| step type | requirements | statement |
0 | instantiation | 1, 2, 3, 4, 5, 6, 7, 8, 9* | ⊢ |
| : , : , : , : , : , : |
1 | theorem | | ⊢ |
| proveit.numbers.multiplication.distribute_through_sum |
2 | reference | 98 | ⊢ |
3 | reference | 196 | ⊢ |
4 | reference | 225 | ⊢ |
5 | reference | 99 | ⊢ |
6 | instantiation | 176 | ⊢ |
| : , : |
7 | reference | 178 | ⊢ |
8 | reference | 10 | ⊢ |
9 | instantiation | 144, 10 | ⊢ |
| : |
10 | instantiation | 223, 185, 11 | ⊢ |
| : , : , : |
11 | instantiation | 12, 170, 13 | ⊢ |
| : , : |
12 | theorem | | ⊢ |
| proveit.numbers.exponentiation.exp_real_closure_nat_power |
13 | instantiation | 14, 15, 16 | ⊢ |
| : |
14 | theorem | | ⊢ |
| proveit.numbers.number_sets.integers.nonneg_int_is_natural |
15 | instantiation | 17, 18, 19 | ⊢ |
| : , : |
16 | instantiation | 20, 21 | ⊢ |
| : , : |
17 | theorem | | ⊢ |
| proveit.numbers.addition.add_int_closure_bin |
18 | instantiation | 223, 22, 106 | ⊢ |
| : , : , : |
19 | instantiation | 223, 23, 24 | ⊢ |
| : , : , : |
20 | theorem | | ⊢ |
| proveit.numbers.addition.subtraction.nonneg_difference |
21 | instantiation | 49, 25, 26 | ⊢ |
| : , : , : |
22 | theorem | | ⊢ |
| proveit.numbers.number_sets.integers.nat_pos_within_int |
23 | theorem | | ⊢ |
| proveit.numbers.number_sets.integers.neg_int_within_int |
24 | instantiation | 27, 213 | ⊢ |
| : |
25 | axiom | | ⊢ |
| proveit.physics.quantum.QPE._n_ge_two |
26 | instantiation | 64, 68, 170, 28, 29, 30*, 31* | ⊢ |
| : , : , : |
27 | theorem | | ⊢ |
| proveit.numbers.negation.int_neg_closure |
28 | instantiation | 83, 33, 170 | ⊢ |
| : , : |
29 | instantiation | 32, 170, 33, 34, 140 | ⊢ |
| : , : , : |
30 | instantiation | 151, 35, 36 | ⊢ |
| : , : , : |
31 | instantiation | 151, 37, 38 | ⊢ |
| : , : , : |
32 | theorem | | ⊢ |
| proveit.numbers.ordering.less_eq_add_right |
33 | instantiation | 83, 85, 123 | ⊢ |
| : , : |
34 | instantiation | 49, 39, 40 | ⊢ |
| : , : , : |
35 | instantiation | 97, 225, 196, 98, 55, 99, 157, 103, 56 | ⊢ |
| : , : , : , : , : , : |
36 | instantiation | 102, 157, 103, 73 | ⊢ |
| : , : , : |
37 | instantiation | 130, 41 | ⊢ |
| : , : , : |
38 | instantiation | 42, 43, 44, 45 | ⊢ |
| : , : , : , : |
39 | instantiation | 46, 222, 62, 47, 48* | ⊢ |
| : , : |
40 | instantiation | 49, 50, 51 | ⊢ |
| : , : , : |
41 | instantiation | 97, 98, 196, 225, 99, 72, 75, 101, 157 | ⊢ |
| : , : , : , : , : , : |
42 | theorem | | ⊢ |
| proveit.logic.equality.four_chain_transitivity |
43 | instantiation | 97, 98, 53, 225, 99, 54, 75, 101, 157, 52 | ⊢ |
| : , : , : , : , : , : |
44 | instantiation | 97, 53, 196, 98, 54, 55, 99, 75, 101, 157, 103, 56 | ⊢ |
| : , : , : , : , : , : |
45 | instantiation | 151, 57, 58 | ⊢ |
| : , : , : |
46 | theorem | | ⊢ |
| proveit.numbers.rounding.ceil_of_real_above_int |
47 | instantiation | 59, 205, 79, 60 | ⊢ |
| : , : |
48 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.add_1_1 |
49 | theorem | | ⊢ |
| proveit.numbers.ordering.transitivity_less_eq_less_eq |
50 | instantiation | 61, 62, 174, 63 | ⊢ |
| : , : |
51 | instantiation | 64, 123, 65, 85, 66, 67* | ⊢ |
| : , : , : |
52 | instantiation | 223, 185, 68 | ⊢ |
| : , : , : |
53 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.nat3 |
54 | instantiation | 69 | ⊢ |
| : , : , : |
55 | instantiation | 176 | ⊢ |
| : , : |
56 | instantiation | 70, 157 | ⊢ |
| : |
57 | instantiation | 71, 196, 225, 98, 72, 99, 75, 101, 157, 103, 73 | ⊢ |
| : , : , : , : , : , : , : , : |
58 | instantiation | 74, 103, 75, 105 | ⊢ |
| : , : , : |
59 | theorem | | ⊢ |
| proveit.numbers.logarithms.log_base_large_a_greater_one |
60 | instantiation | 76, 197, 77 | ⊢ |
| : , : |
61 | theorem | | ⊢ |
| proveit.numbers.rounding.ceil_increasing_less_eq |
62 | instantiation | 180, 205, 79, 182 | ⊢ |
| : , : |
63 | instantiation | 78, 205, 79, 181, 80, 197 | ⊢ |
| : , : , : |
64 | theorem | | ⊢ |
| proveit.numbers.addition.weak_bound_via_left_term_bound |
65 | instantiation | 83, 146, 124 | ⊢ |
| : , : |
66 | axiom | | ⊢ |
| proveit.physics.quantum.QPE._t_req |
67 | instantiation | 151, 81, 82 | ⊢ |
| : , : , : |
68 | instantiation | 83, 146, 84 | ⊢ |
| : , : |
69 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.tuple_len_3_typical_eq |
70 | theorem | | ⊢ |
| proveit.numbers.negation.complex_closure |
71 | theorem | | ⊢ |
| proveit.numbers.addition.subtraction.add_cancel_general |
72 | instantiation | 176 | ⊢ |
| : , : |
73 | instantiation | 125 | ⊢ |
| : |
74 | theorem | | ⊢ |
| proveit.numbers.addition.subtraction.add_cancel_triple_32 |
75 | instantiation | 223, 185, 85 | ⊢ |
| : , : , : |
76 | theorem | | ⊢ |
| proveit.logic.booleans.conjunction.and_if_both |
77 | instantiation | 86, 170, 87, 88, 89, 90*, 91* | ⊢ |
| : , : , : |
78 | theorem | | ⊢ |
| proveit.numbers.logarithms.log_increasing_less_eq |
79 | instantiation | 223, 207, 92 | ⊢ |
| : , : , : |
80 | instantiation | 93, 170, 164, 94, 95, 96* | ⊢ |
| : , : , : |
81 | instantiation | 97, 98, 196, 225, 99, 100, 103, 104, 101 | ⊢ |
| : , : , : , : , : , : |
82 | instantiation | 102, 103, 104, 105 | ⊢ |
| : , : , : |
83 | theorem | | ⊢ |
| proveit.numbers.addition.add_real_closure_bin |
84 | instantiation | 145, 170 | ⊢ |
| : |
85 | instantiation | 160, 161, 106 | ⊢ |
| : , : , : |
86 | theorem | | ⊢ |
| proveit.numbers.addition.strong_bound_via_left_term_bound |
87 | instantiation | 107, 164, 216 | ⊢ |
| : , : |
88 | instantiation | 223, 219, 108 | ⊢ |
| : , : , : |
89 | instantiation | 109, 164, 216, 217, 110, 111 | ⊢ |
| : , : , : |
90 | instantiation | 151, 112, 113 | ⊢ |
| : , : , : |
91 | instantiation | 151, 114, 115 | ⊢ |
| : , : , : |
92 | instantiation | 191, 116, 208 | ⊢ |
| : , : |
93 | theorem | | ⊢ |
| proveit.numbers.addition.weak_bound_via_right_term_bound |
94 | instantiation | 223, 117, 188 | ⊢ |
| : , : , : |
95 | instantiation | 118, 119, 203, 205, 120 | ⊢ |
| : , : , : |
96 | instantiation | 132, 186, 222, 133*, 121*, 122* | ⊢ |
| : , : , : , : |
97 | theorem | | ⊢ |
| proveit.numbers.addition.disassociation |
98 | axiom | | ⊢ |
| proveit.numbers.number_sets.natural_numbers.zero_in_nats |
99 | theorem | | ⊢ |
| proveit.core_expr_types.tuples.tuple_len_0_typical_eq |
100 | instantiation | 176 | ⊢ |
| : , : |
101 | instantiation | 223, 185, 123 | ⊢ |
| : , : , : |
102 | theorem | | ⊢ |
| proveit.numbers.addition.subtraction.add_cancel_triple_13 |
103 | instantiation | 223, 185, 146 | ⊢ |
| : , : , : |
104 | instantiation | 223, 185, 124 | ⊢ |
| : , : , : |
105 | instantiation | 125 | ⊢ |
| : |
106 | axiom | | ⊢ |
| proveit.physics.quantum.QPE._t_in_natural_pos |
107 | theorem | | ⊢ |
| proveit.numbers.multiplication.mult_real_closure_bin |
108 | instantiation | 126, 175, 220 | ⊢ |
| : , : |
109 | theorem | | ⊢ |
| proveit.numbers.multiplication.strong_bound_via_right_factor_bound |
110 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.less_0_1 |
111 | instantiation | 127, 184 | ⊢ |
| : |
112 | instantiation | 130, 128 | ⊢ |
| : , : , : |
113 | instantiation | 129, 157 | ⊢ |
| : |
114 | instantiation | 130, 131 | ⊢ |
| : , : , : |
115 | instantiation | 132, 222, 186, 133*, 134*, 141* | ⊢ |
| : , : , : , : |
116 | instantiation | 223, 212, 135 | ⊢ |
| : , : , : |
117 | theorem | | ⊢ |
| proveit.numbers.number_sets.real_numbers.real_pos_within_real |
118 | theorem | | ⊢ |
| proveit.numbers.division.weak_div_from_denom_bound__all_pos |
119 | instantiation | 223, 136, 137 | ⊢ |
| : , : , : |
120 | instantiation | 138, 170, 210, 217, 139, 140, 141* | ⊢ |
| : , : , : |
121 | instantiation | 151, 142, 143 | ⊢ |
| : , : , : |
122 | instantiation | 144, 157 | ⊢ |
| : |
123 | instantiation | 145, 146 | ⊢ |
| : |
124 | instantiation | 223, 219, 147 | ⊢ |
| : , : , : |
125 | axiom | | ⊢ |
| proveit.logic.equality.equals_reflexivity |
126 | theorem | | ⊢ |
| proveit.numbers.multiplication.mult_rational_closure_bin |
127 | theorem | | ⊢ |
| proveit.numbers.number_sets.rational_numbers.positive_if_in_rational_pos |
128 | instantiation | 148, 149 | ⊢ |
| : |
129 | theorem | | ⊢ |
| proveit.numbers.addition.elim_zero_left |
130 | axiom | | ⊢ |
| proveit.logic.equality.substitution |
131 | instantiation | 177, 149 | ⊢ |
| : |
132 | theorem | | ⊢ |
| proveit.numbers.addition.rational_pair_addition |
133 | instantiation | 150, 157 | ⊢ |
| : |
134 | instantiation | 151, 152, 153 | ⊢ |
| : , : , : |
135 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.posnat5 |
136 | theorem | | ⊢ |
| proveit.numbers.number_sets.real_numbers.rational_nonneg_within_real_nonneg |
137 | instantiation | 223, 154, 225 | ⊢ |
| : , : , : |
138 | theorem | | ⊢ |
| proveit.numbers.multiplication.weak_bound_via_right_factor_bound |
139 | instantiation | 155, 216, 217, 218 | ⊢ |
| : , : , : |
140 | instantiation | 156, 196 | ⊢ |
| : |
141 | instantiation | 177, 157 | ⊢ |
| : |
142 | instantiation | 165, 196, 158, 159, 169, 168 | ⊢ |
| : , : , : , : |
143 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.add_4_1 |
144 | theorem | | ⊢ |
| proveit.numbers.multiplication.elim_one_left |
145 | theorem | | ⊢ |
| proveit.numbers.negation.real_closure |
146 | instantiation | 160, 161, 162 | ⊢ |
| : , : , : |
147 | instantiation | 223, 221, 163 | ⊢ |
| : , : , : |
148 | theorem | | ⊢ |
| proveit.numbers.multiplication.mult_zero_right |
149 | instantiation | 223, 185, 164 | ⊢ |
| : , : , : |
150 | theorem | | ⊢ |
| proveit.numbers.division.frac_one_denom |
151 | axiom | | ⊢ |
| proveit.logic.equality.equals_transitivity |
152 | instantiation | 165, 196, 166, 167, 168, 169 | ⊢ |
| : , : , : , : |
153 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.add_1_4 |
154 | theorem | | ⊢ |
| proveit.numbers.number_sets.rational_numbers.nat_within_rational_nonneg |
155 | theorem | | ⊢ |
| proveit.numbers.number_sets.real_numbers.interval_oc_upper_bound |
156 | theorem | | ⊢ |
| proveit.numbers.number_sets.natural_numbers.natural_lower_bound |
157 | instantiation | 223, 185, 170 | ⊢ |
| : , : , : |
158 | instantiation | 176 | ⊢ |
| : , : |
159 | instantiation | 176 | ⊢ |
| : , : |
160 | theorem | | ⊢ |
| proveit.logic.sets.inclusion.unfold_subset_eq |
161 | instantiation | 171, 172 | ⊢ |
| : , : |
162 | axiom | | ⊢ |
| proveit.physics.quantum.QPE._n_in_natural_pos |
163 | instantiation | 173, 174 | ⊢ |
| : |
164 | instantiation | 223, 219, 175 | ⊢ |
| : , : , : |
165 | axiom | | ⊢ |
| proveit.core_expr_types.operations.operands_substitution |
166 | instantiation | 176 | ⊢ |
| : , : |
167 | instantiation | 176 | ⊢ |
| : , : |
168 | instantiation | 177, 178 | ⊢ |
| : |
169 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.mult_2_2 |
170 | instantiation | 223, 219, 179 | ⊢ |
| : , : , : |
171 | theorem | | ⊢ |
| proveit.logic.sets.inclusion.relax_proper_subset |
172 | theorem | | ⊢ |
| proveit.numbers.number_sets.real_numbers.nat_pos_within_real |
173 | axiom | | ⊢ |
| proveit.numbers.rounding.ceil_is_an_int |
174 | instantiation | 180, 205, 181, 182 | ⊢ |
| : , : |
175 | instantiation | 223, 183, 184 | ⊢ |
| : , : , : |
176 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.tuple_len_2_typical_eq |
177 | theorem | | ⊢ |
| proveit.numbers.multiplication.elim_one_right |
178 | instantiation | 223, 185, 217 | ⊢ |
| : , : , : |
179 | instantiation | 223, 221, 186 | ⊢ |
| : , : , : |
180 | theorem | | ⊢ |
| proveit.numbers.logarithms.log_real_pos_real_closure |
181 | instantiation | 187, 205, 188 | ⊢ |
| : , : |
182 | instantiation | 189, 190 | ⊢ |
| : , : |
183 | theorem | | ⊢ |
| proveit.numbers.number_sets.rational_numbers.rational_pos_within_rational |
184 | instantiation | 191, 198, 208 | ⊢ |
| : , : |
185 | theorem | | ⊢ |
| proveit.numbers.number_sets.complex_numbers.real_within_complex |
186 | instantiation | 223, 224, 196 | ⊢ |
| : , : , : |
187 | theorem | | ⊢ |
| proveit.numbers.addition.add_real_pos_closure_bin |
188 | instantiation | 192, 193, 203, 194 | ⊢ |
| : , : |
189 | theorem | | ⊢ |
| proveit.logic.equality.not_equals_symmetry |
190 | instantiation | 195, 225, 196, 197 | ⊢ |
| : , : |
191 | theorem | | ⊢ |
| proveit.numbers.division.div_rational_pos_closure |
192 | theorem | | ⊢ |
| proveit.numbers.division.div_real_pos_closure |
193 | instantiation | 223, 207, 198 | ⊢ |
| : , : , : |
194 | instantiation | 199, 200 | ⊢ |
| : |
195 | theorem | | ⊢ |
| proveit.numbers.ordering.less_is_not_eq_nat |
196 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.nat2 |
197 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.less_1_2 |
198 | instantiation | 223, 212, 201 | ⊢ |
| : , : , : |
199 | theorem | | ⊢ |
| proveit.numbers.number_sets.real_numbers.nonzero_if_in_real_nonzero |
200 | instantiation | 223, 202, 203 | ⊢ |
| : , : , : |
201 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.posnat1 |
202 | theorem | | ⊢ |
| proveit.numbers.number_sets.real_numbers.real_pos_within_real_nonzero |
203 | instantiation | 204, 205, 206 | ⊢ |
| : , : |
204 | theorem | | ⊢ |
| proveit.numbers.multiplication.mult_real_pos_closure_bin |
205 | instantiation | 223, 207, 208 | ⊢ |
| : , : , : |
206 | instantiation | 209, 210, 211 | ⊢ |
| : |
207 | theorem | | ⊢ |
| proveit.numbers.number_sets.real_numbers.rational_pos_within_real_pos |
208 | instantiation | 223, 212, 213 | ⊢ |
| : , : , : |
209 | theorem | | ⊢ |
| proveit.numbers.number_sets.real_numbers.pos_real_is_real_pos |
210 | instantiation | 214, 216, 217, 218 | ⊢ |
| : , : , : |
211 | instantiation | 215, 216, 217, 218 | ⊢ |
| : , : , : |
212 | theorem | | ⊢ |
| proveit.numbers.number_sets.rational_numbers.nat_pos_within_rational_pos |
213 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.posnat2 |
214 | theorem | | ⊢ |
| proveit.numbers.number_sets.real_numbers.all_in_interval_oc__is__real |
215 | theorem | | ⊢ |
| proveit.numbers.number_sets.real_numbers.interval_oc_lower_bound |
216 | theorem | | ⊢ |
| proveit.numbers.number_sets.real_numbers.zero_is_real |
217 | instantiation | 223, 219, 220 | ⊢ |
| : , : , : |
218 | axiom | | ⊢ |
| proveit.physics.quantum.QPE._eps_in_interval |
219 | theorem | | ⊢ |
| proveit.numbers.number_sets.real_numbers.rational_within_real |
220 | instantiation | 223, 221, 222 | ⊢ |
| : , : , : |
221 | theorem | | ⊢ |
| proveit.numbers.number_sets.rational_numbers.int_within_rational |
222 | instantiation | 223, 224, 225 | ⊢ |
| : , : , : |
223 | theorem | | ⊢ |
| proveit.logic.sets.inclusion.superset_membership_from_proper_subset |
224 | theorem | | ⊢ |
| proveit.numbers.number_sets.integers.nat_within_int |
225 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.nat1 |
*equality replacement requirements |