| step type | requirements | statement |
0 | instantiation | 1, 2, 3 | ⊢ |
| : , : , : |
1 | theorem | | ⊢ |
| proveit.logic.equality.sub_left_side_into |
2 | instantiation | 86, 4, 5 | ⊢ |
| : , : , : |
3 | instantiation | 6, 93 | ⊢ |
| : |
4 | theorem | | ⊢ |
| proveit.physics.quantum.QPE._precision_guarantee_lemma_01 |
5 | instantiation | 7, 38, 8, 9, 10, 11* | ⊢ |
| : , : , : |
6 | theorem | | ⊢ |
| proveit.physics.quantum.QPE._success_complements_failure |
7 | theorem | | ⊢ |
| proveit.numbers.addition.weak_bound_via_right_term_bound |
8 | instantiation | 25, 30, 31 | ⊢ |
| : , : |
9 | instantiation | 33, 13 | ⊢ |
| : |
10 | instantiation | 12, 13, 14, 15, 16* | ⊢ |
| : , : |
11 | instantiation | 17, 94, 105, 18, 19, 20, 21, 22, 23 | ⊢ |
| : , : , : , : , : , : |
12 | theorem | | ⊢ |
| proveit.numbers.negation.negated_weak_bound |
13 | instantiation | 24, 93 | ⊢ |
| : |
14 | instantiation | 25, 32, 34 | ⊢ |
| : , : |
15 | instantiation | 26, 93 | ⊢ |
| : |
16 | instantiation | 27, 28, 29 | ⊢ |
| : , : |
17 | theorem | | ⊢ |
| proveit.numbers.addition.disassociation |
18 | axiom | | ⊢ |
| proveit.numbers.number_sets.natural_numbers.zero_in_nats |
19 | instantiation | 55 | ⊢ |
| : , : |
20 | theorem | | ⊢ |
| proveit.core_expr_types.tuples.tuple_len_0_typical_eq |
21 | instantiation | 112, 66, 38 | ⊢ |
| : , : , : |
22 | instantiation | 112, 66, 30 | ⊢ |
| : , : , : |
23 | instantiation | 112, 66, 31 | ⊢ |
| : , : , : |
24 | theorem | | ⊢ |
| proveit.physics.quantum.QPE._pfail_in_real |
25 | theorem | | ⊢ |
| proveit.numbers.addition.add_real_closure_bin |
26 | theorem | | ⊢ |
| proveit.physics.quantum.QPE._failure_upper_bound |
27 | theorem | | ⊢ |
| proveit.numbers.negation.distribute_neg_through_binary_sum |
28 | instantiation | 112, 66, 32 | ⊢ |
| : , : , : |
29 | instantiation | 112, 66, 34 | ⊢ |
| : , : , : |
30 | instantiation | 33, 32 | ⊢ |
| : |
31 | instantiation | 33, 34 | ⊢ |
| : |
32 | instantiation | 37, 38, 35, 36 | ⊢ |
| : , : |
33 | theorem | | ⊢ |
| proveit.numbers.negation.real_closure |
34 | instantiation | 37, 38, 39, 40 | ⊢ |
| : , : |
35 | instantiation | 44, 67, 54 | ⊢ |
| : , : |
36 | instantiation | 47, 105, 41, 42, 58 | ⊢ |
| : , : |
37 | theorem | | ⊢ |
| proveit.numbers.division.div_real_closure |
38 | instantiation | 112, 73, 43 | ⊢ |
| : , : , : |
39 | instantiation | 44, 45, 46 | ⊢ |
| : , : |
40 | instantiation | 47, 105, 48, 49, 50 | ⊢ |
| : , : |
41 | instantiation | 55 | ⊢ |
| : , : |
42 | instantiation | 112, 64, 51 | ⊢ |
| : , : , : |
43 | instantiation | 112, 79, 91 | ⊢ |
| : , : , : |
44 | theorem | | ⊢ |
| proveit.numbers.multiplication.mult_real_closure_bin |
45 | instantiation | 112, 73, 52 | ⊢ |
| : , : , : |
46 | instantiation | 53, 54, 105 | ⊢ |
| : , : |
47 | theorem | | ⊢ |
| proveit.numbers.multiplication.mult_not_eq_zero |
48 | instantiation | 55 | ⊢ |
| : , : |
49 | instantiation | 112, 64, 56 | ⊢ |
| : , : , : |
50 | instantiation | 57, 58, 59 | ⊢ |
| : , : |
51 | instantiation | 112, 71, 60 | ⊢ |
| : , : , : |
52 | instantiation | 112, 79, 61 | ⊢ |
| : , : , : |
53 | theorem | | ⊢ |
| proveit.numbers.exponentiation.exp_real_closure_nat_power |
54 | instantiation | 112, 73, 62 | ⊢ |
| : , : , : |
55 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.tuple_len_2_typical_eq |
56 | instantiation | 112, 71, 63 | ⊢ |
| : , : , : |
57 | theorem | | ⊢ |
| proveit.numbers.exponentiation.exp_complex_nonzero_closure |
58 | instantiation | 112, 64, 65 | ⊢ |
| : , : , : |
59 | instantiation | 112, 66, 67 | ⊢ |
| : , : , : |
60 | instantiation | 112, 77, 68 | ⊢ |
| : , : , : |
61 | instantiation | 112, 104, 69 | ⊢ |
| : , : , : |
62 | instantiation | 112, 79, 83 | ⊢ |
| : , : , : |
63 | instantiation | 112, 77, 70 | ⊢ |
| : , : , : |
64 | theorem | | ⊢ |
| proveit.numbers.number_sets.complex_numbers.real_nonzero_within_complex_nonzero |
65 | instantiation | 112, 71, 72 | ⊢ |
| : , : , : |
66 | theorem | | ⊢ |
| proveit.numbers.number_sets.complex_numbers.real_within_complex |
67 | instantiation | 112, 73, 74 | ⊢ |
| : , : , : |
68 | instantiation | 112, 80, 75 | ⊢ |
| : , : , : |
69 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.nat4 |
70 | instantiation | 112, 80, 76 | ⊢ |
| : , : , : |
71 | theorem | | ⊢ |
| proveit.numbers.number_sets.real_numbers.rational_nonzero_within_real_nonzero |
72 | instantiation | 112, 77, 78 | ⊢ |
| : , : , : |
73 | theorem | | ⊢ |
| proveit.numbers.number_sets.real_numbers.rational_within_real |
74 | instantiation | 112, 79, 100 | ⊢ |
| : , : , : |
75 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.posnat2 |
76 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.posnat4 |
77 | theorem | | ⊢ |
| proveit.numbers.number_sets.rational_numbers.nonzero_int_within_rational_nonzero |
78 | instantiation | 112, 80, 81 | ⊢ |
| : , : , : |
79 | theorem | | ⊢ |
| proveit.numbers.number_sets.rational_numbers.int_within_rational |
80 | theorem | | ⊢ |
| proveit.numbers.number_sets.integers.nat_pos_within_nonzero_int |
81 | instantiation | 82, 83, 84 | ⊢ |
| : |
82 | theorem | | ⊢ |
| proveit.numbers.number_sets.integers.pos_int_is_natural_pos |
83 | instantiation | 112, 85, 93 | ⊢ |
| : , : , : |
84 | instantiation | 86, 87, 88 | ⊢ |
| : , : , : |
85 | instantiation | 89, 91, 92 | ⊢ |
| : , : |
86 | theorem | | ⊢ |
| proveit.numbers.ordering.transitivity_less_less_eq |
87 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.less_0_1 |
88 | instantiation | 90, 91, 92, 93 | ⊢ |
| : , : , : |
89 | theorem | | ⊢ |
| proveit.numbers.number_sets.integers.int_interval_within_int |
90 | theorem | | ⊢ |
| proveit.numbers.number_sets.integers.interval_lower_bound |
91 | instantiation | 112, 104, 94 | ⊢ |
| : , : , : |
92 | instantiation | 106, 95, 96 | ⊢ |
| : , : |
93 | theorem | | ⊢ |
| proveit.physics.quantum.QPE._e_value_in_e_domain |
94 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.nat1 |
95 | instantiation | 97, 100, 98 | ⊢ |
| : , : |
96 | instantiation | 99, 100 | ⊢ |
| : |
97 | theorem | | ⊢ |
| proveit.numbers.exponentiation.exp_int_closure |
98 | instantiation | 101, 102, 103 | ⊢ |
| : |
99 | theorem | | ⊢ |
| proveit.numbers.negation.int_closure |
100 | instantiation | 112, 104, 105 | ⊢ |
| : , : , : |
101 | theorem | | ⊢ |
| proveit.numbers.number_sets.integers.nonneg_int_is_natural |
102 | instantiation | 106, 107, 108 | ⊢ |
| : , : |
103 | instantiation | 109, 110 | ⊢ |
| : , : |
104 | theorem | | ⊢ |
| proveit.numbers.number_sets.integers.nat_within_int |
105 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.nat2 |
106 | theorem | | ⊢ |
| proveit.numbers.addition.add_int_closure_bin |
107 | instantiation | 112, 111, 116 | ⊢ |
| : , : , : |
108 | instantiation | 112, 113, 114 | ⊢ |
| : , : , : |
109 | theorem | | ⊢ |
| proveit.numbers.addition.subtraction.nonneg_difference |
110 | instantiation | 115, 116 | ⊢ |
| : |
111 | theorem | | ⊢ |
| proveit.numbers.number_sets.integers.nat_pos_within_int |
112 | theorem | | ⊢ |
| proveit.logic.sets.inclusion.superset_membership_from_proper_subset |
113 | theorem | | ⊢ |
| proveit.numbers.number_sets.integers.neg_int_within_int |
114 | instantiation | 117, 118 | ⊢ |
| : |
115 | theorem | | ⊢ |
| proveit.numbers.number_sets.natural_numbers.natural_pos_lower_bound |
116 | axiom | | ⊢ |
| proveit.physics.quantum.QPE._t_in_natural_pos |
117 | theorem | | ⊢ |
| proveit.numbers.negation.int_neg_closure |
118 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.posnat1 |
*equality replacement requirements |