| step type | requirements | statement |
0 | instantiation | 1, 2, 3, 4, 5* | ⊢ |
| : , : |
1 | theorem | | ⊢ |
| proveit.numbers.absolute_value.abs_eq |
2 | instantiation | 39, 100, 6 | ⊢ |
| : , : , : |
3 | reference | 100 | ⊢ |
4 | reference | 6 | ⊢ |
5 | instantiation | 7, 8 | ⊢ |
| : |
6 | instantiation | 39, 9, 10 | ⊢ |
| : , : , : |
7 | theorem | | ⊢ |
| proveit.numbers.absolute_value.abs_non_neg_elim |
8 | instantiation | 11, 140 | ⊢ |
| : |
9 | instantiation | 83, 12, 40 | ⊢ |
| : , : , : |
10 | instantiation | 13, 149, 14 | ⊢ |
| : , : |
11 | theorem | | ⊢ |
| proveit.numbers.number_sets.natural_numbers.natural_lower_bound |
12 | modus ponens | 15, 16 | ⊢ |
13 | theorem | | ⊢ |
| proveit.numbers.modular.int_mod_elimination |
14 | instantiation | 18, 19, 20, 141, 17 | ⊢ |
| : , : , : |
15 | theorem | | ⊢ |
| proveit.physics.quantum.QPE._alpha_ideal_case |
16 | instantiation | 18, 19, 20, 33, 21 | ⊢ |
| : , : , : |
17 | instantiation | 25, 22, 23 | ⊢ |
| : , : |
18 | theorem | | ⊢ |
| proveit.numbers.number_sets.integers.in_interval |
19 | theorem | | ⊢ |
| proveit.numbers.number_sets.integers.zero_is_int |
20 | instantiation | 24, 143, 59 | ⊢ |
| : , : |
21 | instantiation | 25, 26, 27 | ⊢ |
| : , : |
22 | instantiation | 83, 26, 40 | ⊢ |
| : , : , : |
23 | instantiation | 83, 27, 40 | ⊢ |
| : , : , : |
24 | theorem | | ⊢ |
| proveit.numbers.addition.add_int_closure_bin |
25 | theorem | | ⊢ |
| proveit.logic.booleans.conjunction.and_if_both |
26 | instantiation | 28, 138, 51, 106, 29, 30, 31* | ⊢ |
| : , : , : |
27 | instantiation | 32, 33, 143, 59, 34, 35 | ⊢ |
| : , : , : |
28 | theorem | | ⊢ |
| proveit.numbers.multiplication.weak_bound_via_right_factor_bound |
29 | instantiation | 36, 51, 115, 52 | ⊢ |
| : , : , : |
30 | instantiation | 37, 43 | ⊢ |
| : , : |
31 | instantiation | 38, 131 | ⊢ |
| : |
32 | theorem | | ⊢ |
| proveit.numbers.ordering.less_add_right_weak_int |
33 | instantiation | 39, 141, 40 | ⊢ |
| : , : , : |
34 | instantiation | 41, 138, 106, 115, 42, 43, 114* | ⊢ |
| : , : , : |
35 | instantiation | 44, 45, 46 | ⊢ |
| : , : |
36 | theorem | | ⊢ |
| proveit.numbers.number_sets.real_numbers.interval_co_lower_bound |
37 | theorem | | ⊢ |
| proveit.numbers.ordering.relax_less |
38 | theorem | | ⊢ |
| proveit.numbers.multiplication.mult_zero_right |
39 | theorem | | ⊢ |
| proveit.logic.equality.sub_left_side_into |
40 | instantiation | 47, 138, 106, 117, 48, 49* | ⊢ |
| : , : , : |
41 | theorem | | ⊢ |
| proveit.numbers.multiplication.strong_bound_via_right_factor_bound |
42 | instantiation | 50, 51, 115, 52 | ⊢ |
| : , : , : |
43 | instantiation | 53, 149 | ⊢ |
| : |
44 | theorem | | ⊢ |
| proveit.numbers.ordering.relax_equal_to_less_eq |
45 | instantiation | 147, 126, 54 | ⊢ |
| : , : , : |
46 | instantiation | 107 | ⊢ |
| : |
47 | theorem | | ⊢ |
| proveit.numbers.multiplication.left_mult_eq_real |
48 | instantiation | 55, 56 | ⊢ |
| : , : |
49 | instantiation | 83, 57, 58 | ⊢ |
| : , : , : |
50 | theorem | | ⊢ |
| proveit.numbers.number_sets.real_numbers.interval_co_upper_bound |
51 | theorem | | ⊢ |
| proveit.numbers.number_sets.real_numbers.zero_is_real |
52 | axiom | | ⊢ |
| proveit.physics.quantum.QPE._phase_in_interval |
53 | theorem | | ⊢ |
| proveit.numbers.number_sets.natural_numbers.natural_pos_is_pos |
54 | instantiation | 147, 142, 59 | ⊢ |
| : , : , : |
55 | theorem | | ⊢ |
| proveit.logic.equality.equals_reversal |
56 | instantiation | 60, 127, 71, 61, 72, 62*, 63* | ⊢ |
| : , : , : |
57 | instantiation | 83, 64, 65 | ⊢ |
| : , : , : |
58 | instantiation | 66, 67, 68, 69 | ⊢ |
| : , : , : , : |
59 | instantiation | 70, 132 | ⊢ |
| : |
60 | theorem | | ⊢ |
| proveit.numbers.addition.right_add_eq_rational |
61 | instantiation | 83, 71, 72 | ⊢ |
| : , : , : |
62 | instantiation | 73, 105 | ⊢ |
| : |
63 | instantiation | 111, 74, 75 | ⊢ |
| : , : , : |
64 | instantiation | 76, 100, 101, 77, 78 | ⊢ |
| : , : , : , : , : |
65 | instantiation | 111, 79, 80 | ⊢ |
| : , : , : |
66 | theorem | | ⊢ |
| proveit.logic.equality.four_chain_transitivity |
67 | instantiation | 121, 81 | ⊢ |
| : , : , : |
68 | instantiation | 121, 82 | ⊢ |
| : , : , : |
69 | instantiation | 130, 101 | ⊢ |
| : |
70 | theorem | | ⊢ |
| proveit.numbers.negation.int_closure |
71 | theorem | | ⊢ |
| proveit.numbers.number_sets.rational_numbers.zero_is_rational |
72 | instantiation | 83, 84, 85 | ⊢ |
| : , : , : |
73 | theorem | | ⊢ |
| proveit.numbers.addition.elim_zero_left |
74 | instantiation | 86, 87, 88, 140, 89, 90, 93, 91, 105 | ⊢ |
| : , : , : , : , : , : |
75 | instantiation | 92, 105, 93, 94 | ⊢ |
| : , : , : |
76 | theorem | | ⊢ |
| proveit.numbers.division.mult_frac_cancel_numer_left |
77 | instantiation | 147, 96, 95 | ⊢ |
| : , : , : |
78 | instantiation | 147, 96, 97 | ⊢ |
| : , : , : |
79 | instantiation | 121, 98 | ⊢ |
| : , : , : |
80 | instantiation | 121, 99 | ⊢ |
| : , : , : |
81 | instantiation | 123, 100 | ⊢ |
| : |
82 | instantiation | 123, 101 | ⊢ |
| : |
83 | theorem | | ⊢ |
| proveit.logic.equality.sub_right_side_into |
84 | instantiation | 102, 141 | ⊢ |
| : |
85 | assumption | | ⊢ |
86 | theorem | | ⊢ |
| proveit.numbers.addition.disassociation |
87 | axiom | | ⊢ |
| proveit.numbers.number_sets.natural_numbers.zero_in_nats |
88 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.nat2 |
89 | theorem | | ⊢ |
| proveit.core_expr_types.tuples.tuple_len_0_typical_eq |
90 | instantiation | 103 | ⊢ |
| : , : |
91 | instantiation | 104, 105 | ⊢ |
| : |
92 | theorem | | ⊢ |
| proveit.numbers.addition.subtraction.add_cancel_triple_32 |
93 | instantiation | 147, 137, 106 | ⊢ |
| : , : , : |
94 | instantiation | 107 | ⊢ |
| : |
95 | instantiation | 147, 109, 108 | ⊢ |
| : , : , : |
96 | theorem | | ⊢ |
| proveit.numbers.number_sets.complex_numbers.real_nonzero_within_complex_nonzero |
97 | instantiation | 147, 109, 110 | ⊢ |
| : , : , : |
98 | instantiation | 111, 112, 113 | ⊢ |
| : , : , : |
99 | instantiation | 121, 114 | ⊢ |
| : , : , : |
100 | instantiation | 147, 137, 115 | ⊢ |
| : , : , : |
101 | instantiation | 147, 137, 116 | ⊢ |
| : , : , : |
102 | axiom | | ⊢ |
| proveit.physics.quantum.QPE._delta_b_def |
103 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.tuple_len_2_typical_eq |
104 | theorem | | ⊢ |
| proveit.numbers.negation.complex_closure |
105 | instantiation | 147, 137, 117 | ⊢ |
| : , : , : |
106 | theorem | | ⊢ |
| proveit.physics.quantum.QPE._phase_is_real |
107 | axiom | | ⊢ |
| proveit.logic.equality.equals_reflexivity |
108 | instantiation | 147, 119, 118 | ⊢ |
| : , : , : |
109 | theorem | | ⊢ |
| proveit.numbers.number_sets.real_numbers.rational_nonzero_within_real_nonzero |
110 | instantiation | 147, 119, 120 | ⊢ |
| : , : , : |
111 | axiom | | ⊢ |
| proveit.logic.equality.equals_transitivity |
112 | instantiation | 121, 122 | ⊢ |
| : , : , : |
113 | instantiation | 123, 131 | ⊢ |
| : |
114 | instantiation | 124, 131 | ⊢ |
| : |
115 | instantiation | 147, 126, 125 | ⊢ |
| : , : , : |
116 | instantiation | 147, 126, 134 | ⊢ |
| : , : , : |
117 | instantiation | 147, 126, 127 | ⊢ |
| : , : , : |
118 | instantiation | 147, 128, 149 | ⊢ |
| : , : , : |
119 | theorem | | ⊢ |
| proveit.numbers.number_sets.rational_numbers.nonzero_int_within_rational_nonzero |
120 | instantiation | 147, 128, 129 | ⊢ |
| : , : , : |
121 | axiom | | ⊢ |
| proveit.logic.equality.substitution |
122 | instantiation | 130, 131 | ⊢ |
| : |
123 | theorem | | ⊢ |
| proveit.numbers.division.frac_one_denom |
124 | theorem | | ⊢ |
| proveit.numbers.multiplication.elim_one_right |
125 | instantiation | 147, 142, 132 | ⊢ |
| : , : , : |
126 | theorem | | ⊢ |
| proveit.numbers.number_sets.real_numbers.rational_within_real |
127 | instantiation | 133, 134, 135, 136 | ⊢ |
| : , : |
128 | theorem | | ⊢ |
| proveit.numbers.number_sets.integers.nat_pos_within_nonzero_int |
129 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.posnat1 |
130 | theorem | | ⊢ |
| proveit.numbers.multiplication.elim_one_left |
131 | instantiation | 147, 137, 138 | ⊢ |
| : , : , : |
132 | instantiation | 147, 139, 140 | ⊢ |
| : , : , : |
133 | theorem | | ⊢ |
| proveit.numbers.division.div_rational_closure |
134 | instantiation | 147, 142, 141 | ⊢ |
| : , : , : |
135 | instantiation | 147, 142, 143 | ⊢ |
| : , : , : |
136 | instantiation | 144, 149 | ⊢ |
| : |
137 | theorem | | ⊢ |
| proveit.numbers.number_sets.complex_numbers.real_within_complex |
138 | instantiation | 145, 146, 149 | ⊢ |
| : , : , : |
139 | theorem | | ⊢ |
| proveit.numbers.number_sets.integers.nat_within_int |
140 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.nat1 |
141 | theorem | | ⊢ |
| proveit.physics.quantum.QPE._best_round_is_int |
142 | theorem | | ⊢ |
| proveit.numbers.number_sets.rational_numbers.int_within_rational |
143 | instantiation | 147, 148, 149 | ⊢ |
| : , : , : |
144 | theorem | | ⊢ |
| proveit.numbers.number_sets.natural_numbers.nonzero_if_is_nat_pos |
145 | theorem | | ⊢ |
| proveit.logic.sets.inclusion.unfold_subset_eq |
146 | instantiation | 150, 151 | ⊢ |
| : , : |
147 | theorem | | ⊢ |
| proveit.logic.sets.inclusion.superset_membership_from_proper_subset |
148 | theorem | | ⊢ |
| proveit.numbers.number_sets.integers.nat_pos_within_int |
149 | theorem | | ⊢ |
| proveit.physics.quantum.QPE._two_pow_t_is_nat_pos |
150 | theorem | | ⊢ |
| proveit.logic.sets.inclusion.relax_proper_subset |
151 | theorem | | ⊢ |
| proveit.numbers.number_sets.real_numbers.nat_pos_within_real |
*equality replacement requirements |