| step type | requirements | statement |
0 | instantiation | 1, 2, 3* | ⊢ |
| : |
1 | theorem | | ⊢ |
| proveit.physics.quantum.QPE._alpha_m_evaluation |
2 | assumption | | ⊢ |
3 | instantiation | 130, 4, 5 | ⊢ |
| : , : , : |
4 | instantiation | 102, 6 | ⊢ |
| : , : , : |
5 | instantiation | 139, 7, 8 | ⊢ |
| : , : , : |
6 | instantiation | 130, 9, 10 | ⊢ |
| : , : , : |
7 | instantiation | 139, 11, 12 | ⊢ |
| : , : , : |
8 | instantiation | 41, 13, 14, 15 | ⊢ |
| : , : , : , : |
9 | instantiation | 102, 16 | ⊢ |
| : , : , : |
10 | instantiation | 17, 182, 183, 54, 18* | ⊢ |
| : , : , : |
11 | instantiation | 19, 54, 106, 105 | ⊢ |
| : , : , : , : , : |
12 | instantiation | 130, 20, 21 | ⊢ |
| : , : , : |
13 | instantiation | 102, 22 | ⊢ |
| : , : , : |
14 | instantiation | 102, 22 | ⊢ |
| : , : , : |
15 | instantiation | 118, 54 | ⊢ |
| : |
16 | modus ponens | 23, 24 | ⊢ |
17 | theorem | | ⊢ |
| proveit.numbers.summation.trivial_sum |
18 | instantiation | 130, 25, 108 | ⊢ |
| : , : , : |
19 | theorem | | ⊢ |
| proveit.numbers.division.mult_frac_cancel_denom_left |
20 | instantiation | 102, 26 | ⊢ |
| : , : , : |
21 | instantiation | 102, 27 | ⊢ |
| : , : , : |
22 | instantiation | 98, 54 | ⊢ |
| : |
23 | instantiation | 28, 149 | ⊢ |
| : , : , : , : , : , : |
24 | generalization | 29 | ⊢ |
25 | instantiation | 102, 30 | ⊢ |
| : , : , : |
26 | instantiation | 102, 31 | ⊢ |
| : , : , : |
27 | instantiation | 130, 32, 33 | ⊢ |
| : , : , : |
28 | axiom | | ⊢ |
| proveit.core_expr_types.lambda_maps.lambda_substitution |
29 | instantiation | 34, 35 | ⊢ |
| : , : , : |
30 | instantiation | 130, 36, 37 | ⊢ |
| : , : , : |
31 | instantiation | 38, 125 | ⊢ |
| : |
32 | instantiation | 102, 108 | ⊢ |
| : , : , : |
33 | instantiation | 98, 125 | ⊢ |
| : |
34 | axiom | | ⊢ |
| proveit.core_expr_types.conditionals.conditional_substitution |
35 | deduction | 39 | ⊢ |
36 | instantiation | 102, 40 | ⊢ |
| : , : , : |
37 | instantiation | 41, 42, 43, 44 | ⊢ |
| : , : , : , : |
38 | theorem | | ⊢ |
| proveit.numbers.multiplication.elim_one_left |
39 | instantiation | 130, 45, 46 | ⊢ |
| : , : , : |
40 | theorem | | ⊢ |
| proveit.numbers.negation.negated_zero |
41 | theorem | | ⊢ |
| proveit.logic.equality.four_chain_transitivity |
42 | instantiation | 47, 152, 178, 153, 51, 48, 125, 52, 49, 54 | ⊢ |
| : , : , : , : , : , : |
43 | instantiation | 50, 178, 193, 51, 125, 52, 54 | ⊢ |
| : , : , : , : |
44 | instantiation | 53, 54, 125, 55 | ⊢ |
| : , : , : |
45 | instantiation | 102, 56 | ⊢ |
| : , : , : |
46 | instantiation | 57, 88, 58, 80, 59* | ⊢ |
| : , : , : |
47 | theorem | | ⊢ |
| proveit.numbers.addition.disassociation |
48 | instantiation | 164 | ⊢ |
| : , : |
49 | theorem | | ⊢ |
| proveit.numbers.number_sets.complex_numbers.zero_is_complex |
50 | theorem | | ⊢ |
| proveit.numbers.addition.elim_zero_any |
51 | instantiation | 164 | ⊢ |
| : , : |
52 | instantiation | 191, 168, 60 | ⊢ |
| : , : , : |
53 | theorem | | ⊢ |
| proveit.numbers.addition.subtraction.add_cancel_triple_32 |
54 | instantiation | 191, 168, 61 | ⊢ |
| : , : , : |
55 | instantiation | 74 | ⊢ |
| : |
56 | instantiation | 62, 63, 64, 65, 66, 67 | ⊢ |
| : , : , : |
57 | theorem | | ⊢ |
| proveit.numbers.exponentiation.product_of_complex_powers |
58 | instantiation | 68, 107 | ⊢ |
| : |
59 | instantiation | 130, 69, 70 | ⊢ |
| : , : , : |
60 | instantiation | 191, 173, 71 | ⊢ |
| : , : , : |
61 | instantiation | 191, 173, 72 | ⊢ |
| : , : , : |
62 | theorem | | ⊢ |
| proveit.core_expr_types.tuples.tuple_eq_via_elem_eq |
63 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.posnat2 |
64 | instantiation | 164 | ⊢ |
| : , : |
65 | instantiation | 164 | ⊢ |
| : , : |
66 | instantiation | 102, 73 | ⊢ |
| : , : , : |
67 | instantiation | 74 | ⊢ |
| : |
68 | theorem | | ⊢ |
| proveit.numbers.negation.complex_closure |
69 | instantiation | 102, 75 | ⊢ |
| : , : , : |
70 | instantiation | 76, 77 | ⊢ |
| : |
71 | instantiation | 191, 176, 186 | ⊢ |
| : , : , : |
72 | instantiation | 191, 176, 190 | ⊢ |
| : , : , : |
73 | instantiation | 102, 78 | ⊢ |
| : , : , : |
74 | axiom | | ⊢ |
| proveit.logic.equality.equals_reflexivity |
75 | instantiation | 79, 107, 80, 81 | ⊢ |
| : , : |
76 | theorem | | ⊢ |
| proveit.numbers.exponentiation.exp_zero_eq_one |
77 | instantiation | 191, 168, 82 | ⊢ |
| : , : , : |
78 | instantiation | 130, 83, 84 | ⊢ |
| : , : , : |
79 | theorem | | ⊢ |
| proveit.numbers.addition.subtraction.add_cancel_reverse |
80 | instantiation | 139, 85, 86 | ⊢ |
| : , : , : |
81 | instantiation | 119, 143, 193, 152, 87, 153, 156, 157, 162, 163, 155 | ⊢ |
| : , : , : , : , : , : , : |
82 | instantiation | 191, 171, 88 | ⊢ |
| : , : , : |
83 | instantiation | 102, 89 | ⊢ |
| : , : , : |
84 | instantiation | 130, 90, 91 | ⊢ |
| : , : , : |
85 | instantiation | 161, 142, 92 | ⊢ |
| : , : |
86 | instantiation | 130, 93, 94 | ⊢ |
| : , : , : |
87 | instantiation | 158 | ⊢ |
| : , : , : |
88 | theorem | | ⊢ |
| proveit.numbers.number_sets.real_numbers.e_is_real_pos |
89 | instantiation | 151, 120, 178, 152, 121, 95, 153, 156, 157, 162, 163, 125, 155 | ⊢ |
| : , : , : , : , : , : |
90 | instantiation | 130, 96, 97 | ⊢ |
| : , : , : |
91 | instantiation | 98, 107 | ⊢ |
| : |
92 | instantiation | 139, 99, 100 | ⊢ |
| : , : , : |
93 | instantiation | 151, 193, 143, 152, 101, 153, 142, 162, 155, 163 | ⊢ |
| : , : , : , : , : , : |
94 | instantiation | 151, 152, 178, 143, 153, 144, 101, 156, 157, 162, 155, 163 | ⊢ |
| : , : , : , : , : , : |
95 | instantiation | 164 | ⊢ |
| : , : |
96 | instantiation | 102, 103 | ⊢ |
| : , : , : |
97 | instantiation | 104, 105, 106, 107, 108* | ⊢ |
| : , : , : |
98 | theorem | | ⊢ |
| proveit.numbers.division.frac_one_denom |
99 | instantiation | 161, 109, 163 | ⊢ |
| : , : |
100 | instantiation | 151, 152, 178, 193, 153, 110, 162, 155, 163 | ⊢ |
| : , : , : , : , : , : |
101 | instantiation | 158 | ⊢ |
| : , : , : |
102 | axiom | | ⊢ |
| proveit.logic.equality.substitution |
103 | instantiation | 130, 111, 112 | ⊢ |
| : , : , : |
104 | theorem | | ⊢ |
| proveit.numbers.division.frac_cancel_left |
105 | instantiation | 191, 114, 113 | ⊢ |
| : , : , : |
106 | instantiation | 191, 114, 115 | ⊢ |
| : , : , : |
107 | instantiation | 139, 116, 117 | ⊢ |
| : , : , : |
108 | instantiation | 118, 125 | ⊢ |
| : |
109 | instantiation | 161, 162, 155 | ⊢ |
| : , : |
110 | instantiation | 164 | ⊢ |
| : , : |
111 | instantiation | 119, 152, 120, 193, 153, 121, 156, 157, 162, 163, 125, 155 | ⊢ |
| : , : , : , : , : , : , : |
112 | instantiation | 122, 193, 123, 152, 124, 153, 125, 156, 157, 162, 163, 155 | ⊢ |
| : , : , : , : , : , : |
113 | instantiation | 191, 127, 126 | ⊢ |
| : , : , : |
114 | theorem | | ⊢ |
| proveit.numbers.number_sets.complex_numbers.real_nonzero_within_complex_nonzero |
115 | instantiation | 191, 127, 128 | ⊢ |
| : , : , : |
116 | instantiation | 161, 142, 129 | ⊢ |
| : , : |
117 | instantiation | 130, 131, 132 | ⊢ |
| : , : , : |
118 | theorem | | ⊢ |
| proveit.numbers.multiplication.elim_one_right |
119 | theorem | | ⊢ |
| proveit.numbers.multiplication.leftward_commutation |
120 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.nat4 |
121 | instantiation | 133 | ⊢ |
| : , : , : , : |
122 | theorem | | ⊢ |
| proveit.numbers.multiplication.association |
123 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.nat5 |
124 | instantiation | 134 | ⊢ |
| : , : , : , : , : |
125 | instantiation | 191, 168, 135 | ⊢ |
| : , : , : |
126 | instantiation | 191, 137, 136 | ⊢ |
| : , : , : |
127 | theorem | | ⊢ |
| proveit.numbers.number_sets.real_numbers.rational_nonzero_within_real_nonzero |
128 | instantiation | 191, 137, 138 | ⊢ |
| : , : , : |
129 | instantiation | 139, 140, 141 | ⊢ |
| : , : , : |
130 | axiom | | ⊢ |
| proveit.logic.equality.equals_transitivity |
131 | instantiation | 151, 193, 143, 152, 145, 153, 142, 162, 163, 155 | ⊢ |
| : , : , : , : , : , : |
132 | instantiation | 151, 152, 178, 143, 153, 144, 145, 156, 157, 162, 163, 155 | ⊢ |
| : , : , : , : , : , : |
133 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.tuple_len_4_typical_eq |
134 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.tuple_len_5_typical_eq |
135 | instantiation | 146, 147, 188 | ⊢ |
| : , : , : |
136 | instantiation | 191, 148, 188 | ⊢ |
| : , : , : |
137 | theorem | | ⊢ |
| proveit.numbers.number_sets.rational_numbers.nonzero_int_within_rational_nonzero |
138 | instantiation | 191, 148, 149 | ⊢ |
| : , : , : |
139 | theorem | | ⊢ |
| proveit.logic.equality.sub_right_side_into |
140 | instantiation | 161, 150, 155 | ⊢ |
| : , : |
141 | instantiation | 151, 152, 178, 193, 153, 154, 162, 163, 155 | ⊢ |
| : , : , : , : , : , : |
142 | instantiation | 161, 156, 157 | ⊢ |
| : , : |
143 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.nat3 |
144 | instantiation | 164 | ⊢ |
| : , : |
145 | instantiation | 158 | ⊢ |
| : , : , : |
146 | theorem | | ⊢ |
| proveit.logic.sets.inclusion.unfold_subset_eq |
147 | instantiation | 159, 160 | ⊢ |
| : , : |
148 | theorem | | ⊢ |
| proveit.numbers.number_sets.integers.nat_pos_within_nonzero_int |
149 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.posnat1 |
150 | instantiation | 161, 162, 163 | ⊢ |
| : , : |
151 | theorem | | ⊢ |
| proveit.numbers.multiplication.disassociation |
152 | axiom | | ⊢ |
| proveit.numbers.number_sets.natural_numbers.zero_in_nats |
153 | theorem | | ⊢ |
| proveit.core_expr_types.tuples.tuple_len_0_typical_eq |
154 | instantiation | 164 | ⊢ |
| : , : |
155 | instantiation | 191, 168, 165 | ⊢ |
| : , : , : |
156 | instantiation | 191, 168, 166 | ⊢ |
| : , : , : |
157 | instantiation | 191, 168, 167 | ⊢ |
| : , : , : |
158 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.tuple_len_3_typical_eq |
159 | theorem | | ⊢ |
| proveit.logic.sets.inclusion.relax_proper_subset |
160 | theorem | | ⊢ |
| proveit.numbers.number_sets.real_numbers.nat_pos_within_real |
161 | theorem | | ⊢ |
| proveit.numbers.multiplication.mult_complex_closure_bin |
162 | theorem | | ⊢ |
| proveit.numbers.number_sets.complex_numbers.i_is_complex |
163 | instantiation | 191, 168, 169 | ⊢ |
| : , : , : |
164 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.tuple_len_2_typical_eq |
165 | theorem | | ⊢ |
| proveit.physics.quantum.QPE._phase_is_real |
166 | instantiation | 191, 173, 170 | ⊢ |
| : , : , : |
167 | instantiation | 191, 171, 172 | ⊢ |
| : , : , : |
168 | theorem | | ⊢ |
| proveit.numbers.number_sets.complex_numbers.real_within_complex |
169 | instantiation | 191, 173, 174 | ⊢ |
| : , : , : |
170 | instantiation | 191, 176, 175 | ⊢ |
| : , : , : |
171 | theorem | | ⊢ |
| proveit.numbers.number_sets.real_numbers.real_pos_within_real |
172 | theorem | | ⊢ |
| proveit.numbers.number_sets.real_numbers.pi_is_real_pos |
173 | theorem | | ⊢ |
| proveit.numbers.number_sets.real_numbers.rational_within_real |
174 | instantiation | 191, 176, 177 | ⊢ |
| : , : , : |
175 | instantiation | 191, 192, 178 | ⊢ |
| : , : , : |
176 | theorem | | ⊢ |
| proveit.numbers.number_sets.rational_numbers.int_within_rational |
177 | instantiation | 191, 179, 180 | ⊢ |
| : , : , : |
178 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.nat2 |
179 | instantiation | 181, 182, 183 | ⊢ |
| : , : |
180 | assumption | | ⊢ |
181 | theorem | | ⊢ |
| proveit.numbers.number_sets.integers.int_interval_within_int |
182 | theorem | | ⊢ |
| proveit.numbers.number_sets.integers.zero_is_int |
183 | instantiation | 184, 185, 186 | ⊢ |
| : , : |
184 | theorem | | ⊢ |
| proveit.numbers.addition.add_int_closure_bin |
185 | instantiation | 191, 187, 188 | ⊢ |
| : , : , : |
186 | instantiation | 189, 190 | ⊢ |
| : |
187 | theorem | | ⊢ |
| proveit.numbers.number_sets.integers.nat_pos_within_int |
188 | theorem | | ⊢ |
| proveit.physics.quantum.QPE._two_pow_t_is_nat_pos |
189 | theorem | | ⊢ |
| proveit.numbers.negation.int_closure |
190 | instantiation | 191, 192, 193 | ⊢ |
| : , : , : |
191 | theorem | | ⊢ |
| proveit.logic.sets.inclusion.superset_membership_from_proper_subset |
192 | theorem | | ⊢ |
| proveit.numbers.number_sets.integers.nat_within_int |
193 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.nat1 |
*equality replacement requirements |