| step type | requirements | statement |
0 | instantiation | 1, 2, 3 | ⊢ |
| : , : , : |
1 | reference | 69 | ⊢ |
2 | modus ponens | 4, 5 | ⊢ |
3 | reference | 26 | ⊢ |
4 | theorem | | ⊢ |
| proveit.physics.quantum.QPE._alpha_ideal_case |
5 | instantiation | 6, 7, 8, 19, 9 | ⊢ |
| : , : , : |
6 | theorem | | ⊢ |
| proveit.numbers.number_sets.integers.in_interval |
7 | theorem | | ⊢ |
| proveit.numbers.number_sets.integers.zero_is_int |
8 | instantiation | 10, 129, 45 | ⊢ |
| : , : |
9 | instantiation | 11, 12, 13 | ⊢ |
| : , : |
10 | theorem | | ⊢ |
| proveit.numbers.addition.add_int_closure_bin |
11 | theorem | | ⊢ |
| proveit.logic.booleans.conjunction.and_if_both |
12 | instantiation | 14, 124, 37, 92, 15, 16, 17* | ⊢ |
| : , : , : |
13 | instantiation | 18, 19, 129, 45, 20, 21 | ⊢ |
| : , : , : |
14 | theorem | | ⊢ |
| proveit.numbers.multiplication.weak_bound_via_right_factor_bound |
15 | instantiation | 22, 37, 101, 38 | ⊢ |
| : , : , : |
16 | instantiation | 23, 29 | ⊢ |
| : , : |
17 | instantiation | 24, 117 | ⊢ |
| : |
18 | theorem | | ⊢ |
| proveit.numbers.ordering.less_add_right_weak_int |
19 | instantiation | 25, 127, 26 | ⊢ |
| : , : , : |
20 | instantiation | 27, 124, 92, 101, 28, 29, 100* | ⊢ |
| : , : , : |
21 | instantiation | 30, 31, 32 | ⊢ |
| : , : |
22 | theorem | | ⊢ |
| proveit.numbers.number_sets.real_numbers.interval_co_lower_bound |
23 | theorem | | ⊢ |
| proveit.numbers.ordering.relax_less |
24 | theorem | | ⊢ |
| proveit.numbers.multiplication.mult_zero_right |
25 | theorem | | ⊢ |
| proveit.logic.equality.sub_left_side_into |
26 | instantiation | 33, 124, 92, 103, 34, 35* | ⊢ |
| : , : , : |
27 | theorem | | ⊢ |
| proveit.numbers.multiplication.strong_bound_via_right_factor_bound |
28 | instantiation | 36, 37, 101, 38 | ⊢ |
| : , : , : |
29 | instantiation | 39, 135 | ⊢ |
| : |
30 | theorem | | ⊢ |
| proveit.numbers.ordering.relax_equal_to_less_eq |
31 | instantiation | 133, 112, 40 | ⊢ |
| : , : , : |
32 | instantiation | 93 | ⊢ |
| : |
33 | theorem | | ⊢ |
| proveit.numbers.multiplication.left_mult_eq_real |
34 | instantiation | 41, 42 | ⊢ |
| : , : |
35 | instantiation | 69, 43, 44 | ⊢ |
| : , : , : |
36 | theorem | | ⊢ |
| proveit.numbers.number_sets.real_numbers.interval_co_upper_bound |
37 | theorem | | ⊢ |
| proveit.numbers.number_sets.real_numbers.zero_is_real |
38 | axiom | | ⊢ |
| proveit.physics.quantum.QPE._phase_in_interval |
39 | theorem | | ⊢ |
| proveit.numbers.number_sets.natural_numbers.natural_pos_is_pos |
40 | instantiation | 133, 128, 45 | ⊢ |
| : , : , : |
41 | theorem | | ⊢ |
| proveit.logic.equality.equals_reversal |
42 | instantiation | 46, 113, 57, 47, 58, 48*, 49* | ⊢ |
| : , : , : |
43 | instantiation | 69, 50, 51 | ⊢ |
| : , : , : |
44 | instantiation | 52, 53, 54, 55 | ⊢ |
| : , : , : , : |
45 | instantiation | 56, 118 | ⊢ |
| : |
46 | theorem | | ⊢ |
| proveit.numbers.addition.right_add_eq_rational |
47 | instantiation | 69, 57, 58 | ⊢ |
| : , : , : |
48 | instantiation | 59, 91 | ⊢ |
| : |
49 | instantiation | 97, 60, 61 | ⊢ |
| : , : , : |
50 | instantiation | 62, 86, 87, 63, 64 | ⊢ |
| : , : , : , : , : |
51 | instantiation | 97, 65, 66 | ⊢ |
| : , : , : |
52 | theorem | | ⊢ |
| proveit.logic.equality.four_chain_transitivity |
53 | instantiation | 107, 67 | ⊢ |
| : , : , : |
54 | instantiation | 107, 68 | ⊢ |
| : , : , : |
55 | instantiation | 116, 87 | ⊢ |
| : |
56 | theorem | | ⊢ |
| proveit.numbers.negation.int_closure |
57 | theorem | | ⊢ |
| proveit.numbers.number_sets.rational_numbers.zero_is_rational |
58 | instantiation | 69, 70, 71 | ⊢ |
| : , : , : |
59 | theorem | | ⊢ |
| proveit.numbers.addition.elim_zero_left |
60 | instantiation | 72, 73, 74, 126, 75, 76, 79, 77, 91 | ⊢ |
| : , : , : , : , : , : |
61 | instantiation | 78, 91, 79, 80 | ⊢ |
| : , : , : |
62 | theorem | | ⊢ |
| proveit.numbers.division.mult_frac_cancel_numer_left |
63 | instantiation | 133, 82, 81 | ⊢ |
| : , : , : |
64 | instantiation | 133, 82, 83 | ⊢ |
| : , : , : |
65 | instantiation | 107, 84 | ⊢ |
| : , : , : |
66 | instantiation | 107, 85 | ⊢ |
| : , : , : |
67 | instantiation | 109, 86 | ⊢ |
| : |
68 | instantiation | 109, 87 | ⊢ |
| : |
69 | theorem | | ⊢ |
| proveit.logic.equality.sub_right_side_into |
70 | instantiation | 88, 127 | ⊢ |
| : |
71 | assumption | | ⊢ |
72 | theorem | | ⊢ |
| proveit.numbers.addition.disassociation |
73 | axiom | | ⊢ |
| proveit.numbers.number_sets.natural_numbers.zero_in_nats |
74 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.nat2 |
75 | theorem | | ⊢ |
| proveit.core_expr_types.tuples.tuple_len_0_typical_eq |
76 | instantiation | 89 | ⊢ |
| : , : |
77 | instantiation | 90, 91 | ⊢ |
| : |
78 | theorem | | ⊢ |
| proveit.numbers.addition.subtraction.add_cancel_triple_32 |
79 | instantiation | 133, 123, 92 | ⊢ |
| : , : , : |
80 | instantiation | 93 | ⊢ |
| : |
81 | instantiation | 133, 95, 94 | ⊢ |
| : , : , : |
82 | theorem | | ⊢ |
| proveit.numbers.number_sets.complex_numbers.real_nonzero_within_complex_nonzero |
83 | instantiation | 133, 95, 96 | ⊢ |
| : , : , : |
84 | instantiation | 97, 98, 99 | ⊢ |
| : , : , : |
85 | instantiation | 107, 100 | ⊢ |
| : , : , : |
86 | instantiation | 133, 123, 101 | ⊢ |
| : , : , : |
87 | instantiation | 133, 123, 102 | ⊢ |
| : , : , : |
88 | axiom | | ⊢ |
| proveit.physics.quantum.QPE._delta_b_def |
89 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.tuple_len_2_typical_eq |
90 | theorem | | ⊢ |
| proveit.numbers.negation.complex_closure |
91 | instantiation | 133, 123, 103 | ⊢ |
| : , : , : |
92 | theorem | | ⊢ |
| proveit.physics.quantum.QPE._phase_is_real |
93 | axiom | | ⊢ |
| proveit.logic.equality.equals_reflexivity |
94 | instantiation | 133, 105, 104 | ⊢ |
| : , : , : |
95 | theorem | | ⊢ |
| proveit.numbers.number_sets.real_numbers.rational_nonzero_within_real_nonzero |
96 | instantiation | 133, 105, 106 | ⊢ |
| : , : , : |
97 | axiom | | ⊢ |
| proveit.logic.equality.equals_transitivity |
98 | instantiation | 107, 108 | ⊢ |
| : , : , : |
99 | instantiation | 109, 117 | ⊢ |
| : |
100 | instantiation | 110, 117 | ⊢ |
| : |
101 | instantiation | 133, 112, 111 | ⊢ |
| : , : , : |
102 | instantiation | 133, 112, 120 | ⊢ |
| : , : , : |
103 | instantiation | 133, 112, 113 | ⊢ |
| : , : , : |
104 | instantiation | 133, 114, 135 | ⊢ |
| : , : , : |
105 | theorem | | ⊢ |
| proveit.numbers.number_sets.rational_numbers.nonzero_int_within_rational_nonzero |
106 | instantiation | 133, 114, 115 | ⊢ |
| : , : , : |
107 | axiom | | ⊢ |
| proveit.logic.equality.substitution |
108 | instantiation | 116, 117 | ⊢ |
| : |
109 | theorem | | ⊢ |
| proveit.numbers.division.frac_one_denom |
110 | theorem | | ⊢ |
| proveit.numbers.multiplication.elim_one_right |
111 | instantiation | 133, 128, 118 | ⊢ |
| : , : , : |
112 | theorem | | ⊢ |
| proveit.numbers.number_sets.real_numbers.rational_within_real |
113 | instantiation | 119, 120, 121, 122 | ⊢ |
| : , : |
114 | theorem | | ⊢ |
| proveit.numbers.number_sets.integers.nat_pos_within_nonzero_int |
115 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.posnat1 |
116 | theorem | | ⊢ |
| proveit.numbers.multiplication.elim_one_left |
117 | instantiation | 133, 123, 124 | ⊢ |
| : , : , : |
118 | instantiation | 133, 125, 126 | ⊢ |
| : , : , : |
119 | theorem | | ⊢ |
| proveit.numbers.division.div_rational_closure |
120 | instantiation | 133, 128, 127 | ⊢ |
| : , : , : |
121 | instantiation | 133, 128, 129 | ⊢ |
| : , : , : |
122 | instantiation | 130, 135 | ⊢ |
| : |
123 | theorem | | ⊢ |
| proveit.numbers.number_sets.complex_numbers.real_within_complex |
124 | instantiation | 131, 132, 135 | ⊢ |
| : , : , : |
125 | theorem | | ⊢ |
| proveit.numbers.number_sets.integers.nat_within_int |
126 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.nat1 |
127 | theorem | | ⊢ |
| proveit.physics.quantum.QPE._best_round_is_int |
128 | theorem | | ⊢ |
| proveit.numbers.number_sets.rational_numbers.int_within_rational |
129 | instantiation | 133, 134, 135 | ⊢ |
| : , : , : |
130 | theorem | | ⊢ |
| proveit.numbers.number_sets.natural_numbers.nonzero_if_is_nat_pos |
131 | theorem | | ⊢ |
| proveit.logic.sets.inclusion.unfold_subset_eq |
132 | instantiation | 136, 137 | ⊢ |
| : , : |
133 | theorem | | ⊢ |
| proveit.logic.sets.inclusion.superset_membership_from_proper_subset |
134 | theorem | | ⊢ |
| proveit.numbers.number_sets.integers.nat_pos_within_int |
135 | theorem | | ⊢ |
| proveit.physics.quantum.QPE._two_pow_t_is_nat_pos |
136 | theorem | | ⊢ |
| proveit.logic.sets.inclusion.relax_proper_subset |
137 | theorem | | ⊢ |
| proveit.numbers.number_sets.real_numbers.nat_pos_within_real |
*equality replacement requirements |