| step type | requirements | statement |
0 | instantiation | 1, 2, 3, 4, 5, 6, 7 | ⊢ |
| : , : , : , : , : , : |
1 | reference | 94 | ⊢ |
2 | reference | 193 | ⊢ |
3 | reference | 95 | ⊢ |
4 | instantiation | 173 | ⊢ |
| : , : |
5 | reference | 96 | ⊢ |
6 | instantiation | 220, 182, 8 | ⊢ |
| : , : , : |
7 | instantiation | 67, 175 | ⊢ |
| : |
8 | instantiation | 9, 167, 10 | ⊢ |
| : , : |
9 | theorem | | ⊢ |
| proveit.numbers.exponentiation.exp_real_closure_nat_power |
10 | instantiation | 11, 12, 13 | ⊢ |
| : |
11 | theorem | | ⊢ |
| proveit.numbers.number_sets.integers.nonneg_int_is_natural |
12 | instantiation | 14, 15, 16 | ⊢ |
| : , : |
13 | instantiation | 17, 18 | ⊢ |
| : , : |
14 | theorem | | ⊢ |
| proveit.numbers.addition.add_int_closure_bin |
15 | instantiation | 220, 19, 103 | ⊢ |
| : , : , : |
16 | instantiation | 220, 20, 21 | ⊢ |
| : , : , : |
17 | theorem | | ⊢ |
| proveit.numbers.addition.subtraction.nonneg_difference |
18 | instantiation | 46, 22, 23 | ⊢ |
| : , : , : |
19 | theorem | | ⊢ |
| proveit.numbers.number_sets.integers.nat_pos_within_int |
20 | theorem | | ⊢ |
| proveit.numbers.number_sets.integers.neg_int_within_int |
21 | instantiation | 24, 210 | ⊢ |
| : |
22 | axiom | | ⊢ |
| proveit.physics.quantum.QPE._n_ge_two |
23 | instantiation | 61, 65, 167, 25, 26, 27*, 28* | ⊢ |
| : , : , : |
24 | theorem | | ⊢ |
| proveit.numbers.negation.int_neg_closure |
25 | instantiation | 80, 30, 167 | ⊢ |
| : , : |
26 | instantiation | 29, 167, 30, 31, 137 | ⊢ |
| : , : , : |
27 | instantiation | 148, 32, 33 | ⊢ |
| : , : , : |
28 | instantiation | 148, 34, 35 | ⊢ |
| : , : , : |
29 | theorem | | ⊢ |
| proveit.numbers.ordering.less_eq_add_right |
30 | instantiation | 80, 82, 120 | ⊢ |
| : , : |
31 | instantiation | 46, 36, 37 | ⊢ |
| : , : , : |
32 | instantiation | 94, 222, 193, 95, 52, 96, 154, 100, 53 | ⊢ |
| : , : , : , : , : , : |
33 | instantiation | 99, 154, 100, 70 | ⊢ |
| : , : , : |
34 | instantiation | 127, 38 | ⊢ |
| : , : , : |
35 | instantiation | 39, 40, 41, 42 | ⊢ |
| : , : , : , : |
36 | instantiation | 43, 219, 59, 44, 45* | ⊢ |
| : , : |
37 | instantiation | 46, 47, 48 | ⊢ |
| : , : , : |
38 | instantiation | 94, 95, 193, 222, 96, 69, 72, 98, 154 | ⊢ |
| : , : , : , : , : , : |
39 | theorem | | ⊢ |
| proveit.logic.equality.four_chain_transitivity |
40 | instantiation | 94, 95, 50, 222, 96, 51, 72, 98, 154, 49 | ⊢ |
| : , : , : , : , : , : |
41 | instantiation | 94, 50, 193, 95, 51, 52, 96, 72, 98, 154, 100, 53 | ⊢ |
| : , : , : , : , : , : |
42 | instantiation | 148, 54, 55 | ⊢ |
| : , : , : |
43 | theorem | | ⊢ |
| proveit.numbers.rounding.ceil_of_real_above_int |
44 | instantiation | 56, 202, 76, 57 | ⊢ |
| : , : |
45 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.add_1_1 |
46 | theorem | | ⊢ |
| proveit.numbers.ordering.transitivity_less_eq_less_eq |
47 | instantiation | 58, 59, 171, 60 | ⊢ |
| : , : |
48 | instantiation | 61, 120, 62, 82, 63, 64* | ⊢ |
| : , : , : |
49 | instantiation | 220, 182, 65 | ⊢ |
| : , : , : |
50 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.nat3 |
51 | instantiation | 66 | ⊢ |
| : , : , : |
52 | instantiation | 173 | ⊢ |
| : , : |
53 | instantiation | 67, 154 | ⊢ |
| : |
54 | instantiation | 68, 193, 222, 95, 69, 96, 72, 98, 154, 100, 70 | ⊢ |
| : , : , : , : , : , : , : , : |
55 | instantiation | 71, 100, 72, 102 | ⊢ |
| : , : , : |
56 | theorem | | ⊢ |
| proveit.numbers.logarithms.log_base_large_a_greater_one |
57 | instantiation | 73, 194, 74 | ⊢ |
| : , : |
58 | theorem | | ⊢ |
| proveit.numbers.rounding.ceil_increasing_less_eq |
59 | instantiation | 177, 202, 76, 179 | ⊢ |
| : , : |
60 | instantiation | 75, 202, 76, 178, 77, 194 | ⊢ |
| : , : , : |
61 | theorem | | ⊢ |
| proveit.numbers.addition.weak_bound_via_left_term_bound |
62 | instantiation | 80, 143, 121 | ⊢ |
| : , : |
63 | axiom | | ⊢ |
| proveit.physics.quantum.QPE._t_req |
64 | instantiation | 148, 78, 79 | ⊢ |
| : , : , : |
65 | instantiation | 80, 143, 81 | ⊢ |
| : , : |
66 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.tuple_len_3_typical_eq |
67 | theorem | | ⊢ |
| proveit.numbers.negation.complex_closure |
68 | theorem | | ⊢ |
| proveit.numbers.addition.subtraction.add_cancel_general |
69 | instantiation | 173 | ⊢ |
| : , : |
70 | instantiation | 122 | ⊢ |
| : |
71 | theorem | | ⊢ |
| proveit.numbers.addition.subtraction.add_cancel_triple_32 |
72 | instantiation | 220, 182, 82 | ⊢ |
| : , : , : |
73 | theorem | | ⊢ |
| proveit.logic.booleans.conjunction.and_if_both |
74 | instantiation | 83, 167, 84, 85, 86, 87*, 88* | ⊢ |
| : , : , : |
75 | theorem | | ⊢ |
| proveit.numbers.logarithms.log_increasing_less_eq |
76 | instantiation | 220, 204, 89 | ⊢ |
| : , : , : |
77 | instantiation | 90, 167, 161, 91, 92, 93* | ⊢ |
| : , : , : |
78 | instantiation | 94, 95, 193, 222, 96, 97, 100, 101, 98 | ⊢ |
| : , : , : , : , : , : |
79 | instantiation | 99, 100, 101, 102 | ⊢ |
| : , : , : |
80 | theorem | | ⊢ |
| proveit.numbers.addition.add_real_closure_bin |
81 | instantiation | 142, 167 | ⊢ |
| : |
82 | instantiation | 157, 158, 103 | ⊢ |
| : , : , : |
83 | theorem | | ⊢ |
| proveit.numbers.addition.strong_bound_via_left_term_bound |
84 | instantiation | 104, 161, 213 | ⊢ |
| : , : |
85 | instantiation | 220, 216, 105 | ⊢ |
| : , : , : |
86 | instantiation | 106, 161, 213, 214, 107, 108 | ⊢ |
| : , : , : |
87 | instantiation | 148, 109, 110 | ⊢ |
| : , : , : |
88 | instantiation | 148, 111, 112 | ⊢ |
| : , : , : |
89 | instantiation | 188, 113, 205 | ⊢ |
| : , : |
90 | theorem | | ⊢ |
| proveit.numbers.addition.weak_bound_via_right_term_bound |
91 | instantiation | 220, 114, 185 | ⊢ |
| : , : , : |
92 | instantiation | 115, 116, 200, 202, 117 | ⊢ |
| : , : , : |
93 | instantiation | 129, 183, 219, 130*, 118*, 119* | ⊢ |
| : , : , : , : |
94 | theorem | | ⊢ |
| proveit.numbers.addition.disassociation |
95 | axiom | | ⊢ |
| proveit.numbers.number_sets.natural_numbers.zero_in_nats |
96 | theorem | | ⊢ |
| proveit.core_expr_types.tuples.tuple_len_0_typical_eq |
97 | instantiation | 173 | ⊢ |
| : , : |
98 | instantiation | 220, 182, 120 | ⊢ |
| : , : , : |
99 | theorem | | ⊢ |
| proveit.numbers.addition.subtraction.add_cancel_triple_13 |
100 | instantiation | 220, 182, 143 | ⊢ |
| : , : , : |
101 | instantiation | 220, 182, 121 | ⊢ |
| : , : , : |
102 | instantiation | 122 | ⊢ |
| : |
103 | axiom | | ⊢ |
| proveit.physics.quantum.QPE._t_in_natural_pos |
104 | theorem | | ⊢ |
| proveit.numbers.multiplication.mult_real_closure_bin |
105 | instantiation | 123, 172, 217 | ⊢ |
| : , : |
106 | theorem | | ⊢ |
| proveit.numbers.multiplication.strong_bound_via_right_factor_bound |
107 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.less_0_1 |
108 | instantiation | 124, 181 | ⊢ |
| : |
109 | instantiation | 127, 125 | ⊢ |
| : , : , : |
110 | instantiation | 126, 154 | ⊢ |
| : |
111 | instantiation | 127, 128 | ⊢ |
| : , : , : |
112 | instantiation | 129, 219, 183, 130*, 131*, 138* | ⊢ |
| : , : , : , : |
113 | instantiation | 220, 209, 132 | ⊢ |
| : , : , : |
114 | theorem | | ⊢ |
| proveit.numbers.number_sets.real_numbers.real_pos_within_real |
115 | theorem | | ⊢ |
| proveit.numbers.division.weak_div_from_denom_bound__all_pos |
116 | instantiation | 220, 133, 134 | ⊢ |
| : , : , : |
117 | instantiation | 135, 167, 207, 214, 136, 137, 138* | ⊢ |
| : , : , : |
118 | instantiation | 148, 139, 140 | ⊢ |
| : , : , : |
119 | instantiation | 141, 154 | ⊢ |
| : |
120 | instantiation | 142, 143 | ⊢ |
| : |
121 | instantiation | 220, 216, 144 | ⊢ |
| : , : , : |
122 | axiom | | ⊢ |
| proveit.logic.equality.equals_reflexivity |
123 | theorem | | ⊢ |
| proveit.numbers.multiplication.mult_rational_closure_bin |
124 | theorem | | ⊢ |
| proveit.numbers.number_sets.rational_numbers.positive_if_in_rational_pos |
125 | instantiation | 145, 146 | ⊢ |
| : |
126 | theorem | | ⊢ |
| proveit.numbers.addition.elim_zero_left |
127 | axiom | | ⊢ |
| proveit.logic.equality.substitution |
128 | instantiation | 174, 146 | ⊢ |
| : |
129 | theorem | | ⊢ |
| proveit.numbers.addition.rational_pair_addition |
130 | instantiation | 147, 154 | ⊢ |
| : |
131 | instantiation | 148, 149, 150 | ⊢ |
| : , : , : |
132 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.posnat5 |
133 | theorem | | ⊢ |
| proveit.numbers.number_sets.real_numbers.rational_nonneg_within_real_nonneg |
134 | instantiation | 220, 151, 222 | ⊢ |
| : , : , : |
135 | theorem | | ⊢ |
| proveit.numbers.multiplication.weak_bound_via_right_factor_bound |
136 | instantiation | 152, 213, 214, 215 | ⊢ |
| : , : , : |
137 | instantiation | 153, 193 | ⊢ |
| : |
138 | instantiation | 174, 154 | ⊢ |
| : |
139 | instantiation | 162, 193, 155, 156, 166, 165 | ⊢ |
| : , : , : , : |
140 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.add_4_1 |
141 | theorem | | ⊢ |
| proveit.numbers.multiplication.elim_one_left |
142 | theorem | | ⊢ |
| proveit.numbers.negation.real_closure |
143 | instantiation | 157, 158, 159 | ⊢ |
| : , : , : |
144 | instantiation | 220, 218, 160 | ⊢ |
| : , : , : |
145 | theorem | | ⊢ |
| proveit.numbers.multiplication.mult_zero_right |
146 | instantiation | 220, 182, 161 | ⊢ |
| : , : , : |
147 | theorem | | ⊢ |
| proveit.numbers.division.frac_one_denom |
148 | axiom | | ⊢ |
| proveit.logic.equality.equals_transitivity |
149 | instantiation | 162, 193, 163, 164, 165, 166 | ⊢ |
| : , : , : , : |
150 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.add_1_4 |
151 | theorem | | ⊢ |
| proveit.numbers.number_sets.rational_numbers.nat_within_rational_nonneg |
152 | theorem | | ⊢ |
| proveit.numbers.number_sets.real_numbers.interval_oc_upper_bound |
153 | theorem | | ⊢ |
| proveit.numbers.number_sets.natural_numbers.natural_lower_bound |
154 | instantiation | 220, 182, 167 | ⊢ |
| : , : , : |
155 | instantiation | 173 | ⊢ |
| : , : |
156 | instantiation | 173 | ⊢ |
| : , : |
157 | theorem | | ⊢ |
| proveit.logic.sets.inclusion.unfold_subset_eq |
158 | instantiation | 168, 169 | ⊢ |
| : , : |
159 | axiom | | ⊢ |
| proveit.physics.quantum.QPE._n_in_natural_pos |
160 | instantiation | 170, 171 | ⊢ |
| : |
161 | instantiation | 220, 216, 172 | ⊢ |
| : , : , : |
162 | axiom | | ⊢ |
| proveit.core_expr_types.operations.operands_substitution |
163 | instantiation | 173 | ⊢ |
| : , : |
164 | instantiation | 173 | ⊢ |
| : , : |
165 | instantiation | 174, 175 | ⊢ |
| : |
166 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.mult_2_2 |
167 | instantiation | 220, 216, 176 | ⊢ |
| : , : , : |
168 | theorem | | ⊢ |
| proveit.logic.sets.inclusion.relax_proper_subset |
169 | theorem | | ⊢ |
| proveit.numbers.number_sets.real_numbers.nat_pos_within_real |
170 | axiom | | ⊢ |
| proveit.numbers.rounding.ceil_is_an_int |
171 | instantiation | 177, 202, 178, 179 | ⊢ |
| : , : |
172 | instantiation | 220, 180, 181 | ⊢ |
| : , : , : |
173 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.tuple_len_2_typical_eq |
174 | theorem | | ⊢ |
| proveit.numbers.multiplication.elim_one_right |
175 | instantiation | 220, 182, 214 | ⊢ |
| : , : , : |
176 | instantiation | 220, 218, 183 | ⊢ |
| : , : , : |
177 | theorem | | ⊢ |
| proveit.numbers.logarithms.log_real_pos_real_closure |
178 | instantiation | 184, 202, 185 | ⊢ |
| : , : |
179 | instantiation | 186, 187 | ⊢ |
| : , : |
180 | theorem | | ⊢ |
| proveit.numbers.number_sets.rational_numbers.rational_pos_within_rational |
181 | instantiation | 188, 195, 205 | ⊢ |
| : , : |
182 | theorem | | ⊢ |
| proveit.numbers.number_sets.complex_numbers.real_within_complex |
183 | instantiation | 220, 221, 193 | ⊢ |
| : , : , : |
184 | theorem | | ⊢ |
| proveit.numbers.addition.add_real_pos_closure_bin |
185 | instantiation | 189, 190, 200, 191 | ⊢ |
| : , : |
186 | theorem | | ⊢ |
| proveit.logic.equality.not_equals_symmetry |
187 | instantiation | 192, 222, 193, 194 | ⊢ |
| : , : |
188 | theorem | | ⊢ |
| proveit.numbers.division.div_rational_pos_closure |
189 | theorem | | ⊢ |
| proveit.numbers.division.div_real_pos_closure |
190 | instantiation | 220, 204, 195 | ⊢ |
| : , : , : |
191 | instantiation | 196, 197 | ⊢ |
| : |
192 | theorem | | ⊢ |
| proveit.numbers.ordering.less_is_not_eq_nat |
193 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.nat2 |
194 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.less_1_2 |
195 | instantiation | 220, 209, 198 | ⊢ |
| : , : , : |
196 | theorem | | ⊢ |
| proveit.numbers.number_sets.real_numbers.nonzero_if_in_real_nonzero |
197 | instantiation | 220, 199, 200 | ⊢ |
| : , : , : |
198 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.posnat1 |
199 | theorem | | ⊢ |
| proveit.numbers.number_sets.real_numbers.real_pos_within_real_nonzero |
200 | instantiation | 201, 202, 203 | ⊢ |
| : , : |
201 | theorem | | ⊢ |
| proveit.numbers.multiplication.mult_real_pos_closure_bin |
202 | instantiation | 220, 204, 205 | ⊢ |
| : , : , : |
203 | instantiation | 206, 207, 208 | ⊢ |
| : |
204 | theorem | | ⊢ |
| proveit.numbers.number_sets.real_numbers.rational_pos_within_real_pos |
205 | instantiation | 220, 209, 210 | ⊢ |
| : , : , : |
206 | theorem | | ⊢ |
| proveit.numbers.number_sets.real_numbers.pos_real_is_real_pos |
207 | instantiation | 211, 213, 214, 215 | ⊢ |
| : , : , : |
208 | instantiation | 212, 213, 214, 215 | ⊢ |
| : , : , : |
209 | theorem | | ⊢ |
| proveit.numbers.number_sets.rational_numbers.nat_pos_within_rational_pos |
210 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.posnat2 |
211 | theorem | | ⊢ |
| proveit.numbers.number_sets.real_numbers.all_in_interval_oc__is__real |
212 | theorem | | ⊢ |
| proveit.numbers.number_sets.real_numbers.interval_oc_lower_bound |
213 | theorem | | ⊢ |
| proveit.numbers.number_sets.real_numbers.zero_is_real |
214 | instantiation | 220, 216, 217 | ⊢ |
| : , : , : |
215 | axiom | | ⊢ |
| proveit.physics.quantum.QPE._eps_in_interval |
216 | theorem | | ⊢ |
| proveit.numbers.number_sets.real_numbers.rational_within_real |
217 | instantiation | 220, 218, 219 | ⊢ |
| : , : , : |
218 | theorem | | ⊢ |
| proveit.numbers.number_sets.rational_numbers.int_within_rational |
219 | instantiation | 220, 221, 222 | ⊢ |
| : , : , : |
220 | theorem | | ⊢ |
| proveit.logic.sets.inclusion.superset_membership_from_proper_subset |
221 | theorem | | ⊢ |
| proveit.numbers.number_sets.integers.nat_within_int |
222 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.nat1 |
*equality replacement requirements |