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