| step type | requirements | statement |
0 | instantiation | 1, 2, 3 | ⊢ |
| : , : |
1 | reference | 79 | ⊢ |
2 | instantiation | 4, 165, 5 | ⊢ |
| : , : |
3 | reference | 211 | ⊢ |
4 | theorem | | ⊢ |
| proveit.numbers.exponentiation.exp_real_closure_nat_power |
5 | instantiation | 6, 7, 8 | ⊢ |
| : |
6 | theorem | | ⊢ |
| proveit.numbers.number_sets.integers.nonneg_int_is_natural |
7 | instantiation | 9, 10, 11 | ⊢ |
| : , : |
8 | instantiation | 12, 13 | ⊢ |
| : , : |
9 | theorem | | ⊢ |
| proveit.numbers.addition.add_int_closure_bin |
10 | instantiation | 217, 14, 106 | ⊢ |
| : , : , : |
11 | instantiation | 217, 15, 16 | ⊢ |
| : , : , : |
12 | theorem | | ⊢ |
| proveit.numbers.addition.subtraction.nonneg_difference |
13 | instantiation | 55, 59, 165, 17, 18, 19*, 20* | ⊢ |
| : , : , : |
14 | theorem | | ⊢ |
| proveit.numbers.number_sets.integers.nat_pos_within_int |
15 | theorem | | ⊢ |
| proveit.numbers.number_sets.integers.neg_int_within_int |
16 | instantiation | 21, 162 | ⊢ |
| : |
17 | instantiation | 79, 23, 165 | ⊢ |
| : , : |
18 | instantiation | 22, 165, 23, 24, 138 | ⊢ |
| : , : , : |
19 | instantiation | 141, 25, 26 | ⊢ |
| : , : , : |
20 | instantiation | 141, 27, 28 | ⊢ |
| : , : , : |
21 | theorem | | ⊢ |
| proveit.numbers.negation.int_neg_closure |
22 | theorem | | ⊢ |
| proveit.numbers.ordering.less_eq_add_right |
23 | instantiation | 79, 81, 125 | ⊢ |
| : , : |
24 | instantiation | 39, 29, 30 | ⊢ |
| : , : , : |
25 | instantiation | 97, 219, 190, 98, 45, 99, 154, 103, 46 | ⊢ |
| : , : , : , : , : , : |
26 | instantiation | 102, 154, 103, 64 | ⊢ |
| : , : , : |
27 | instantiation | 111, 31 | ⊢ |
| : , : , : |
28 | instantiation | 32, 33, 34, 35 | ⊢ |
| : , : , : , : |
29 | instantiation | 36, 216, 53, 37, 38* | ⊢ |
| : , : |
30 | instantiation | 39, 40, 41 | ⊢ |
| : , : , : |
31 | instantiation | 97, 98, 190, 219, 99, 63, 66, 101, 154 | ⊢ |
| : , : , : , : , : , : |
32 | theorem | | ⊢ |
| proveit.logic.equality.four_chain_transitivity |
33 | instantiation | 97, 98, 43, 219, 99, 44, 66, 101, 154, 42 | ⊢ |
| : , : , : , : , : , : |
34 | instantiation | 97, 43, 190, 98, 44, 45, 99, 66, 101, 154, 103, 46 | ⊢ |
| : , : , : , : , : , : |
35 | instantiation | 141, 47, 48 | ⊢ |
| : , : , : |
36 | theorem | | ⊢ |
| proveit.numbers.rounding.ceil_of_real_above_int |
37 | instantiation | 49, 199, 75, 50, 191, 51* | ⊢ |
| : , : , : |
38 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.add_1_1 |
39 | theorem | | ⊢ |
| proveit.numbers.ordering.transitivity_less_eq_less_eq |
40 | instantiation | 52, 53, 172, 54 | ⊢ |
| : , : |
41 | instantiation | 55, 125, 56, 81, 57, 58* | ⊢ |
| : , : , : |
42 | instantiation | 217, 176, 59 | ⊢ |
| : , : , : |
43 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.nat3 |
44 | instantiation | 60 | ⊢ |
| : , : , : |
45 | instantiation | 166 | ⊢ |
| : , : |
46 | instantiation | 61, 154 | ⊢ |
| : |
47 | instantiation | 62, 190, 219, 98, 63, 99, 66, 101, 154, 103, 64 | ⊢ |
| : , : , : , : , : , : , : , : |
48 | instantiation | 65, 103, 66, 105 | ⊢ |
| : , : , : |
49 | theorem | | ⊢ |
| proveit.numbers.logarithms.log_increasing_less |
50 | instantiation | 67, 165, 68, 69, 70, 71*, 72* | ⊢ |
| : , : , : |
51 | instantiation | 73, 199 | ⊢ |
| : |
52 | theorem | | ⊢ |
| proveit.numbers.rounding.ceil_increasing_less_eq |
53 | instantiation | 177, 199, 75, 179 | ⊢ |
| : , : |
54 | instantiation | 74, 199, 75, 178, 76, 191 | ⊢ |
| : , : , : |
55 | theorem | | ⊢ |
| proveit.numbers.addition.weak_bound_via_left_term_bound |
56 | instantiation | 79, 146, 126 | ⊢ |
| : , : |
57 | axiom | | ⊢ |
| proveit.physics.quantum.QPE._t_req |
58 | instantiation | 141, 77, 78 | ⊢ |
| : , : , : |
59 | instantiation | 79, 146, 80 | ⊢ |
| : , : |
60 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.tuple_len_3_typical_eq |
61 | theorem | | ⊢ |
| proveit.numbers.negation.complex_closure |
62 | theorem | | ⊢ |
| proveit.numbers.addition.subtraction.add_cancel_general |
63 | instantiation | 166 | ⊢ |
| : , : |
64 | instantiation | 127 | ⊢ |
| : |
65 | theorem | | ⊢ |
| proveit.numbers.addition.subtraction.add_cancel_triple_32 |
66 | instantiation | 217, 176, 81 | ⊢ |
| : , : , : |
67 | theorem | | ⊢ |
| proveit.numbers.addition.strong_bound_via_left_term_bound |
68 | instantiation | 82, 148, 210 | ⊢ |
| : , : |
69 | instantiation | 217, 213, 83 | ⊢ |
| : , : , : |
70 | instantiation | 84, 148, 210, 211, 85, 86 | ⊢ |
| : , : , : |
71 | instantiation | 141, 87, 88 | ⊢ |
| : , : , : |
72 | instantiation | 141, 89, 90 | ⊢ |
| : , : , : |
73 | theorem | | ⊢ |
| proveit.numbers.logarithms.log_eq_1 |
74 | theorem | | ⊢ |
| proveit.numbers.logarithms.log_increasing_less_eq |
75 | instantiation | 186, 91, 199, 116 | ⊢ |
| : , : |
76 | instantiation | 92, 165, 93, 94, 95, 96* | ⊢ |
| : , : , : |
77 | instantiation | 97, 98, 190, 219, 99, 100, 103, 104, 101 | ⊢ |
| : , : , : , : , : , : |
78 | instantiation | 102, 103, 104, 105 | ⊢ |
| : , : , : |
79 | theorem | | ⊢ |
| proveit.numbers.addition.add_real_closure_bin |
80 | instantiation | 145, 165 | ⊢ |
| : |
81 | instantiation | 160, 161, 106 | ⊢ |
| : , : , : |
82 | theorem | | ⊢ |
| proveit.numbers.multiplication.mult_real_closure_bin |
83 | instantiation | 107, 164, 214 | ⊢ |
| : , : |
84 | theorem | | ⊢ |
| proveit.numbers.multiplication.strong_bound_via_right_factor_bound |
85 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.less_0_1 |
86 | instantiation | 108, 174 | ⊢ |
| : |
87 | instantiation | 111, 109 | ⊢ |
| : , : , : |
88 | instantiation | 110, 154 | ⊢ |
| : |
89 | instantiation | 111, 112 | ⊢ |
| : , : , : |
90 | instantiation | 121, 216, 181, 122*, 113*, 139* | ⊢ |
| : , : , : , : |
91 | instantiation | 217, 201, 114 | ⊢ |
| : , : , : |
92 | theorem | | ⊢ |
| proveit.numbers.addition.weak_bound_via_right_term_bound |
93 | instantiation | 115, 211, 165, 116 | ⊢ |
| : , : |
94 | instantiation | 217, 117, 183 | ⊢ |
| : , : , : |
95 | instantiation | 118, 119, 197, 199, 120 | ⊢ |
| : , : , : |
96 | instantiation | 121, 181, 216, 122*, 123*, 124* | ⊢ |
| : , : , : , : |
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 | 166 | ⊢ |
| : , : |
101 | instantiation | 217, 176, 125 | ⊢ |
| : , : , : |
102 | theorem | | ⊢ |
| proveit.numbers.addition.subtraction.add_cancel_triple_13 |
103 | instantiation | 217, 176, 146 | ⊢ |
| : , : , : |
104 | instantiation | 217, 176, 126 | ⊢ |
| : , : , : |
105 | instantiation | 127 | ⊢ |
| : |
106 | axiom | | ⊢ |
| proveit.physics.quantum.QPE._t_in_natural_pos |
107 | theorem | | ⊢ |
| proveit.numbers.multiplication.mult_rational_closure_bin |
108 | theorem | | ⊢ |
| proveit.numbers.number_sets.rational_numbers.positive_if_in_rational_pos |
109 | instantiation | 128, 129 | ⊢ |
| : |
110 | theorem | | ⊢ |
| proveit.numbers.addition.elim_zero_left |
111 | axiom | | ⊢ |
| proveit.logic.equality.substitution |
112 | instantiation | 167, 129 | ⊢ |
| : |
113 | instantiation | 141, 130, 131 | ⊢ |
| : , : , : |
114 | instantiation | 217, 206, 132 | ⊢ |
| : , : , : |
115 | theorem | | ⊢ |
| proveit.numbers.division.div_real_closure |
116 | instantiation | 133, 207 | ⊢ |
| : |
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 | 217, 134, 135 | ⊢ |
| : , : , : |
120 | instantiation | 136, 165, 204, 211, 137, 138, 139* | ⊢ |
| : , : , : |
121 | theorem | | ⊢ |
| proveit.numbers.addition.rational_pair_addition |
122 | instantiation | 140, 154 | ⊢ |
| : |
123 | instantiation | 141, 142, 143 | ⊢ |
| : , : , : |
124 | instantiation | 144, 154 | ⊢ |
| : |
125 | instantiation | 145, 146 | ⊢ |
| : |
126 | instantiation | 217, 213, 147 | ⊢ |
| : , : , : |
127 | axiom | | ⊢ |
| proveit.logic.equality.equals_reflexivity |
128 | theorem | | ⊢ |
| proveit.numbers.multiplication.mult_zero_right |
129 | instantiation | 217, 176, 148 | ⊢ |
| : , : , : |
130 | instantiation | 155, 190, 149, 150, 159, 158 | ⊢ |
| : , : , : , : |
131 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.add_1_4 |
132 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.posnat5 |
133 | theorem | | ⊢ |
| proveit.numbers.number_sets.natural_numbers.nonzero_if_is_nat_pos |
134 | theorem | | ⊢ |
| proveit.numbers.number_sets.real_numbers.rational_nonneg_within_real_nonneg |
135 | instantiation | 217, 151, 219 | ⊢ |
| : , : , : |
136 | theorem | | ⊢ |
| proveit.numbers.multiplication.weak_bound_via_right_factor_bound |
137 | instantiation | 152, 210, 211, 212 | ⊢ |
| : , : , : |
138 | instantiation | 153, 190 | ⊢ |
| : |
139 | instantiation | 167, 154 | ⊢ |
| : |
140 | theorem | | ⊢ |
| proveit.numbers.division.frac_one_denom |
141 | axiom | | ⊢ |
| proveit.logic.equality.equals_transitivity |
142 | instantiation | 155, 190, 156, 157, 158, 159 | ⊢ |
| : , : , : , : |
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 | 217, 215, 163 | ⊢ |
| : , : , : |
148 | instantiation | 217, 213, 164 | ⊢ |
| : , : , : |
149 | instantiation | 166 | ⊢ |
| : , : |
150 | instantiation | 166 | ⊢ |
| : , : |
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 | 217, 176, 165 | ⊢ |
| : , : , : |
155 | axiom | | ⊢ |
| proveit.core_expr_types.operations.operands_substitution |
156 | instantiation | 166 | ⊢ |
| : , : |
157 | instantiation | 166 | ⊢ |
| : , : |
158 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.mult_2_2 |
159 | instantiation | 167, 168 | ⊢ |
| : |
160 | theorem | | ⊢ |
| proveit.logic.sets.inclusion.unfold_subset_eq |
161 | instantiation | 169, 170 | ⊢ |
| : , : |
162 | axiom | | ⊢ |
| proveit.physics.quantum.QPE._n_in_natural_pos |
163 | instantiation | 171, 172 | ⊢ |
| : |
164 | instantiation | 217, 173, 174 | ⊢ |
| : , : , : |
165 | instantiation | 217, 213, 175 | ⊢ |
| : , : , : |
166 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.tuple_len_2_typical_eq |
167 | theorem | | ⊢ |
| proveit.numbers.multiplication.elim_one_right |
168 | instantiation | 217, 176, 211 | ⊢ |
| : , : , : |
169 | theorem | | ⊢ |
| proveit.logic.sets.inclusion.relax_proper_subset |
170 | theorem | | ⊢ |
| proveit.numbers.number_sets.real_numbers.nat_pos_within_real |
171 | axiom | | ⊢ |
| proveit.numbers.rounding.ceil_is_an_int |
172 | instantiation | 177, 199, 178, 179 | ⊢ |
| : , : |
173 | theorem | | ⊢ |
| proveit.numbers.number_sets.rational_numbers.rational_pos_within_rational |
174 | instantiation | 180, 192, 202 | ⊢ |
| : , : |
175 | instantiation | 217, 215, 181 | ⊢ |
| : , : , : |
176 | theorem | | ⊢ |
| proveit.numbers.number_sets.complex_numbers.real_within_complex |
177 | theorem | | ⊢ |
| proveit.numbers.logarithms.log_real_pos_real_closure |
178 | instantiation | 182, 199, 183 | ⊢ |
| : , : |
179 | instantiation | 184, 185 | ⊢ |
| : , : |
180 | theorem | | ⊢ |
| proveit.numbers.division.div_rational_pos_closure |
181 | instantiation | 217, 218, 190 | ⊢ |
| : , : , : |
182 | theorem | | ⊢ |
| proveit.numbers.addition.add_real_pos_closure_bin |
183 | instantiation | 186, 187, 197, 188 | ⊢ |
| : , : |
184 | theorem | | ⊢ |
| proveit.logic.equality.not_equals_symmetry |
185 | instantiation | 189, 219, 190, 191 | ⊢ |
| : , : |
186 | theorem | | ⊢ |
| proveit.numbers.division.div_real_pos_closure |
187 | instantiation | 217, 201, 192 | ⊢ |
| : , : , : |
188 | instantiation | 193, 194 | ⊢ |
| : |
189 | theorem | | ⊢ |
| proveit.numbers.ordering.less_is_not_eq_nat |
190 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.nat2 |
191 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.less_1_2 |
192 | instantiation | 217, 206, 195 | ⊢ |
| : , : , : |
193 | theorem | | ⊢ |
| proveit.numbers.number_sets.real_numbers.nonzero_if_in_real_nonzero |
194 | instantiation | 217, 196, 197 | ⊢ |
| : , : , : |
195 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.posnat1 |
196 | theorem | | ⊢ |
| proveit.numbers.number_sets.real_numbers.real_pos_within_real_nonzero |
197 | instantiation | 198, 199, 200 | ⊢ |
| : , : |
198 | theorem | | ⊢ |
| proveit.numbers.multiplication.mult_real_pos_closure_bin |
199 | instantiation | 217, 201, 202 | ⊢ |
| : , : , : |
200 | instantiation | 203, 204, 205 | ⊢ |
| : |
201 | theorem | | ⊢ |
| proveit.numbers.number_sets.real_numbers.rational_pos_within_real_pos |
202 | instantiation | 217, 206, 207 | ⊢ |
| : , : , : |
203 | theorem | | ⊢ |
| proveit.numbers.number_sets.real_numbers.pos_real_is_real_pos |
204 | instantiation | 208, 210, 211, 212 | ⊢ |
| : , : , : |
205 | instantiation | 209, 210, 211, 212 | ⊢ |
| : , : , : |
206 | theorem | | ⊢ |
| proveit.numbers.number_sets.rational_numbers.nat_pos_within_rational_pos |
207 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.posnat2 |
208 | theorem | | ⊢ |
| proveit.numbers.number_sets.real_numbers.all_in_interval_oc__is__real |
209 | theorem | | ⊢ |
| proveit.numbers.number_sets.real_numbers.interval_oc_lower_bound |
210 | theorem | | ⊢ |
| proveit.numbers.number_sets.real_numbers.zero_is_real |
211 | instantiation | 217, 213, 214 | ⊢ |
| : , : , : |
212 | axiom | | ⊢ |
| proveit.physics.quantum.QPE._eps_in_interval |
213 | theorem | | ⊢ |
| proveit.numbers.number_sets.real_numbers.rational_within_real |
214 | instantiation | 217, 215, 216 | ⊢ |
| : , : , : |
215 | theorem | | ⊢ |
| proveit.numbers.number_sets.rational_numbers.int_within_rational |
216 | instantiation | 217, 218, 219 | ⊢ |
| : , : , : |
217 | theorem | | ⊢ |
| proveit.logic.sets.inclusion.superset_membership_from_proper_subset |
218 | theorem | | ⊢ |
| proveit.numbers.number_sets.integers.nat_within_int |
219 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.nat1 |
*equality replacement requirements |