165, 101, 100 | ⊢ |
| : , : , : , : , : , : |
81 | instantiation | 196, 96 | ⊢ |
| : , : , : |
82 | instantiation | 97, 230, 143, 144, 165, 101, 100 | ⊢ |
| : , : , : , : , : , : , : |
83 | instantiation | 98, 143, 232, 230, 144, 99, 165, 100, 101, 102* | ⊢ |
| : , : , : , : , : , : |
84 | theorem | | ⊢ |
| proveit.numbers.multiplication.distribute_through_sum |
85 | instantiation | 166 | ⊢ |
| : , : |
86 | instantiation | 103, 105 | ⊢ |
| : |
87 | instantiation | 104, 179, 105, 106* | ⊢ |
| : , : |
88 | instantiation | 195, 107 | ⊢ |
| : |
89 | theorem | | ⊢ |
| proveit.physics.quantum.QPE._two_pow_t_is_nat_pos |
90 | instantiation | 204, 108 | ⊢ |
| : |
91 | theorem | | ⊢ |
| proveit.numbers.multiplication.mult_complex_closure_bin |
92 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.nat3 |
93 | instantiation | 166 | ⊢ |
| : , : |
94 | instantiation | 109 | ⊢ |
| : , : , : |
95 | instantiation | 233, 211, 110 | ⊢ |
| : , : , : |
96 | instantiation | 125, 111, 112 | ⊢ |
| : , : , : |
97 | theorem | | ⊢ |
| proveit.numbers.multiplication.leftward_commutation |
98 | theorem | | ⊢ |
| proveit.numbers.multiplication.association |
99 | instantiation | 166 | ⊢ |
| : , : |
100 | instantiation | 113, 165, 114 | ⊢ |
| : , : |
101 | instantiation | 233, 211, 115 | ⊢ |
| : , : , : |
102 | instantiation | 116, 165, 190, 132, 117, 118*, 119* | ⊢ |
| : , : , : |
103 | theorem | | ⊢ |
| proveit.numbers.negation.complex_closure |
104 | theorem | | ⊢ |
| proveit.numbers.multiplication.mult_neg_right |
105 | instantiation | 233, 211, 159 | ⊢ |
| : , : , : |
106 | instantiation | 185, 120, 121 | ⊢ |
| : , : , : |
107 | instantiation | 233, 211, 135 | ⊢ |
| : , : , : |
108 | instantiation | 233, 211, 122 | ⊢ |
| : , : , : |
109 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.tuple_len_3_typical_eq |
110 | instantiation | 123, 190, 212, 124 | ⊢ |
| : , : |
111 | instantiation | 125, 126, 127 | ⊢ |
| : , : , : |
112 | instantiation | 128, 129, 130, 131 | ⊢ |
| : , : , : , : |
113 | theorem | | ⊢ |
| proveit.numbers.exponentiation.exp_complex_closure |
114 | instantiation | 233, 211, 132 | ⊢ |
| : , : , : |
115 | instantiation | 133, 134, 135 | ⊢ |
| : , : |
116 | theorem | | ⊢ |
| proveit.numbers.exponentiation.product_of_real_powers |
117 | instantiation | 136, 137 | ⊢ |
| : |
118 | instantiation | 138, 165 | ⊢ |
| : |
119 | instantiation | 185, 139, 140 | ⊢ |
| : , : , : |
120 | instantiation | 141, 230, 232, 143, 145, 144, 179, 146, 147 | ⊢ |
| : , : , : , : , : , : |
121 | instantiation | 142, 143, 232, 144, 145, 146, 147 | ⊢ |
| : , : , : , : |
122 | instantiation | 148, 149, 225 | ⊢ |
| : , : , : |
123 | theorem | | ⊢ |
| proveit.numbers.division.div_real_closure |
124 | instantiation | 150, 224 | ⊢ |
| : |
125 | theorem | | ⊢ |
| proveit.logic.equality.sub_right_side_into |
126 | instantiation | 151, 179, 152, 153 | ⊢ |
| : , : , : , : , : |
127 | instantiation | 185, 154, 155 | ⊢ |
| : , : , : |
128 | theorem | | ⊢ |
| proveit.logic.equality.four_chain_transitivity |
129 | instantiation | 196, 156 | ⊢ |
| : , : , : |
130 | instantiation | 196, 156 | ⊢ |
| : , : , : |
131 | instantiation | 204, 179 | ⊢ |
| : |
132 | instantiation | 233, 218, 157 | ⊢ |
| : , : , : |
133 | theorem | | ⊢ |
| proveit.numbers.addition.add_real_closure_bin |
134 | instantiation | 158, 159 | ⊢ |
| : |
135 | instantiation | 160, 161 | ⊢ |
| : |
136 | theorem | | ⊢ |
| proveit.numbers.number_sets.real_numbers.nonzero_if_in_real_nonzero |
137 | instantiation | 233, 162, 193 | ⊢ |
| : , : , : |
138 | theorem | | ⊢ |
| proveit.numbers.exponentiation.complex_x_to_first_power_is_x |
139 | instantiation | 196, 163 | ⊢ |
| : , : , : |
140 | instantiation | 164, 165 | ⊢ |
| : |
141 | theorem | | ⊢ |
| proveit.numbers.multiplication.disassociation |
142 | theorem | | ⊢ |
| proveit.numbers.multiplication.elim_one_any |
143 | axiom | | ⊢ |
| proveit.numbers.number_sets.natural_numbers.zero_in_nats |
144 | theorem | | ⊢ |
| proveit.core_expr_types.tuples.tuple_len_0_typical_eq |
145 | instantiation | 166 | ⊢ |
| : , : |
146 | instantiation | 233, 211, 176 | ⊢ |
| : , : , : |
147 | instantiation | 233, 211, 177 | ⊢ |
| : , : , : |
148 | theorem | | ⊢ |
| proveit.logic.sets.inclusion.unfold_subset_eq |
149 | instantiation | 167, 168 | ⊢ |
| : , : |
150 | theorem | | ⊢ |
| proveit.numbers.number_sets.natural_numbers.nonzero_if_is_nat_pos |
151 | theorem | | ⊢ |
| proveit.numbers.division.mult_frac_cancel_denom_left |
152 | instantiation | 233, 170, 169 | ⊢ |
| : , : , : |
153 | instantiation | 233, 170, 171 | ⊢ |
| : , : , : |
154 | instantiation | 196, 172 | ⊢ |
| : , : , : |
155 | instantiation | 196, 173 | ⊢ |
| : , : , : |
156 | instantiation | 198, 179 | ⊢ |
| : |
157 | instantiation | 233, 226, 174 | ⊢ |
| : , : , : |
158 | theorem | | ⊢ |
| proveit.numbers.negation.real_closure |
159 | instantiation | 175, 176, 177 | ⊢ |
| : , : |
160 | theorem | | ⊢ |
| proveit.physics.quantum.QPE._delta_b_is_real |
161 | theorem | | ⊢ |
| proveit.physics.quantum.QPE._best_floor_is_int |
162 | theorem | | ⊢ |
| proveit.numbers.number_sets.real_numbers.real_pos_within_real_nonzero |
163 | instantiation | 178, 179, 180 | ⊢ |
| : , : |
164 | theorem | | ⊢ |
| proveit.numbers.exponentiation.exp_zero_eq_one |
165 | instantiation | 233, 211, 181 | ⊢ |
| : , : , : |
166 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.tuple_len_2_typical_eq |
167 | theorem | | ⊢ |
| proveit.logic.sets.inclusion.relax_proper_subset |
168 | theorem | | ⊢ |
| proveit.numbers.number_sets.real_numbers.nat_pos_within_real |
169 | instantiation | 233, 183, 182 | ⊢ |
| : , : , : |
170 | theorem | | ⊢ |
| proveit.numbers.number_sets.complex_numbers.real_nonzero_within_complex_nonzero |
171 | instantiation | 233, 183, 209 | ⊢ |
| : , : , : |
172 | instantiation | 196, 184 | ⊢ |
| : , : , : |
173 | instantiation | 185, 186, 187 | ⊢ |
| : , : , : |
174 | instantiation | 228, 222 | ⊢ |
| : |
175 | theorem | | ⊢ |
| proveit.numbers.multiplication.mult_real_closure_bin |
176 | instantiation | 233, 218, 188 | ⊢ |
| : , : , : |
177 | instantiation | 233, 218, 189 | ⊢ |
| : , : , : |
178 | theorem | | ⊢ |
| proveit.numbers.addition.subtraction.add_cancel_basic |
179 | instantiation | 233, 211, 190 | ⊢ |
| : , : , : |
180 | instantiation | 191 | ⊢ |
| : |
181 | instantiation | 233, 192, 193 | ⊢ |
| : , : , : |
182 | instantiation | 233, 215, 194 | ⊢ |
| : , : , : |
183 | theorem | | ⊢ |
| proveit.numbers.number_sets.real_numbers.rational_nonzero_within_real_nonzero |
184 | instantiation | 195, 205 | ⊢ |
| : |
185 | axiom | | ⊢ |
| proveit.logic.equality.equals_transitivity |
186 | instantiation | 196, 197 | ⊢ |
| : , : , : |
187 | instantiation | 198, 205 | ⊢ |
| : |
188 | instantiation | 233, 226, 199 | ⊢ |
| : , : , : |
189 | instantiation | 233, 200, 201 | ⊢ |
| : , : , : |
190 | instantiation | 233, 218, 202 | ⊢ |
| : , : , : |
191 | axiom | | ⊢ |
| proveit.logic.equality.equals_reflexivity |
192 | theorem | | ⊢ |
| proveit.numbers.number_sets.real_numbers.real_pos_within_real |
193 | theorem | | ⊢ |
| proveit.numbers.number_sets.real_numbers.pi_is_real_pos |
194 | instantiation | 233, 223, 203 | ⊢ |
| : , : , : |
195 | theorem | | ⊢ |
| proveit.numbers.multiplication.elim_one_left |
196 | axiom | | ⊢ |
| proveit.logic.equality.substitution |
197 | instantiation | 204, 205 | ⊢ |
| : |
198 | theorem | | ⊢ |
| proveit.numbers.division.frac_one_denom |
199 | instantiation | 233, 206, 207 | ⊢ |
| : , : , : |
200 | theorem | | ⊢ |
| proveit.numbers.number_sets.rational_numbers.rational_nonzero_within_rational |
201 | instantiation | 208, 209, 210 | ⊢ |
| : , : |
202 | instantiation | 233, 226, 222 | ⊢ |
| : , : , : |
203 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.posnat1 |
204 | theorem | | ⊢ |
| proveit.numbers.multiplication.elim_one_right |
205 | instantiation | 233, 211, 212 | ⊢ |
| : , : , : |
206 | instantiation | 213, 214, 229 | ⊢ |
| : , : |
207 | assumption | | ⊢ |
208 | theorem | | ⊢ |
| proveit.numbers.exponentiation.exp_rational_nonzero_closure |
209 | instantiation | 233, 215, 216 | ⊢ |
| : , : , : |
210 | instantiation | 228, 217 | ⊢ |
| : |
211 | theorem | | ⊢ |
| proveit.numbers.number_sets.complex_numbers.real_within_complex |
212 | instantiation | 233, 218, 219 | ⊢ |
| : , : , : |
213 | theorem | | ⊢ |
| proveit.numbers.number_sets.integers.int_interval_within_int |
214 | instantiation | 220, 221, 222 | ⊢ |
| : , : |
215 | theorem | | ⊢ |
| proveit.numbers.number_sets.rational_numbers.nonzero_int_within_rational_nonzero |
216 | instantiation | 233, 223, 224 | ⊢ |
| : , : , : |
217 | instantiation | 233, 234, 225 | ⊢ |
| : , : , : |
218 | theorem | | ⊢ |
| proveit.numbers.number_sets.real_numbers.rational_within_real |
219 | instantiation | 233, 226, 227 | ⊢ |
| : , : , : |
220 | theorem | | ⊢ |
| proveit.numbers.addition.add_int_closure_bin |
221 | instantiation | 228, 229 | ⊢ |
| : |
222 | instantiation | 233, 231, 230 | ⊢ |
| : , : , : |
223 | theorem | | ⊢ |
| proveit.numbers.number_sets.integers.nat_pos_within_nonzero_int |
224 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.posnat2 |
225 | axiom | | ⊢ |
| proveit.physics.quantum.QPE._t_in_natural_pos |
226 | theorem | | ⊢ |
| proveit.numbers.number_sets.rational_numbers.int_within_rational |
227 | instantiation | 233, 231, 232 | ⊢ |
| : , : , : |
228 | theorem | | ⊢ |
| proveit.numbers.negation.int_closure |
229 | instantiation | 233, 234, 235 | ⊢ |
| : , : , : |
230 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.nat1 |
231 | theorem | | ⊢ |
| proveit.numbers.number_sets.integers.nat_within_int |
232 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.nat2 |
233 | theorem | | ⊢ |
| proveit.logic.sets.inclusion.superset_membership_from_proper_subset |
234 | theorem | | ⊢ |
| proveit.numbers.number_sets.integers.nat_pos_within_int |
235 | theorem | | ⊢ |
| proveit.physics.quantum.QPE._two_pow_t_minus_one_is_nat_pos |
*equality replacement requirements |