| step type | requirements | statement |
0 | instantiation | 1, 2, 3 | ⊢ |
| : , : , : |
1 | reference | 9 | ⊢ |
2 | instantiation | 4, 5, 6, 7* | ⊢ |
| : |
3 | instantiation | 156, 8 | ⊢ |
| : , : , : |
4 | theorem | | ⊢ |
| proveit.numbers.exponentiation.unit_complex_polar_num_neq_one |
5 | instantiation | 111, 46, 36 | ⊢ |
| : , : , : |
6 | instantiation | 9, 10, 11 | ⊢ |
| : , : , : |
7 | instantiation | 12, 13 | ⊢ |
| : , : |
8 | instantiation | 75, 175, 168, 80, 47, 82, 164, 121, 41, 86 | ⊢ |
| : , : , : , : , : , : , : |
9 | theorem | | ⊢ |
| proveit.logic.equality.sub_left_side_into |
10 | instantiation | 14, 15, 16, 34, 32 | ⊢ |
| : , : |
11 | instantiation | 114, 17, 18, 19 | ⊢ |
| : , : , : , : |
12 | theorem | | ⊢ |
| proveit.logic.equality.equals_reversal |
13 | instantiation | 156, 20 | ⊢ |
| : , : , : |
14 | theorem | | ⊢ |
| proveit.logic.booleans.disjunction.right_if_not_left |
15 | instantiation | 21, 22 | ⊢ |
| : |
16 | instantiation | 23, 24 | ⊢ |
| : , : |
17 | instantiation | 25, 26, 27, 28, 29* | ⊢ |
| : , : |
18 | instantiation | 155, 86 | ⊢ |
| : |
19 | instantiation | 140 | ⊢ |
| : |
20 | instantiation | 148, 30, 31 | ⊢ |
| : , : , : |
21 | axiom | | ⊢ |
| proveit.logic.booleans.negation.operand_is_bool |
22 | instantiation | 33, 32 | ⊢ |
| : |
23 | axiom | | ⊢ |
| proveit.logic.booleans.disjunction.right_in_bool |
24 | instantiation | 33, 34 | ⊢ |
| : |
25 | theorem | | ⊢ |
| proveit.numbers.division.div_as_mult |
26 | instantiation | 111, 35, 36 | ⊢ |
| : , : , : |
27 | instantiation | 173, 166, 52 | ⊢ |
| : , : , : |
28 | instantiation | 37, 175, 47, 126, 38 | ⊢ |
| : , : |
29 | instantiation | 148, 39, 40 | ⊢ |
| : , : , : |
30 | instantiation | 75, 80, 81, 82, 72, 164, 121, 86, 41 | ⊢ |
| : , : , : , : , : , : , : |
31 | instantiation | 79, 168, 81, 80, 72, 82, 41, 164, 121, 86 | ⊢ |
| : , : , : , : , : , : |
32 | instantiation | 42, 43 | ⊢ |
| : , : |
33 | theorem | | ⊢ |
| proveit.logic.booleans.in_bool_if_true |
34 | instantiation | 44, 45 | ⊢ |
| : |
35 | instantiation | 173, 166, 46 | ⊢ |
| : , : , : |
36 | instantiation | 70, 80, 175, 168, 82, 47, 164, 121, 86 | ⊢ |
| : , : , : , : , : , : |
37 | theorem | | ⊢ |
| proveit.numbers.multiplication.mult_not_eq_zero |
38 | instantiation | 173, 135, 102 | ⊢ |
| : , : , : |
39 | instantiation | 156, 48 | ⊢ |
| : , : , : |
40 | instantiation | 148, 49, 50 | ⊢ |
| : , : , : |
41 | theorem | | ⊢ |
| proveit.numbers.number_sets.complex_numbers.i_is_complex |
42 | theorem | | ⊢ |
| proveit.logic.equality.unfold_not_equals |
43 | assumption | | ⊢ |
44 | theorem | | ⊢ |
| proveit.physics.quantum.QPE._delta_b_is_zero_or_non_int |
45 | instantiation | 51, 168, 80, 82 | ⊢ |
| : , : , : , : , : |
46 | instantiation | 59, 52, 96 | ⊢ |
| : , : |
47 | instantiation | 93 | ⊢ |
| : , : |
48 | instantiation | 53, 164, 121, 110, 107, 90, 54* | ⊢ |
| : , : , : |
49 | instantiation | 148, 55, 56 | ⊢ |
| : , : , : |
50 | instantiation | 148, 57, 58 | ⊢ |
| : , : , : |
51 | theorem | | ⊢ |
| proveit.logic.sets.enumeration.in_enumerated_set |
52 | instantiation | 59, 167, 132 | ⊢ |
| : , : |
53 | theorem | | ⊢ |
| proveit.numbers.exponentiation.real_power_of_product |
54 | instantiation | 60, 126, 160, 61* | ⊢ |
| : , : |
55 | instantiation | 148, 62, 63 | ⊢ |
| : , : , : |
56 | instantiation | 148, 64, 65 | ⊢ |
| : , : , : |
57 | instantiation | 66, 80, 81, 82, 84, 121, 86, 87 | ⊢ |
| : , : , : , : |
58 | instantiation | 148, 67, 68 | ⊢ |
| : , : , : |
59 | theorem | | ⊢ |
| proveit.numbers.multiplication.mult_real_closure_bin |
60 | theorem | | ⊢ |
| proveit.numbers.exponentiation.neg_power_as_div |
61 | instantiation | 103, 164 | ⊢ |
| : |
62 | instantiation | 70, 80, 81, 168, 82, 72, 164, 121, 86, 69 | ⊢ |
| : , : , : , : , : , : |
63 | instantiation | 70, 81, 175, 80, 72, 71, 82, 164, 121, 86, 85, 87 | ⊢ |
| : , : , : , : , : , : |
64 | instantiation | 75, 80, 81, 168, 82, 72, 164, 121, 86, 85, 87 | ⊢ |
| : , : , : , : , : , : , : |
65 | instantiation | 148, 73, 74 | ⊢ |
| : , : , : |
66 | theorem | | ⊢ |
| proveit.numbers.multiplication.elim_one_any |
67 | instantiation | 75, 168, 80, 82, 121, 86, 87 | ⊢ |
| : , : , : , : , : , : , : |
68 | instantiation | 79, 80, 175, 168, 82, 76, 121, 87, 86, 77* | ⊢ |
| : , : , : , : , : , : |
69 | instantiation | 78, 85, 87 | ⊢ |
| : , : |
70 | theorem | | ⊢ |
| proveit.numbers.multiplication.disassociation |
71 | instantiation | 93 | ⊢ |
| : , : |
72 | instantiation | 94 | ⊢ |
| : , : , : |
73 | instantiation | 79, 80, 175, 81, 82, 83, 84, 85, 164, 121, 86, 87 | ⊢ |
| : , : , : , : , : , : |
74 | instantiation | 156, 88 | ⊢ |
| : , : , : |
75 | theorem | | ⊢ |
| proveit.numbers.multiplication.leftward_commutation |
76 | instantiation | 93 | ⊢ |
| : , : |
77 | instantiation | 89, 121, 151, 110, 90, 91*, 92* | ⊢ |
| : , : , : |
78 | theorem | | ⊢ |
| proveit.numbers.multiplication.mult_complex_closure_bin |
79 | theorem | | ⊢ |
| proveit.numbers.multiplication.association |
80 | axiom | | ⊢ |
| proveit.numbers.number_sets.natural_numbers.zero_in_nats |
81 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.nat3 |
82 | theorem | | ⊢ |
| proveit.core_expr_types.tuples.tuple_len_0_typical_eq |
83 | instantiation | 93 | ⊢ |
| : , : |
84 | instantiation | 94 | ⊢ |
| : , : , : |
85 | instantiation | 173, 166, 95 | ⊢ |
| : , : , : |
86 | instantiation | 173, 166, 96 | ⊢ |
| : , : , : |
87 | instantiation | 97, 121, 98 | ⊢ |
| : , : |
88 | instantiation | 111, 99, 100 | ⊢ |
| : , : , : |
89 | theorem | | ⊢ |
| proveit.numbers.exponentiation.product_of_real_powers |
90 | instantiation | 101, 102 | ⊢ |
| : |
91 | instantiation | 103, 121 | ⊢ |
| : |
92 | instantiation | 148, 104, 105 | ⊢ |
| : , : , : |
93 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.tuple_len_2_typical_eq |
94 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.tuple_len_3_typical_eq |
95 | instantiation | 106, 151, 167, 107 | ⊢ |
| : , : |
96 | instantiation | 108, 109 | ⊢ |
| : |
97 | theorem | | ⊢ |
| proveit.numbers.exponentiation.exp_complex_closure |
98 | instantiation | 173, 166, 110 | ⊢ |
| : , : , : |
99 | instantiation | 111, 112, 113 | ⊢ |
| : , : , : |
100 | instantiation | 114, 115, 116, 117 | ⊢ |
| : , : , : , : |
101 | theorem | | ⊢ |
| proveit.numbers.number_sets.real_numbers.nonzero_if_in_real_nonzero |
102 | instantiation | 173, 118, 142 | ⊢ |
| : , : , : |
103 | theorem | | ⊢ |
| proveit.numbers.exponentiation.complex_x_to_first_power_is_x |
104 | instantiation | 156, 119 | ⊢ |
| : , : , : |
105 | instantiation | 120, 121 | ⊢ |
| : |
106 | theorem | | ⊢ |
| proveit.numbers.division.div_real_closure |
107 | instantiation | 122, 162 | ⊢ |
| : |
108 | theorem | | ⊢ |
| proveit.physics.quantum.QPE._delta_b_is_real |
109 | theorem | | ⊢ |
| proveit.physics.quantum.QPE._best_round_is_int |
110 | instantiation | 173, 169, 123 | ⊢ |
| : , : , : |
111 | theorem | | ⊢ |
| proveit.logic.equality.sub_right_side_into |
112 | instantiation | 124, 139, 125, 126 | ⊢ |
| : , : , : , : , : |
113 | instantiation | 148, 127, 128 | ⊢ |
| : , : , : |
114 | theorem | | ⊢ |
| proveit.logic.equality.four_chain_transitivity |
115 | instantiation | 156, 129 | ⊢ |
| : , : , : |
116 | instantiation | 156, 129 | ⊢ |
| : , : , : |
117 | instantiation | 163, 139 | ⊢ |
| : |
118 | theorem | | ⊢ |
| proveit.numbers.number_sets.real_numbers.real_pos_within_real_nonzero |
119 | instantiation | 130, 139, 131 | ⊢ |
| : , : |
120 | theorem | | ⊢ |
| proveit.numbers.exponentiation.exp_zero_eq_one |
121 | instantiation | 173, 166, 132 | ⊢ |
| : , : , : |
122 | theorem | | ⊢ |
| proveit.numbers.number_sets.natural_numbers.nonzero_if_is_nat_pos |
123 | instantiation | 173, 171, 133 | ⊢ |
| : , : , : |
124 | theorem | | ⊢ |
| proveit.numbers.division.mult_frac_cancel_denom_left |
125 | instantiation | 173, 135, 134 | ⊢ |
| : , : , : |
126 | instantiation | 173, 135, 136 | ⊢ |
| : , : , : |
127 | instantiation | 156, 137 | ⊢ |
| : , : , : |
128 | instantiation | 156, 138 | ⊢ |
| : , : , : |
129 | instantiation | 158, 139 | ⊢ |
| : |
130 | theorem | | ⊢ |
| proveit.numbers.addition.subtraction.add_cancel_basic |
131 | instantiation | 140 | ⊢ |
| : |
132 | instantiation | 173, 141, 142 | ⊢ |
| : , : , : |
133 | instantiation | 143, 165 | ⊢ |
| : |
134 | instantiation | 173, 145, 144 | ⊢ |
| : , : , : |
135 | theorem | | ⊢ |
| proveit.numbers.number_sets.complex_numbers.real_nonzero_within_complex_nonzero |
136 | instantiation | 173, 145, 146 | ⊢ |
| : , : , : |
137 | instantiation | 156, 147 | ⊢ |
| : , : , : |
138 | instantiation | 148, 149, 150 | ⊢ |
| : , : , : |
139 | instantiation | 173, 166, 151 | ⊢ |
| : , : , : |
140 | axiom | | ⊢ |
| proveit.logic.equality.equals_reflexivity |
141 | theorem | | ⊢ |
| proveit.numbers.number_sets.real_numbers.real_pos_within_real |
142 | theorem | | ⊢ |
| proveit.numbers.number_sets.real_numbers.pi_is_real_pos |
143 | theorem | | ⊢ |
| proveit.numbers.negation.int_closure |
144 | instantiation | 173, 153, 152 | ⊢ |
| : , : , : |
145 | theorem | | ⊢ |
| proveit.numbers.number_sets.real_numbers.rational_nonzero_within_real_nonzero |
146 | instantiation | 173, 153, 154 | ⊢ |
| : , : , : |
147 | instantiation | 155, 164 | ⊢ |
| : |
148 | axiom | | ⊢ |
| proveit.logic.equality.equals_transitivity |
149 | instantiation | 156, 157 | ⊢ |
| : , : , : |
150 | instantiation | 158, 164 | ⊢ |
| : |
151 | instantiation | 173, 169, 159 | ⊢ |
| : , : , : |
152 | instantiation | 173, 161, 160 | ⊢ |
| : , : , : |
153 | theorem | | ⊢ |
| proveit.numbers.number_sets.rational_numbers.nonzero_int_within_rational_nonzero |
154 | instantiation | 173, 161, 162 | ⊢ |
| : , : , : |
155 | theorem | | ⊢ |
| proveit.numbers.multiplication.elim_one_left |
156 | axiom | | ⊢ |
| proveit.logic.equality.substitution |
157 | instantiation | 163, 164 | ⊢ |
| : |
158 | theorem | | ⊢ |
| proveit.numbers.division.frac_one_denom |
159 | instantiation | 173, 171, 165 | ⊢ |
| : , : , : |
160 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.posnat1 |
161 | theorem | | ⊢ |
| proveit.numbers.number_sets.integers.nat_pos_within_nonzero_int |
162 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.posnat2 |
163 | theorem | | ⊢ |
| proveit.numbers.multiplication.elim_one_right |
164 | instantiation | 173, 166, 167 | ⊢ |
| : , : , : |
165 | instantiation | 173, 174, 168 | ⊢ |
| : , : , : |
166 | theorem | | ⊢ |
| proveit.numbers.number_sets.complex_numbers.real_within_complex |
167 | instantiation | 173, 169, 170 | ⊢ |
| : , : , : |
168 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.nat1 |
169 | theorem | | ⊢ |
| proveit.numbers.number_sets.real_numbers.rational_within_real |
170 | instantiation | 173, 171, 172 | ⊢ |
| : , : , : |
171 | theorem | | ⊢ |
| proveit.numbers.number_sets.rational_numbers.int_within_rational |
172 | instantiation | 173, 174, 175 | ⊢ |
| : , : , : |
173 | theorem | | ⊢ |
| proveit.logic.sets.inclusion.superset_membership_from_proper_subset |
174 | theorem | | ⊢ |
| proveit.numbers.number_sets.integers.nat_within_int |
175 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.nat2 |
*equality replacement requirements |