| step type | requirements | statement |
0 | instantiation | 1, 2, 3 | ⊢ |
| : , : , : |
1 | reference | 33 | ⊢ |
2 | reference | 94 | ⊢ |
3 | instantiation | 33, 4, 5 | ⊢ |
| : , : , : |
4 | instantiation | 77, 6, 34 | ⊢ |
| : , : , : |
5 | instantiation | 7, 143, 8 | ⊢ |
| : , : |
6 | modus ponens | 9, 10 | ⊢ |
7 | theorem | | ⊢ |
| proveit.numbers.modular.int_mod_elimination |
8 | instantiation | 12, 13, 14, 135, 11 | ⊢ |
| : , : , : |
9 | theorem | | ⊢ |
| proveit.physics.quantum.QPE._alpha_ideal_case |
10 | instantiation | 12, 13, 14, 27, 15 | ⊢ |
| : , : , : |
11 | instantiation | 19, 16, 17 | ⊢ |
| : , : |
12 | theorem | | ⊢ |
| proveit.numbers.number_sets.integers.in_interval |
13 | theorem | | ⊢ |
| proveit.numbers.number_sets.integers.zero_is_int |
14 | instantiation | 18, 137, 53 | ⊢ |
| : , : |
15 | instantiation | 19, 20, 21 | ⊢ |
| : , : |
16 | instantiation | 77, 20, 34 | ⊢ |
| : , : , : |
17 | instantiation | 77, 21, 34 | ⊢ |
| : , : , : |
18 | theorem | | ⊢ |
| proveit.numbers.addition.add_int_closure_bin |
19 | theorem | | ⊢ |
| proveit.logic.booleans.conjunction.and_if_both |
20 | instantiation | 22, 132, 45, 100, 23, 24, 25* | ⊢ |
| : , : , : |
21 | instantiation | 26, 27, 137, 53, 28, 29 | ⊢ |
| : , : , : |
22 | theorem | | ⊢ |
| proveit.numbers.multiplication.weak_bound_via_right_factor_bound |
23 | instantiation | 30, 45, 109, 46 | ⊢ |
| : , : , : |
24 | instantiation | 31, 37 | ⊢ |
| : , : |
25 | instantiation | 32, 125 | ⊢ |
| : |
26 | theorem | | ⊢ |
| proveit.numbers.ordering.less_add_right_weak_int |
27 | instantiation | 33, 135, 34 | ⊢ |
| : , : , : |
28 | instantiation | 35, 132, 100, 109, 36, 37, 108* | ⊢ |
| : , : , : |
29 | instantiation | 38, 39, 40 | ⊢ |
| : , : |
30 | theorem | | ⊢ |
| proveit.numbers.number_sets.real_numbers.interval_co_lower_bound |
31 | theorem | | ⊢ |
| proveit.numbers.ordering.relax_less |
32 | theorem | | ⊢ |
| proveit.numbers.multiplication.mult_zero_right |
33 | theorem | | ⊢ |
| proveit.logic.equality.sub_left_side_into |
34 | instantiation | 41, 132, 100, 111, 42, 43* | ⊢ |
| : , : , : |
35 | theorem | | ⊢ |
| proveit.numbers.multiplication.strong_bound_via_right_factor_bound |
36 | instantiation | 44, 45, 109, 46 | ⊢ |
| : , : , : |
37 | instantiation | 47, 143 | ⊢ |
| : |
38 | theorem | | ⊢ |
| proveit.numbers.ordering.relax_equal_to_less_eq |
39 | instantiation | 141, 120, 48 | ⊢ |
| : , : , : |
40 | instantiation | 101 | ⊢ |
| : |
41 | theorem | | ⊢ |
| proveit.numbers.multiplication.left_mult_eq_real |
42 | instantiation | 49, 50 | ⊢ |
| : , : |
43 | instantiation | 77, 51, 52 | ⊢ |
| : , : , : |
44 | theorem | | ⊢ |
| proveit.numbers.number_sets.real_numbers.interval_co_upper_bound |
45 | theorem | | ⊢ |
| proveit.numbers.number_sets.real_numbers.zero_is_real |
46 | axiom | | ⊢ |
| proveit.physics.quantum.QPE._phase_in_interval |
47 | theorem | | ⊢ |
| proveit.numbers.number_sets.natural_numbers.natural_pos_is_pos |
48 | instantiation | 141, 136, 53 | ⊢ |
| : , : , : |
49 | theorem | | ⊢ |
| proveit.logic.equality.equals_reversal |
50 | instantiation | 54, 121, 65, 55, 66, 56*, 57* | ⊢ |
| : , : , : |
51 | instantiation | 77, 58, 59 | ⊢ |
| : , : , : |
52 | instantiation | 60, 61, 62, 63 | ⊢ |
| : , : , : , : |
53 | instantiation | 64, 126 | ⊢ |
| : |
54 | theorem | | ⊢ |
| proveit.numbers.addition.right_add_eq_rational |
55 | instantiation | 77, 65, 66 | ⊢ |
| : , : , : |
56 | instantiation | 67, 99 | ⊢ |
| : |
57 | instantiation | 105, 68, 69 | ⊢ |
| : , : , : |
58 | instantiation | 70, 94, 95, 71, 72 | ⊢ |
| : , : , : , : , : |
59 | instantiation | 105, 73, 74 | ⊢ |
| : , : , : |
60 | theorem | | ⊢ |
| proveit.logic.equality.four_chain_transitivity |
61 | instantiation | 115, 75 | ⊢ |
| : , : , : |
62 | instantiation | 115, 76 | ⊢ |
| : , : , : |
63 | instantiation | 124, 95 | ⊢ |
| : |
64 | theorem | | ⊢ |
| proveit.numbers.negation.int_closure |
65 | theorem | | ⊢ |
| proveit.numbers.number_sets.rational_numbers.zero_is_rational |
66 | instantiation | 77, 78, 79 | ⊢ |
| : , : , : |
67 | theorem | | ⊢ |
| proveit.numbers.addition.elim_zero_left |
68 | instantiation | 80, 81, 82, 134, 83, 84, 87, 85, 99 | ⊢ |
| : , : , : , : , : , : |
69 | instantiation | 86, 99, 87, 88 | ⊢ |
| : , : , : |
70 | theorem | | ⊢ |
| proveit.numbers.division.mult_frac_cancel_numer_left |
71 | instantiation | 141, 90, 89 | ⊢ |
| : , : , : |
72 | instantiation | 141, 90, 91 | ⊢ |
| : , : , : |
73 | instantiation | 115, 92 | ⊢ |
| : , : , : |
74 | instantiation | 115, 93 | ⊢ |
| : , : , : |
75 | instantiation | 117, 94 | ⊢ |
| : |
76 | instantiation | 117, 95 | ⊢ |
| : |
77 | theorem | | ⊢ |
| proveit.logic.equality.sub_right_side_into |
78 | instantiation | 96, 135 | ⊢ |
| : |
79 | assumption | | ⊢ |
80 | theorem | | ⊢ |
| proveit.numbers.addition.disassociation |
81 | axiom | | ⊢ |
| proveit.numbers.number_sets.natural_numbers.zero_in_nats |
82 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.nat2 |
83 | theorem | | ⊢ |
| proveit.core_expr_types.tuples.tuple_len_0_typical_eq |
84 | instantiation | 97 | ⊢ |
| : , : |
85 | instantiation | 98, 99 | ⊢ |
| : |
86 | theorem | | ⊢ |
| proveit.numbers.addition.subtraction.add_cancel_triple_32 |
87 | instantiation | 141, 131, 100 | ⊢ |
| : , : , : |
88 | instantiation | 101 | ⊢ |
| : |
89 | instantiation | 141, 103, 102 | ⊢ |
| : , : , : |
90 | theorem | | ⊢ |
| proveit.numbers.number_sets.complex_numbers.real_nonzero_within_complex_nonzero |
91 | instantiation | 141, 103, 104 | ⊢ |
| : , : , : |
92 | instantiation | 105, 106, 107 | ⊢ |
| : , : , : |
93 | instantiation | 115, 108 | ⊢ |
| : , : , : |
94 | instantiation | 141, 131, 109 | ⊢ |
| : , : , : |
95 | instantiation | 141, 131, 110 | ⊢ |
| : , : , : |
96 | axiom | | ⊢ |
| proveit.physics.quantum.QPE._delta_b_def |
97 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.tuple_len_2_typical_eq |
98 | theorem | | ⊢ |
| proveit.numbers.negation.complex_closure |
99 | instantiation | 141, 131, 111 | ⊢ |
| : , : , : |
100 | theorem | | ⊢ |
| proveit.physics.quantum.QPE._phase_is_real |
101 | axiom | | ⊢ |
| proveit.logic.equality.equals_reflexivity |
102 | instantiation | 141, 113, 112 | ⊢ |
| : , : , : |
103 | theorem | | ⊢ |
| proveit.numbers.number_sets.real_numbers.rational_nonzero_within_real_nonzero |
104 | instantiation | 141, 113, 114 | ⊢ |
| : , : , : |
105 | axiom | | ⊢ |
| proveit.logic.equality.equals_transitivity |
106 | instantiation | 115, 116 | ⊢ |
| : , : , : |
107 | instantiation | 117, 125 | ⊢ |
| : |
108 | instantiation | 118, 125 | ⊢ |
| : |
109 | instantiation | 141, 120, 119 | ⊢ |
| : , : , : |
110 | instantiation | 141, 120, 128 | ⊢ |
| : , : , : |
111 | instantiation | 141, 120, 121 | ⊢ |
| : , : , : |
112 | instantiation | 141, 122, 143 | ⊢ |
| : , : , : |
113 | theorem | | ⊢ |
| proveit.numbers.number_sets.rational_numbers.nonzero_int_within_rational_nonzero |
114 | instantiation | 141, 122, 123 | ⊢ |
| : , : , : |
115 | axiom | | ⊢ |
| proveit.logic.equality.substitution |
116 | instantiation | 124, 125 | ⊢ |
| : |
117 | theorem | | ⊢ |
| proveit.numbers.division.frac_one_denom |
118 | theorem | | ⊢ |
| proveit.numbers.multiplication.elim_one_right |
119 | instantiation | 141, 136, 126 | ⊢ |
| : , : , : |
120 | theorem | | ⊢ |
| proveit.numbers.number_sets.real_numbers.rational_within_real |
121 | instantiation | 127, 128, 129, 130 | ⊢ |
| : , : |
122 | theorem | | ⊢ |
| proveit.numbers.number_sets.integers.nat_pos_within_nonzero_int |
123 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.posnat1 |
124 | theorem | | ⊢ |
| proveit.numbers.multiplication.elim_one_left |
125 | instantiation | 141, 131, 132 | ⊢ |
| : , : , : |
126 | instantiation | 141, 133, 134 | ⊢ |
| : , : , : |
127 | theorem | | ⊢ |
| proveit.numbers.division.div_rational_closure |
128 | instantiation | 141, 136, 135 | ⊢ |
| : , : , : |
129 | instantiation | 141, 136, 137 | ⊢ |
| : , : , : |
130 | instantiation | 138, 143 | ⊢ |
| : |
131 | theorem | | ⊢ |
| proveit.numbers.number_sets.complex_numbers.real_within_complex |
132 | instantiation | 139, 140, 143 | ⊢ |
| : , : , : |
133 | theorem | | ⊢ |
| proveit.numbers.number_sets.integers.nat_within_int |
134 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.nat1 |
135 | theorem | | ⊢ |
| proveit.physics.quantum.QPE._best_round_is_int |
136 | theorem | | ⊢ |
| proveit.numbers.number_sets.rational_numbers.int_within_rational |
137 | instantiation | 141, 142, 143 | ⊢ |
| : , : , : |
138 | theorem | | ⊢ |
| proveit.numbers.number_sets.natural_numbers.nonzero_if_is_nat_pos |
139 | theorem | | ⊢ |
| proveit.logic.sets.inclusion.unfold_subset_eq |
140 | instantiation | 144, 145 | ⊢ |
| : , : |
141 | theorem | | ⊢ |
| proveit.logic.sets.inclusion.superset_membership_from_proper_subset |
142 | theorem | | ⊢ |
| proveit.numbers.number_sets.integers.nat_pos_within_int |
143 | theorem | | ⊢ |
| proveit.physics.quantum.QPE._two_pow_t_is_nat_pos |
144 | theorem | | ⊢ |
| proveit.logic.sets.inclusion.relax_proper_subset |
145 | theorem | | ⊢ |
| proveit.numbers.number_sets.real_numbers.nat_pos_within_real |
*equality replacement requirements |