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