| step type | requirements | statement |
0 | instantiation | 1, 2 | ⊢ |
| : , : |
1 | theorem | | ⊢ |
| proveit.numbers.ordering.relax_less |
2 | instantiation | 106, 3, 4 | ⊢ |
| : , : , : |
3 | instantiation | 5, 6, 7 | ⊢ |
| : , : , : |
4 | modus ponens | 8, 9 | ⊢ |
5 | theorem | | ⊢ |
| proveit.logic.equality.sub_right_side_into |
6 | instantiation | 10, 11, 12 | ⊢ |
| : , : , : |
7 | instantiation | 13, 113 | ⊢ |
| : |
8 | instantiation | 14, 15, 16 | ⊢ |
| : , : , : , : , : , : |
9 | theorem | | ⊢ |
| proveit.physics.quantum.QPE._precision_guarantee_lemma_02 |
10 | theorem | | ⊢ |
| proveit.logic.equality.sub_left_side_into |
11 | instantiation | 106, 17, 18 | ⊢ |
| : , : , : |
12 | instantiation | 19, 113 | ⊢ |
| : |
13 | axiom | | ⊢ |
| proveit.physics.quantum.QPE._success_def |
14 | theorem | | ⊢ |
| proveit.statistics.constrained_event_prob_bound |
15 | theorem | | ⊢ |
| proveit.physics.quantum.QPE._Omega_is_sample_space |
16 | instantiation | 40, 20 | ⊢ |
| : , : |
17 | theorem | | ⊢ |
| proveit.physics.quantum.QPE._precision_guarantee_lemma_01 |
18 | instantiation | 21, 58, 22, 23, 24, 25* | ⊢ |
| : , : , : |
19 | theorem | | ⊢ |
| proveit.physics.quantum.QPE._success_complements_failure |
20 | instantiation | 26, 27 | ⊢ |
| : , : , : |
21 | theorem | | ⊢ |
| proveit.numbers.addition.weak_bound_via_right_term_bound |
22 | instantiation | 43, 48, 49 | ⊢ |
| : , : |
23 | instantiation | 53, 29 | ⊢ |
| : |
24 | instantiation | 28, 29, 30, 31, 32* | ⊢ |
| : , : |
25 | instantiation | 33, 114, 125, 34, 35, 36, 37, 38, 39 | ⊢ |
| : , : , : , : , : , : |
26 | theorem | | ⊢ |
| proveit.logic.sets.functions.injections.membership_unfolding |
27 | instantiation | 40, 41 | ⊢ |
| : , : |
28 | theorem | | ⊢ |
| proveit.numbers.negation.negated_weak_bound |
29 | instantiation | 42, 113 | ⊢ |
| : |
30 | instantiation | 43, 52, 54 | ⊢ |
| : , : |
31 | instantiation | 44, 113 | ⊢ |
| : |
32 | instantiation | 45, 46, 47 | ⊢ |
| : , : |
33 | theorem | | ⊢ |
| proveit.numbers.addition.disassociation |
34 | axiom | | ⊢ |
| proveit.numbers.number_sets.natural_numbers.zero_in_nats |
35 | instantiation | 75 | ⊢ |
| : , : |
36 | theorem | | ⊢ |
| proveit.core_expr_types.tuples.tuple_len_0_typical_eq |
37 | instantiation | 132, 86, 58 | ⊢ |
| : , : , : |
38 | instantiation | 132, 86, 48 | ⊢ |
| : , : , : |
39 | instantiation | 132, 86, 49 | ⊢ |
| : , : , : |
40 | theorem | | ⊢ |
| proveit.logic.booleans.conjunction.left_from_and |
41 | instantiation | 50, 51 | ⊢ |
| : , : , : |
42 | theorem | | ⊢ |
| proveit.physics.quantum.QPE._pfail_in_real |
43 | theorem | | ⊢ |
| proveit.numbers.addition.add_real_closure_bin |
44 | theorem | | ⊢ |
| proveit.physics.quantum.QPE._failure_upper_bound |
45 | theorem | | ⊢ |
| proveit.numbers.negation.distribute_neg_through_binary_sum |
46 | instantiation | 132, 86, 52 | ⊢ |
| : , : , : |
47 | instantiation | 132, 86, 54 | ⊢ |
| : , : , : |
48 | instantiation | 53, 52 | ⊢ |
| : |
49 | instantiation | 53, 54 | ⊢ |
| : |
50 | theorem | | ⊢ |
| proveit.logic.sets.functions.bijections.membership_unfolding |
51 | theorem | | ⊢ |
| proveit.physics.quantum.QPE._sample_space_bijection |
52 | instantiation | 57, 58, 55, 56 | ⊢ |
| : , : |
53 | theorem | | ⊢ |
| proveit.numbers.negation.real_closure |
54 | instantiation | 57, 58, 59, 60 | ⊢ |
| : , : |
55 | instantiation | 64, 87, 74 | ⊢ |
| : , : |
56 | instantiation | 67, 125, 61, 62, 78 | ⊢ |
| : , : |
57 | theorem | | ⊢ |
| proveit.numbers.division.div_real_closure |
58 | instantiation | 132, 93, 63 | ⊢ |
| : , : , : |
59 | instantiation | 64, 65, 66 | ⊢ |
| : , : |
60 | instantiation | 67, 125, 68, 69, 70 | ⊢ |
| : , : |
61 | instantiation | 75 | ⊢ |
| : , : |
62 | instantiation | 132, 84, 71 | ⊢ |
| : , : , : |
63 | instantiation | 132, 99, 111 | ⊢ |
| : , : , : |
64 | theorem | | ⊢ |
| proveit.numbers.multiplication.mult_real_closure_bin |
65 | instantiation | 132, 93, 72 | ⊢ |
| : , : , : |
66 | instantiation | 73, 74, 125 | ⊢ |
| : , : |
67 | theorem | | ⊢ |
| proveit.numbers.multiplication.mult_not_eq_zero |
68 | instantiation | 75 | ⊢ |
| : , : |
69 | instantiation | 132, 84, 76 | ⊢ |
| : , : , : |
70 | instantiation | 77, 78, 79 | ⊢ |
| : , : |
71 | instantiation | 132, 91, 80 | ⊢ |
| : , : , : |
72 | instantiation | 132, 99, 81 | ⊢ |
| : , : , : |
73 | theorem | | ⊢ |
| proveit.numbers.exponentiation.exp_real_closure_nat_power |
74 | instantiation | 132, 93, 82 | ⊢ |
| : , : , : |
75 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.tuple_len_2_typical_eq |
76 | instantiation | 132, 91, 83 | ⊢ |
| : , : , : |
77 | theorem | | ⊢ |
| proveit.numbers.exponentiation.exp_complex_nonzero_closure |
78 | instantiation | 132, 84, 85 | ⊢ |
| : , : , : |
79 | instantiation | 132, 86, 87 | ⊢ |
| : , : , : |
80 | instantiation | 132, 97, 88 | ⊢ |
| : , : , : |
81 | instantiation | 132, 124, 89 | ⊢ |
| : , : , : |
82 | instantiation | 132, 99, 103 | ⊢ |
| : , : , : |
83 | instantiation | 132, 97, 90 | ⊢ |
| : , : , : |
84 | theorem | | ⊢ |
| proveit.numbers.number_sets.complex_numbers.real_nonzero_within_complex_nonzero |
85 | instantiation | 132, 91, 92 | ⊢ |
| : , : , : |
86 | theorem | | ⊢ |
| proveit.numbers.number_sets.complex_numbers.real_within_complex |
87 | instantiation | 132, 93, 94 | ⊢ |
| : , : , : |
88 | instantiation | 132, 100, 95 | ⊢ |
| : , : , : |
89 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.nat4 |
90 | instantiation | 132, 100, 96 | ⊢ |
| : , : , : |
91 | theorem | | ⊢ |
| proveit.numbers.number_sets.real_numbers.rational_nonzero_within_real_nonzero |
92 | instantiation | 132, 97, 98 | ⊢ |
| : , : , : |
93 | theorem | | ⊢ |
| proveit.numbers.number_sets.real_numbers.rational_within_real |
94 | instantiation | 132, 99, 120 | ⊢ |
| : , : , : |
95 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.posnat2 |
96 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.posnat4 |
97 | theorem | | ⊢ |
| proveit.numbers.number_sets.rational_numbers.nonzero_int_within_rational_nonzero |
98 | instantiation | 132, 100, 101 | ⊢ |
| : , : , : |
99 | theorem | | ⊢ |
| proveit.numbers.number_sets.rational_numbers.int_within_rational |
100 | theorem | | ⊢ |
| proveit.numbers.number_sets.integers.nat_pos_within_nonzero_int |
101 | instantiation | 102, 103, 104 | ⊢ |
| : |
102 | theorem | | ⊢ |
| proveit.numbers.number_sets.integers.pos_int_is_natural_pos |
103 | instantiation | 132, 105, 113 | ⊢ |
| : , : , : |
104 | instantiation | 106, 107, 108 | ⊢ |
| : , : , : |
105 | instantiation | 109, 111, 112 | ⊢ |
| : , : |
106 | theorem | | ⊢ |
| proveit.numbers.ordering.transitivity_less_less_eq |
107 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.less_0_1 |
108 | instantiation | 110, 111, 112, 113 | ⊢ |
| : , : , : |
109 | theorem | | ⊢ |
| proveit.numbers.number_sets.integers.int_interval_within_int |
110 | theorem | | ⊢ |
| proveit.numbers.number_sets.integers.interval_lower_bound |
111 | instantiation | 132, 124, 114 | ⊢ |
| : , : , : |
112 | instantiation | 126, 115, 116 | ⊢ |
| : , : |
113 | theorem | | ⊢ |
| proveit.physics.quantum.QPE._e_value_in_e_domain |
114 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.nat1 |
115 | instantiation | 117, 120, 118 | ⊢ |
| : , : |
116 | instantiation | 119, 120 | ⊢ |
| : |
117 | theorem | | ⊢ |
| proveit.numbers.exponentiation.exp_int_closure |
118 | instantiation | 121, 122, 123 | ⊢ |
| : |
119 | theorem | | ⊢ |
| proveit.numbers.negation.int_closure |
120 | instantiation | 132, 124, 125 | ⊢ |
| : , : , : |
121 | theorem | | ⊢ |
| proveit.numbers.number_sets.integers.nonneg_int_is_natural |
122 | instantiation | 126, 127, 128 | ⊢ |
| : , : |
123 | instantiation | 129, 130 | ⊢ |
| : , : |
124 | theorem | | ⊢ |
| proveit.numbers.number_sets.integers.nat_within_int |
125 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.nat2 |
126 | theorem | | ⊢ |
| proveit.numbers.addition.add_int_closure_bin |
127 | instantiation | 132, 131, 136 | ⊢ |
| : , : , : |
128 | instantiation | 132, 133, 134 | ⊢ |
| : , : , : |
129 | theorem | | ⊢ |
| proveit.numbers.addition.subtraction.nonneg_difference |
130 | instantiation | 135, 136 | ⊢ |
| : |
131 | theorem | | ⊢ |
| proveit.numbers.number_sets.integers.nat_pos_within_int |
132 | theorem | | ⊢ |
| proveit.logic.sets.inclusion.superset_membership_from_proper_subset |
133 | theorem | | ⊢ |
| proveit.numbers.number_sets.integers.neg_int_within_int |
134 | instantiation | 137, 138 | ⊢ |
| : |
135 | theorem | | ⊢ |
| proveit.numbers.number_sets.natural_numbers.natural_pos_lower_bound |
136 | axiom | | ⊢ |
| proveit.physics.quantum.QPE._t_in_natural_pos |
137 | theorem | | ⊢ |
| proveit.numbers.negation.int_neg_closure |
138 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.posnat1 |
*equality replacement requirements |