| step type | requirements | statement |
0 | instantiation | 1, 2, 3, 4, 5 | ⊢ |
| : , : , : |
1 | theorem | | ⊢ |
| proveit.numbers.addition.weak_bound_via_left_term_bound |
2 | modus ponens | 6, 7 | ⊢ |
3 | modus ponens | 8, 9 | ⊢ |
4 | modus ponens | 10, 11 | ⊢ |
5 | modus ponens | 12, 13 | ⊢ |
6 | instantiation | 16 | ⊢ |
| : , : , : |
7 | generalization | 14 | ⊢ |
8 | instantiation | 16 | ⊢ |
| : , : , : |
9 | generalization | 15 | ⊢ |
10 | instantiation | 16 | ⊢ |
| : , : , : |
11 | generalization | 17 | ⊢ |
12 | instantiation | 18 | ⊢ |
| : , : , : |
13 | generalization | 19 | ⊢ |
14 | instantiation | 24, 163, 20, 21 | , ⊢ |
| : , : |
15 | instantiation | 24, 163, 22, 23 | , ⊢ |
| : , : |
16 | theorem | | ⊢ |
| proveit.numbers.summation.summation_real_closure |
17 | instantiation | 24, 163, 25, 26 | , ⊢ |
| : , : |
18 | theorem | | ⊢ |
| proveit.numbers.summation.weak_summation_from_summands_bound |
19 | instantiation | 27, 28, 43, 41, 29 | , ⊢ |
| : , : , : |
20 | instantiation | 32, 68, 186 | , ⊢ |
| : , : |
21 | instantiation | 33, 30 | , ⊢ |
| : |
22 | instantiation | 32, 57, 186 | , ⊢ |
| : , : |
23 | instantiation | 33, 31 | , ⊢ |
| : |
24 | theorem | | ⊢ |
| proveit.numbers.division.div_real_closure |
25 | instantiation | 32, 78, 186 | , ⊢ |
| : , : |
26 | instantiation | 33, 34 | , ⊢ |
| : |
27 | theorem | | ⊢ |
| proveit.numbers.division.weak_div_from_denom_bound__all_pos |
28 | instantiation | 184, 35, 36 | ⊢ |
| : , : , : |
29 | instantiation | 37, 134, 57, 78, 38, 39 | , ⊢ |
| : , : , : |
30 | instantiation | 184, 42, 40 | , ⊢ |
| : , : , : |
31 | instantiation | 184, 42, 41 | , ⊢ |
| : , : , : |
32 | theorem | | ⊢ |
| proveit.numbers.exponentiation.exp_real_closure_nat_power |
33 | theorem | | ⊢ |
| proveit.numbers.number_sets.real_numbers.nonzero_if_in_real_nonzero |
34 | instantiation | 184, 42, 43 | , ⊢ |
| : , : , : |
35 | theorem | | ⊢ |
| proveit.numbers.number_sets.real_numbers.rational_nonneg_within_real_nonneg |
36 | instantiation | 184, 44, 179 | ⊢ |
| : , : , : |
37 | theorem | | ⊢ |
| proveit.numbers.exponentiation.exp_even_neg_base_lesseq |
38 | instantiation | 45, 46, 84 | , ⊢ |
| : , : |
39 | instantiation | 47 | ⊢ |
| : |
40 | instantiation | 50, 68, 48 | , ⊢ |
| : |
41 | instantiation | 50, 57, 49 | , ⊢ |
| : |
42 | theorem | | ⊢ |
| proveit.numbers.number_sets.real_numbers.real_pos_within_real_nonzero |
43 | instantiation | 50, 78, 51 | , ⊢ |
| : |
44 | theorem | | ⊢ |
| proveit.numbers.number_sets.rational_numbers.nat_within_rational_nonneg |
45 | theorem | | ⊢ |
| proveit.logic.booleans.conjunction.and_if_both |
46 | instantiation | 52, 78, 81, 128, 53, 54* | , ⊢ |
| : , : , : |
47 | axiom | | ⊢ |
| proveit.logic.equality.equals_reflexivity |
48 | instantiation | 55, 56 | , ⊢ |
| : , : |
49 | instantiation | 67, 57, 128, 58 | , ⊢ |
| : , : |
50 | theorem | | ⊢ |
| proveit.numbers.exponentiation.sqrd_pos_closure |
51 | instantiation | 59, 109, 60, 84 | , ⊢ |
| : , : |
52 | theorem | | ⊢ |
| proveit.numbers.addition.weak_bound_via_right_term_bound |
53 | instantiation | 61, 62, 128, 94, 85, 63, 64*, 65* | ⊢ |
| : , : , : |
54 | instantiation | 153, 66 | , ⊢ |
| : |
55 | theorem | | ⊢ |
| proveit.logic.equality.not_equals_symmetry |
56 | instantiation | 67, 128, 68, 69 | , ⊢ |
| : , : |
57 | instantiation | 79, 78, 81 | , ⊢ |
| : , : |
58 | instantiation | 70, 71 | , ⊢ |
| : , : |
59 | theorem | | ⊢ |
| proveit.numbers.ordering.less_is_not_eq_int |
60 | theorem | | ⊢ |
| proveit.numbers.number_sets.integers.zero_is_int |
61 | theorem | | ⊢ |
| proveit.numbers.multiplication.reversed_weak_bound_via_right_factor_bound |
62 | instantiation | 93, 163 | ⊢ |
| : |
63 | instantiation | 72, 73 | ⊢ |
| : , : |
64 | instantiation | 74, 75, 76 | ⊢ |
| : , : , : |
65 | instantiation | 77, 88 | ⊢ |
| : |
66 | instantiation | 184, 162, 78 | , ⊢ |
| : , : , : |
67 | theorem | | ⊢ |
| proveit.numbers.ordering.less_is_not_eq |
68 | instantiation | 79, 80, 81 | , ⊢ |
| : , : |
69 | instantiation | 82, 83 | , ⊢ |
| : , : |
70 | theorem | | ⊢ |
| proveit.numbers.addition.subtraction.neg_difference |
71 | instantiation | 164, 84, 85 | , ⊢ |
| : , : , : |
72 | theorem | | ⊢ |
| proveit.numbers.ordering.relax_less |
73 | instantiation | 117, 86 | ⊢ |
| : |
74 | axiom | | ⊢ |
| proveit.logic.equality.equals_transitivity |
75 | instantiation | 87, 179, 186, 104, 106, 105, 88, 107, 108 | ⊢ |
| : , : , : , : , : , : |
76 | instantiation | 89, 104, 186, 105, 106, 155, 107, 108, 90* | ⊢ |
| : , : , : , : , : |
77 | theorem | | ⊢ |
| proveit.numbers.multiplication.mult_zero_right |
78 | instantiation | 184, 168, 91 | , ⊢ |
| : , : , : |
79 | theorem | | ⊢ |
| proveit.numbers.addition.add_real_closure_bin |
80 | instantiation | 184, 168, 92 | , ⊢ |
| : , : , : |
81 | instantiation | 93, 94 | ⊢ |
| : |
82 | theorem | | ⊢ |
| proveit.numbers.addition.subtraction.pos_difference |
83 | instantiation | 95, 96, 97 | , ⊢ |
| : , : , : |
84 | instantiation | 98, 99, 100 | , ⊢ |
| : , : , : |
85 | instantiation | 101, 128, 163, 113 | ⊢ |
| : , : , : |
86 | instantiation | 132, 146 | ⊢ |
| : |
87 | theorem | | ⊢ |
| proveit.numbers.multiplication.disassociation |
88 | instantiation | 102, 155 | ⊢ |
| : |
89 | theorem | | ⊢ |
| proveit.numbers.multiplication.mult_neg_any |
90 | instantiation | 103, 104, 186, 105, 106, 107, 108 | ⊢ |
| : , : , : , : |
91 | instantiation | 184, 174, 109 | , ⊢ |
| : , : , : |
92 | instantiation | 184, 174, 110 | , ⊢ |
| : , : , : |
93 | theorem | | ⊢ |
| proveit.numbers.negation.real_closure |
94 | instantiation | 111, 128, 163, 113 | ⊢ |
| : , : , : |
95 | axiom | | ⊢ |
| proveit.numbers.ordering.transitivity_less_less |
96 | instantiation | 112, 128, 163, 113 | ⊢ |
| : , : , : |
97 | instantiation | 164, 114, 115 | , ⊢ |
| : , : , : |
98 | theorem | | ⊢ |
| proveit.numbers.ordering.transitivity_less_eq_less |
99 | instantiation | 116, 138, 139, 125 | , ⊢ |
| : , : , : |
100 | instantiation | 117, 118 | ⊢ |
| : |
101 | theorem | | ⊢ |
| proveit.numbers.number_sets.real_numbers.interval_co_lower_bound |
102 | theorem | | ⊢ |
| proveit.numbers.negation.complex_closure |
103 | theorem | | ⊢ |
| proveit.numbers.multiplication.elim_one_any |
104 | axiom | | ⊢ |
| proveit.numbers.number_sets.natural_numbers.zero_in_nats |
105 | theorem | | ⊢ |
| proveit.core_expr_types.tuples.tuple_len_0_typical_eq |
106 | instantiation | 119 | ⊢ |
| : , : |
107 | instantiation | 120, 121, 122 | ⊢ |
| : , : |
108 | instantiation | 184, 162, 123 | ⊢ |
| : , : , : |
109 | instantiation | 184, 124, 125 | , ⊢ |
| : , : , : |
110 | instantiation | 184, 126, 131 | , ⊢ |
| : , : , : |
111 | theorem | | ⊢ |
| proveit.numbers.number_sets.real_numbers.all_in_interval_co__is__real |
112 | theorem | | ⊢ |
| proveit.numbers.number_sets.real_numbers.interval_co_upper_bound |
113 | theorem | | ⊢ |
| proveit.physics.quantum.QPE._scaled_delta_b_floor_in_interval |
114 | instantiation | 127, 163, 128, 129, 158, 130* | ⊢ |
| : , : , : |
115 | instantiation | 170, 152, 177, 131 | , ⊢ |
| : , : , : |
116 | theorem | | ⊢ |
| proveit.numbers.number_sets.integers.interval_upper_bound |
117 | theorem | | ⊢ |
| proveit.numbers.number_sets.integers.negative_if_in_neg_int |
118 | instantiation | 132, 133 | ⊢ |
| : |
119 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.tuple_len_2_typical_eq |
120 | theorem | | ⊢ |
| proveit.numbers.exponentiation.exp_complex_closure |
121 | instantiation | 184, 162, 134 | ⊢ |
| : , : , : |
122 | instantiation | 184, 162, 135 | ⊢ |
| : , : , : |
123 | instantiation | 136, 137 | ⊢ |
| : |
124 | instantiation | 172, 138, 139 | ⊢ |
| : , : |
125 | assumption | | ⊢ |
126 | instantiation | 172, 152, 177 | ⊢ |
| : , : |
127 | theorem | | ⊢ |
| proveit.numbers.addition.strong_bound_via_left_term_bound |
128 | theorem | | ⊢ |
| proveit.numbers.number_sets.real_numbers.zero_is_real |
129 | instantiation | 184, 168, 140 | ⊢ |
| : , : , : |
130 | instantiation | 141, 142, 143 | ⊢ |
| : , : , : |
131 | assumption | | ⊢ |
132 | theorem | | ⊢ |
| proveit.numbers.negation.int_neg_closure |
133 | instantiation | 144, 145, 146 | ⊢ |
| : , : |
134 | instantiation | 184, 168, 147 | ⊢ |
| : , : , : |
135 | instantiation | 148, 149, 150 | ⊢ |
| : , : , : |
136 | theorem | | ⊢ |
| proveit.physics.quantum.QPE._delta_b_is_real |
137 | theorem | | ⊢ |
| proveit.physics.quantum.QPE._best_floor_is_int |
138 | instantiation | 176, 151, 175 | ⊢ |
| : , : |
139 | instantiation | 182, 152 | ⊢ |
| : |
140 | instantiation | 184, 174, 161 | ⊢ |
| : , : , : |
141 | theorem | | ⊢ |
| proveit.logic.equality.sub_right_side_into |
142 | instantiation | 153, 155 | ⊢ |
| : |
143 | instantiation | 154, 155, 156 | ⊢ |
| : , : |
144 | theorem | | ⊢ |
| proveit.numbers.addition.add_nat_pos_closure_bin |
145 | instantiation | 157, 161, 158 | ⊢ |
| : |
146 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.posnat1 |
147 | instantiation | 184, 174, 183 | ⊢ |
| : , : , : |
148 | theorem | | ⊢ |
| proveit.logic.sets.inclusion.unfold_subset_eq |
149 | instantiation | 159, 160 | ⊢ |
| : , : |
150 | axiom | | ⊢ |
| proveit.physics.quantum.QPE._t_in_natural_pos |
151 | instantiation | 182, 177 | ⊢ |
| : |
152 | instantiation | 176, 161, 175 | ⊢ |
| : , : |
153 | theorem | | ⊢ |
| proveit.numbers.addition.elim_zero_right |
154 | theorem | | ⊢ |
| proveit.numbers.addition.commutation |
155 | instantiation | 184, 162, 163 | ⊢ |
| : , : , : |
156 | theorem | | ⊢ |
| proveit.numbers.number_sets.complex_numbers.zero_is_complex |
157 | theorem | | ⊢ |
| proveit.numbers.number_sets.integers.pos_int_is_natural_pos |
158 | instantiation | 164, 165, 166 | ⊢ |
| : , : , : |
159 | theorem | | ⊢ |
| proveit.logic.sets.inclusion.relax_proper_subset |
160 | theorem | | ⊢ |
| proveit.numbers.number_sets.real_numbers.nat_pos_within_real |
161 | instantiation | 184, 167, 171 | ⊢ |
| : , : , : |
162 | theorem | | ⊢ |
| proveit.numbers.number_sets.complex_numbers.real_within_complex |
163 | instantiation | 184, 168, 169 | ⊢ |
| : , : , : |
164 | theorem | | ⊢ |
| proveit.numbers.ordering.transitivity_less_less_eq |
165 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.less_0_1 |
166 | instantiation | 170, 175, 173, 171 | ⊢ |
| : , : , : |
167 | instantiation | 172, 175, 173 | ⊢ |
| : , : |
168 | theorem | | ⊢ |
| proveit.numbers.number_sets.real_numbers.rational_within_real |
169 | instantiation | 184, 174, 175 | ⊢ |
| : , : , : |
170 | theorem | | ⊢ |
| proveit.numbers.number_sets.integers.interval_lower_bound |
171 | assumption | | ⊢ |
172 | theorem | | ⊢ |
| proveit.numbers.number_sets.integers.int_interval_within_int |
173 | instantiation | 176, 177, 178 | ⊢ |
| : , : |
174 | theorem | | ⊢ |
| proveit.numbers.number_sets.rational_numbers.int_within_rational |
175 | instantiation | 184, 185, 179 | ⊢ |
| : , : , : |
176 | theorem | | ⊢ |
| proveit.numbers.addition.add_int_closure_bin |
177 | instantiation | 184, 180, 181 | ⊢ |
| : , : , : |
178 | instantiation | 182, 183 | ⊢ |
| : |
179 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.nat1 |
180 | theorem | | ⊢ |
| proveit.numbers.number_sets.integers.nat_pos_within_int |
181 | theorem | | ⊢ |
| proveit.physics.quantum.QPE._two_pow_t_minus_one_is_nat_pos |
182 | theorem | | ⊢ |
| proveit.numbers.negation.int_closure |
183 | instantiation | 184, 185, 186 | ⊢ |
| : , : , : |
184 | theorem | | ⊢ |
| proveit.logic.sets.inclusion.superset_membership_from_proper_subset |
185 | theorem | | ⊢ |
| proveit.numbers.number_sets.integers.nat_within_int |
186 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.nat2 |
*equality replacement requirements |