| step type | requirements | statement |
0 | instantiation | 1, 2, 3 | ⊢ |
| : , : , : |
1 | reference | 83 | ⊢ |
2 | instantiation | 4, 30, 47, 5, 6, 7* | ⊢ |
| : , : , : |
3 | instantiation | 8, 36, 9, 159, 10, 11* | ⊢ |
| : , : , : |
4 | theorem | | ⊢ |
| proveit.numbers.division.strong_div_from_numer_bound__pos_denom |
5 | instantiation | 12, 47, 95, 13, 14, 15*, 16* | ⊢ |
| : , : , : |
6 | instantiation | 97, 31 | ⊢ |
| : |
7 | instantiation | 17, 18, 19 | ⊢ |
| : |
8 | theorem | | ⊢ |
| proveit.numbers.exponentiation.exp_eq_real |
9 | instantiation | 191, 20, 21 | ⊢ |
| : , : , : |
10 | instantiation | 22, 33, 144, 43, 23* | ⊢ |
| : , : |
11 | instantiation | 24, 25 | ⊢ |
| : |
12 | theorem | | ⊢ |
| proveit.numbers.addition.strong_bound_via_left_term_bound |
13 | instantiation | 191, 170, 26 | ⊢ |
| : , : , : |
14 | instantiation | 97, 27 | ⊢ |
| : |
15 | instantiation | 127, 28, 29 | ⊢ |
| : , : , : |
16 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.add_5_4 |
17 | theorem | | ⊢ |
| proveit.numbers.division.frac_cancel_complete |
18 | instantiation | 191, 181, 30 | ⊢ |
| : , : , : |
19 | instantiation | 188, 31 | ⊢ |
| : |
20 | theorem | | ⊢ |
| proveit.numbers.number_sets.real_numbers.real_nonneg_within_real |
21 | instantiation | 32, 33 | ⊢ |
| : |
22 | theorem | | ⊢ |
| proveit.numbers.absolute_value.abs_eq |
23 | instantiation | 34, 35 | ⊢ |
| : |
24 | theorem | | ⊢ |
| proveit.numbers.exponentiation.exponentiated_one |
25 | instantiation | 191, 181, 36 | ⊢ |
| : , : , : |
26 | instantiation | 191, 186, 37 | ⊢ |
| : , : , : |
27 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.posnat5 |
28 | instantiation | 38, 40 | ⊢ |
| : |
29 | instantiation | 39, 40, 41 | ⊢ |
| : , : |
30 | instantiation | 191, 170, 42 | ⊢ |
| : , : , : |
31 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.posnat9 |
32 | theorem | | ⊢ |
| proveit.numbers.absolute_value.abs_complex_closure |
33 | instantiation | 83, 144, 43 | ⊢ |
| : , : , : |
34 | theorem | | ⊢ |
| proveit.numbers.absolute_value.abs_non_neg_elim |
35 | instantiation | 44, 184 | ⊢ |
| : |
36 | instantiation | 191, 170, 45 | ⊢ |
| : , : , : |
37 | instantiation | 191, 183, 46 | ⊢ |
| : , : , : |
38 | theorem | | ⊢ |
| proveit.numbers.addition.elim_zero_right |
39 | theorem | | ⊢ |
| proveit.numbers.addition.commutation |
40 | instantiation | 191, 181, 47 | ⊢ |
| : , : , : |
41 | theorem | | ⊢ |
| proveit.numbers.number_sets.complex_numbers.zero_is_complex |
42 | instantiation | 191, 186, 48 | ⊢ |
| : , : , : |
43 | instantiation | 83, 49, 50 | ⊢ |
| : , : , : |
44 | theorem | | ⊢ |
| proveit.numbers.number_sets.natural_numbers.natural_lower_bound |
45 | instantiation | 191, 186, 51 | ⊢ |
| : , : , : |
46 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.nat5 |
47 | instantiation | 191, 170, 52 | ⊢ |
| : , : , : |
48 | instantiation | 191, 183, 53 | ⊢ |
| : , : , : |
49 | instantiation | 127, 54, 84 | ⊢ |
| : , : , : |
50 | instantiation | 55, 193, 56 | ⊢ |
| : , : |
51 | instantiation | 191, 183, 132 | ⊢ |
| : , : , : |
52 | instantiation | 191, 186, 57 | ⊢ |
| : , : , : |
53 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.nat9 |
54 | modus ponens | 58, 59 | ⊢ |
55 | theorem | | ⊢ |
| proveit.numbers.modular.int_mod_elimination |
56 | instantiation | 62, 63, 64, 185, 60 | ⊢ |
| : , : , : |
57 | instantiation | 191, 183, 61 | ⊢ |
| : , : , : |
58 | theorem | | ⊢ |
| proveit.physics.quantum.QPE._alpha_ideal_case |
59 | instantiation | 62, 63, 64, 77, 65 | ⊢ |
| : , : , : |
60 | instantiation | 69, 66, 67 | ⊢ |
| : , : |
61 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.nat4 |
62 | theorem | | ⊢ |
| proveit.numbers.number_sets.integers.in_interval |
63 | theorem | | ⊢ |
| proveit.numbers.number_sets.integers.zero_is_int |
64 | instantiation | 68, 187, 103 | ⊢ |
| : , : |
65 | instantiation | 69, 70, 71 | ⊢ |
| : , : |
66 | instantiation | 127, 70, 84 | ⊢ |
| : , : , : |
67 | instantiation | 127, 71, 84 | ⊢ |
| : , : , : |
68 | theorem | | ⊢ |
| proveit.numbers.addition.add_int_closure_bin |
69 | theorem | | ⊢ |
| proveit.logic.booleans.conjunction.and_if_both |
70 | instantiation | 72, 182, 95, 150, 73, 74, 75* | ⊢ |
| : , : , : |
71 | instantiation | 76, 77, 187, 103, 78, 79 | ⊢ |
| : , : , : |
72 | theorem | | ⊢ |
| proveit.numbers.multiplication.weak_bound_via_right_factor_bound |
73 | instantiation | 80, 95, 159, 96 | ⊢ |
| : , : , : |
74 | instantiation | 81, 87 | ⊢ |
| : , : |
75 | instantiation | 82, 175 | ⊢ |
| : |
76 | theorem | | ⊢ |
| proveit.numbers.ordering.less_add_right_weak_int |
77 | instantiation | 83, 185, 84 | ⊢ |
| : , : , : |
78 | instantiation | 85, 182, 150, 159, 86, 87, 158* | ⊢ |
| : , : , : |
79 | instantiation | 88, 89, 90 | ⊢ |
| : , : |
80 | theorem | | ⊢ |
| proveit.numbers.number_sets.real_numbers.interval_co_lower_bound |
81 | theorem | | ⊢ |
| proveit.numbers.ordering.relax_less |
82 | theorem | | ⊢ |
| proveit.numbers.multiplication.mult_zero_right |
83 | theorem | | ⊢ |
| proveit.logic.equality.sub_left_side_into |
84 | instantiation | 91, 182, 150, 161, 92, 93* | ⊢ |
| : , : , : |
85 | theorem | | ⊢ |
| proveit.numbers.multiplication.strong_bound_via_right_factor_bound |
86 | instantiation | 94, 95, 159, 96 | ⊢ |
| : , : , : |
87 | instantiation | 97, 193 | ⊢ |
| : |
88 | theorem | | ⊢ |
| proveit.numbers.ordering.relax_equal_to_less_eq |
89 | instantiation | 191, 170, 98 | ⊢ |
| : , : , : |
90 | instantiation | 151 | ⊢ |
| : |
91 | theorem | | ⊢ |
| proveit.numbers.multiplication.left_mult_eq_real |
92 | instantiation | 99, 100 | ⊢ |
| : , : |
93 | instantiation | 127, 101, 102 | ⊢ |
| : , : , : |
94 | theorem | | ⊢ |
| proveit.numbers.number_sets.real_numbers.interval_co_upper_bound |
95 | theorem | | ⊢ |
| proveit.numbers.number_sets.real_numbers.zero_is_real |
96 | axiom | | ⊢ |
| proveit.physics.quantum.QPE._phase_in_interval |
97 | theorem | | ⊢ |
| proveit.numbers.number_sets.natural_numbers.natural_pos_is_pos |
98 | instantiation | 191, 186, 103 | ⊢ |
| : , : , : |
99 | theorem | | ⊢ |
| proveit.logic.equality.equals_reversal |
100 | instantiation | 104, 171, 115, 105, 116, 106*, 107* | ⊢ |
| : , : , : |
101 | instantiation | 127, 108, 109 | ⊢ |
| : , : , : |
102 | instantiation | 110, 111, 112, 113 | ⊢ |
| : , : , : , : |
103 | instantiation | 114, 176 | ⊢ |
| : |
104 | theorem | | ⊢ |
| proveit.numbers.addition.right_add_eq_rational |
105 | instantiation | 127, 115, 116 | ⊢ |
| : , : , : |
106 | instantiation | 117, 149 | ⊢ |
| : |
107 | instantiation | 155, 118, 119 | ⊢ |
| : , : , : |
108 | instantiation | 120, 144, 145, 121, 122 | ⊢ |
| : , : , : , : , : |
109 | instantiation | 155, 123, 124 | ⊢ |
| : , : , : |
110 | theorem | | ⊢ |
| proveit.logic.equality.four_chain_transitivity |
111 | instantiation | 165, 125 | ⊢ |
| : , : , : |
112 | instantiation | 165, 126 | ⊢ |
| : , : , : |
113 | instantiation | 174, 145 | ⊢ |
| : |
114 | theorem | | ⊢ |
| proveit.numbers.negation.int_closure |
115 | theorem | | ⊢ |
| proveit.numbers.number_sets.rational_numbers.zero_is_rational |
116 | instantiation | 127, 128, 129 | ⊢ |
| : , : , : |
117 | theorem | | ⊢ |
| proveit.numbers.addition.elim_zero_left |
118 | instantiation | 130, 131, 132, 184, 133, 134, 137, 135, 149 | ⊢ |
| : , : , : , : , : , : |
119 | instantiation | 136, 149, 137, 138 | ⊢ |
| : , : , : |
120 | theorem | | ⊢ |
| proveit.numbers.division.mult_frac_cancel_numer_left |
121 | instantiation | 191, 140, 139 | ⊢ |
| : , : , : |
122 | instantiation | 191, 140, 141 | ⊢ |
| : , : , : |
123 | instantiation | 165, 142 | ⊢ |
| : , : , : |
124 | instantiation | 165, 143 | ⊢ |
| : , : , : |
125 | instantiation | 167, 144 | ⊢ |
| : |
126 | instantiation | 167, 145 | ⊢ |
| : |
127 | theorem | | ⊢ |
| proveit.logic.equality.sub_right_side_into |
128 | instantiation | 146, 185 | ⊢ |
| : |
129 | assumption | | ⊢ |
130 | theorem | | ⊢ |
| proveit.numbers.addition.disassociation |
131 | axiom | | ⊢ |
| proveit.numbers.number_sets.natural_numbers.zero_in_nats |
132 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.nat2 |
133 | theorem | | ⊢ |
| proveit.core_expr_types.tuples.tuple_len_0_typical_eq |
134 | instantiation | 147 | ⊢ |
| : , : |
135 | instantiation | 148, 149 | ⊢ |
| : |
136 | theorem | | ⊢ |
| proveit.numbers.addition.subtraction.add_cancel_triple_32 |
137 | instantiation | 191, 181, 150 | ⊢ |
| : , : , : |
138 | instantiation | 151 | ⊢ |
| : |
139 | instantiation | 191, 153, 152 | ⊢ |
| : , : , : |
140 | theorem | | ⊢ |
| proveit.numbers.number_sets.complex_numbers.real_nonzero_within_complex_nonzero |
141 | instantiation | 191, 153, 154 | ⊢ |
| : , : , : |
142 | instantiation | 155, 156, 157 | ⊢ |
| : , : , : |
143 | instantiation | 165, 158 | ⊢ |
| : , : , : |
144 | instantiation | 191, 181, 159 | ⊢ |
| : , : , : |
145 | instantiation | 191, 181, 160 | ⊢ |
| : , : , : |
146 | axiom | | ⊢ |
| proveit.physics.quantum.QPE._delta_b_def |
147 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.tuple_len_2_typical_eq |
148 | theorem | | ⊢ |
| proveit.numbers.negation.complex_closure |
149 | instantiation | 191, 181, 161 | ⊢ |
| : , : , : |
150 | theorem | | ⊢ |
| proveit.physics.quantum.QPE._phase_is_real |
151 | axiom | | ⊢ |
| proveit.logic.equality.equals_reflexivity |
152 | instantiation | 191, 163, 162 | ⊢ |
| : , : , : |
153 | theorem | | ⊢ |
| proveit.numbers.number_sets.real_numbers.rational_nonzero_within_real_nonzero |
154 | instantiation | 191, 163, 164 | ⊢ |
| : , : , : |
155 | axiom | | ⊢ |
| proveit.logic.equality.equals_transitivity |
156 | instantiation | 165, 166 | ⊢ |
| : , : , : |
157 | instantiation | 167, 175 | ⊢ |
| : |
158 | instantiation | 168, 175 | ⊢ |
| : |
159 | instantiation | 191, 170, 169 | ⊢ |
| : , : , : |
160 | instantiation | 191, 170, 178 | ⊢ |
| : , : , : |
161 | instantiation | 191, 170, 171 | ⊢ |
| : , : , : |
162 | instantiation | 191, 172, 193 | ⊢ |
| : , : , : |
163 | theorem | | ⊢ |
| proveit.numbers.number_sets.rational_numbers.nonzero_int_within_rational_nonzero |
164 | instantiation | 191, 172, 173 | ⊢ |
| : , : , : |
165 | axiom | | ⊢ |
| proveit.logic.equality.substitution |
166 | instantiation | 174, 175 | ⊢ |
| : |
167 | theorem | | ⊢ |
| proveit.numbers.division.frac_one_denom |
168 | theorem | | ⊢ |
| proveit.numbers.multiplication.elim_one_right |
169 | instantiation | 191, 186, 176 | ⊢ |
| : , : , : |
170 | theorem | | ⊢ |
| proveit.numbers.number_sets.real_numbers.rational_within_real |
171 | instantiation | 177, 178, 179, 180 | ⊢ |
| : , : |
172 | theorem | | ⊢ |
| proveit.numbers.number_sets.integers.nat_pos_within_nonzero_int |
173 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.posnat1 |
174 | theorem | | ⊢ |
| proveit.numbers.multiplication.elim_one_left |
175 | instantiation | 191, 181, 182 | ⊢ |
| : , : , : |
176 | instantiation | 191, 183, 184 | ⊢ |
| : , : , : |
177 | theorem | | ⊢ |
| proveit.numbers.division.div_rational_closure |
178 | instantiation | 191, 186, 185 | ⊢ |
| : , : , : |
179 | instantiation | 191, 186, 187 | ⊢ |
| : , : , : |
180 | instantiation | 188, 193 | ⊢ |
| : |
181 | theorem | | ⊢ |
| proveit.numbers.number_sets.complex_numbers.real_within_complex |
182 | instantiation | 189, 190, 193 | ⊢ |
| : , : , : |
183 | theorem | | ⊢ |
| proveit.numbers.number_sets.integers.nat_within_int |
184 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.nat1 |
185 | theorem | | ⊢ |
| proveit.physics.quantum.QPE._best_round_is_int |
186 | theorem | | ⊢ |
| proveit.numbers.number_sets.rational_numbers.int_within_rational |
187 | instantiation | 191, 192, 193 | ⊢ |
| : , : , : |
188 | theorem | | ⊢ |
| proveit.numbers.number_sets.natural_numbers.nonzero_if_is_nat_pos |
189 | theorem | | ⊢ |
| proveit.logic.sets.inclusion.unfold_subset_eq |
190 | instantiation | 194, 195 | ⊢ |
| : , : |
191 | theorem | | ⊢ |
| proveit.logic.sets.inclusion.superset_membership_from_proper_subset |
192 | theorem | | ⊢ |
| proveit.numbers.number_sets.integers.nat_pos_within_int |
193 | theorem | | ⊢ |
| proveit.physics.quantum.QPE._two_pow_t_is_nat_pos |
194 | theorem | | ⊢ |
| proveit.logic.sets.inclusion.relax_proper_subset |
195 | theorem | | ⊢ |
| proveit.numbers.number_sets.real_numbers.nat_pos_within_real |
*equality replacement requirements |