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