| step type | requirements | statement |
0 | instantiation | 1, 2 | , ⊢ |
| : , : , : |
1 | reference | 41 | ⊢ |
2 | instantiation | 3, 4, 5, 62, 51, 6, 63, 96, 52, 7, 8*, 53* | , ⊢ |
| : , : , : |
3 | theorem | | ⊢ |
| proveit.numbers.exponentiation.real_power_of_products |
4 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.posnat3 |
5 | instantiation | 9 | ⊢ |
| : , : , : |
6 | instantiation | 127, 99, 10 | ⊢ |
| : , : , : |
7 | instantiation | 11, 12 | , ⊢ |
| : |
8 | instantiation | 13, 14, 15, 16* | ⊢ |
| : , : |
9 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.tuple_len_3_typical_eq |
10 | instantiation | 127, 17, 18 | ⊢ |
| : , : , : |
11 | theorem | | ⊢ |
| proveit.numbers.number_sets.complex_numbers.nonzero_if_in_complex_nonzero |
12 | instantiation | 19, 20, 21 | , ⊢ |
| : , : , : |
13 | theorem | | ⊢ |
| proveit.numbers.exponentiation.neg_power_as_div |
14 | instantiation | 127, 26, 22 | ⊢ |
| : , : , : |
15 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.posnat1 |
16 | instantiation | 23, 62 | ⊢ |
| : |
17 | theorem | | ⊢ |
| proveit.numbers.number_sets.real_numbers.real_nonneg_within_real |
18 | instantiation | 24, 25 | ⊢ |
| : |
19 | theorem | | ⊢ |
| proveit.logic.equality.sub_right_side_into |
20 | instantiation | 127, 26, 27 | , ⊢ |
| : , : , : |
21 | instantiation | 41, 28 | ⊢ |
| : , : , : |
22 | instantiation | 127, 29, 91 | ⊢ |
| : , : , : |
23 | theorem | | ⊢ |
| proveit.numbers.exponentiation.complex_x_to_first_power_is_x |
24 | theorem | | ⊢ |
| proveit.numbers.absolute_value.abs_complex_closure |
25 | instantiation | 30, 31, 32 | ⊢ |
| : , : |
26 | theorem | | ⊢ |
| proveit.numbers.number_sets.complex_numbers.real_nonzero_within_complex_nonzero |
27 | instantiation | 127, 33, 34 | , ⊢ |
| : , : , : |
28 | instantiation | 41, 35 | ⊢ |
| : , : , : |
29 | theorem | | ⊢ |
| proveit.numbers.number_sets.real_numbers.rational_nonzero_within_real_nonzero |
30 | theorem | | ⊢ |
| proveit.numbers.addition.add_complex_closure_bin |
31 | instantiation | 127, 99, 36 | ⊢ |
| : , : , : |
32 | instantiation | 37, 38 | ⊢ |
| : |
33 | theorem | | ⊢ |
| proveit.numbers.number_sets.real_numbers.real_pos_within_real_nonzero |
34 | instantiation | 39, 40 | , ⊢ |
| : |
35 | instantiation | 41, 42 | ⊢ |
| : , : , : |
36 | instantiation | 43, 44 | ⊢ |
| : |
37 | theorem | | ⊢ |
| proveit.numbers.negation.complex_closure |
38 | instantiation | 127, 99, 45 | ⊢ |
| : , : , : |
39 | theorem | | ⊢ |
| proveit.numbers.absolute_value.abs_nonzero_closure |
40 | instantiation | 46, 47, 48 | , ⊢ |
| : |
41 | axiom | | ⊢ |
| proveit.logic.equality.substitution |
42 | instantiation | 49, 50, 51, 52, 53* | ⊢ |
| : , : |
43 | theorem | | ⊢ |
| proveit.physics.quantum.QPE._delta_b_is_real |
44 | theorem | | ⊢ |
| proveit.physics.quantum.QPE._best_floor_is_int |
45 | instantiation | 54, 59, 55 | ⊢ |
| : , : |
46 | theorem | | ⊢ |
| proveit.numbers.number_sets.complex_numbers.nonzero_complex_is_complex_nonzero |
47 | instantiation | 127, 99, 56 | ⊢ |
| : , : , : |
48 | instantiation | 57, 58 | , ⊢ |
| : , : |
49 | theorem | | ⊢ |
| proveit.numbers.division.div_as_mult |
50 | instantiation | 127, 99, 59 | ⊢ |
| : , : , : |
51 | instantiation | 127, 99, 60 | ⊢ |
| : , : , : |
52 | instantiation | 107, 73 | ⊢ |
| : |
53 | instantiation | 61, 62, 100, 63, 96, 64* | ⊢ |
| : , : , : |
54 | theorem | | ⊢ |
| proveit.numbers.multiplication.mult_real_closure_bin |
55 | instantiation | 127, 105, 65 | ⊢ |
| : , : , : |
56 | instantiation | 66, 67, 81, 68 | ⊢ |
| : , : , : |
57 | theorem | | ⊢ |
| proveit.numbers.addition.subtraction.nonzero_difference_if_different |
58 | instantiation | 69, 70, 86, 71 | , ⊢ |
| : , : |
59 | instantiation | 127, 105, 72 | ⊢ |
| : , : , : |
60 | instantiation | 110, 111, 73 | ⊢ |
| : , : , : |
61 | theorem | | ⊢ |
| proveit.numbers.exponentiation.real_power_of_real_power |
62 | instantiation | 127, 99, 95 | ⊢ |
| : , : , : |
63 | instantiation | 127, 105, 74 | ⊢ |
| : , : , : |
64 | instantiation | 75, 89, 76, 77* | ⊢ |
| : , : |
65 | instantiation | 127, 78, 79 | ⊢ |
| : , : , : |
66 | theorem | | ⊢ |
| proveit.numbers.number_sets.real_numbers.all_in_interval_co__is__real |
67 | instantiation | 80, 81 | ⊢ |
| : |
68 | instantiation | 82, 98 | ⊢ |
| : |
69 | theorem | | ⊢ |
| proveit.physics.quantum.QPE._delta_b_not_eq_scaledNonzeroInt |
70 | instantiation | 83, 84, 126, 85 | ⊢ |
| : , : , : , : , : |
71 | assumption | | ⊢ |
72 | instantiation | 127, 115, 86 | ⊢ |
| : , : , : |
73 | theorem | | ⊢ |
| proveit.physics.quantum.QPE._two_pow_t_is_nat_pos |
74 | instantiation | 127, 115, 87 | ⊢ |
| : , : , : |
75 | theorem | | ⊢ |
| proveit.numbers.multiplication.mult_neg_right |
76 | instantiation | 127, 99, 94 | ⊢ |
| : , : , : |
77 | instantiation | 88, 89 | ⊢ |
| : |
78 | theorem | | ⊢ |
| proveit.numbers.number_sets.rational_numbers.rational_nonzero_within_rational |
79 | instantiation | 90, 91, 92 | ⊢ |
| : , : |
80 | theorem | | ⊢ |
| proveit.numbers.negation.real_closure |
81 | instantiation | 93, 94, 95, 96 | ⊢ |
| : , : |
82 | theorem | | ⊢ |
| proveit.physics.quantum.QPE._delta_b_floor_diff_in_interval |
83 | theorem | | ⊢ |
| proveit.logic.sets.enumeration.in_enumerated_set |
84 | axiom | | ⊢ |
| proveit.numbers.number_sets.natural_numbers.zero_in_nats |
85 | theorem | | ⊢ |
| proveit.core_expr_types.tuples.tuple_len_0_typical_eq |
86 | instantiation | 127, 97, 98 | ⊢ |
| : , : , : |
87 | instantiation | 123, 119 | ⊢ |
| : |
88 | theorem | | ⊢ |
| proveit.numbers.multiplication.elim_one_right |
89 | instantiation | 127, 99, 100 | ⊢ |
| : , : , : |
90 | theorem | | ⊢ |
| proveit.numbers.exponentiation.exp_rational_nonzero_closure |
91 | instantiation | 127, 101, 102 | ⊢ |
| : , : , : |
92 | instantiation | 123, 103 | ⊢ |
| : |
93 | theorem | | ⊢ |
| proveit.numbers.division.div_real_closure |
94 | instantiation | 127, 105, 104 | ⊢ |
| : , : , : |
95 | instantiation | 127, 105, 106 | ⊢ |
| : , : , : |
96 | instantiation | 107, 113 | ⊢ |
| : |
97 | instantiation | 108, 109, 124 | ⊢ |
| : , : |
98 | assumption | | ⊢ |
99 | theorem | | ⊢ |
| proveit.numbers.number_sets.complex_numbers.real_within_complex |
100 | instantiation | 110, 111, 114 | ⊢ |
| : , : , : |
101 | theorem | | ⊢ |
| proveit.numbers.number_sets.rational_numbers.nonzero_int_within_rational_nonzero |
102 | instantiation | 127, 112, 113 | ⊢ |
| : , : , : |
103 | instantiation | 127, 128, 114 | ⊢ |
| : , : , : |
104 | instantiation | 127, 115, 119 | ⊢ |
| : , : , : |
105 | theorem | | ⊢ |
| proveit.numbers.number_sets.real_numbers.rational_within_real |
106 | instantiation | 127, 115, 116 | ⊢ |
| : , : , : |
107 | theorem | | ⊢ |
| proveit.numbers.number_sets.natural_numbers.nonzero_if_is_nat_pos |
108 | theorem | | ⊢ |
| proveit.numbers.number_sets.integers.int_interval_within_int |
109 | instantiation | 117, 118, 119 | ⊢ |
| : , : |
110 | theorem | | ⊢ |
| proveit.logic.sets.inclusion.unfold_subset_eq |
111 | instantiation | 120, 121 | ⊢ |
| : , : |
112 | theorem | | ⊢ |
| proveit.numbers.number_sets.integers.nat_pos_within_nonzero_int |
113 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.posnat2 |
114 | axiom | | ⊢ |
| proveit.physics.quantum.QPE._t_in_natural_pos |
115 | theorem | | ⊢ |
| proveit.numbers.number_sets.rational_numbers.int_within_rational |
116 | instantiation | 127, 125, 122 | ⊢ |
| : , : , : |
117 | theorem | | ⊢ |
| proveit.numbers.addition.add_int_closure_bin |
118 | instantiation | 123, 124 | ⊢ |
| : |
119 | instantiation | 127, 125, 126 | ⊢ |
| : , : , : |
120 | theorem | | ⊢ |
| proveit.logic.sets.inclusion.relax_proper_subset |
121 | theorem | | ⊢ |
| proveit.numbers.number_sets.real_numbers.nat_pos_within_real |
122 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.nat2 |
123 | theorem | | ⊢ |
| proveit.numbers.negation.int_closure |
124 | instantiation | 127, 128, 129 | ⊢ |
| : , : , : |
125 | theorem | | ⊢ |
| proveit.numbers.number_sets.integers.nat_within_int |
126 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.nat1 |
127 | theorem | | ⊢ |
| proveit.logic.sets.inclusion.superset_membership_from_proper_subset |
128 | theorem | | ⊢ |
| proveit.numbers.number_sets.integers.nat_pos_within_int |
129 | theorem | | ⊢ |
| proveit.physics.quantum.QPE._two_pow_t_minus_one_is_nat_pos |
*equality replacement requirements |