| step type | requirements | statement |
0 | instantiation | 1, 2, 3, 4, 5 | , ⊢ |
| : , : , : |
1 | theorem | | ⊢ |
| proveit.numbers.number_sets.real_numbers.in_IntervalOO |
2 | instantiation | 139, 6, 197 | ⊢ |
| : , : |
3 | instantiation | 210, 211, 47 | ⊢ |
| : , : , : |
4 | instantiation | 139, 54, 57 | , ⊢ |
| : , : |
5 | instantiation | 7, 8, 9 | , ⊢ |
| : , : |
6 | theorem | | ⊢ |
| proveit.numbers.number_sets.real_numbers.zero_is_real |
7 | theorem | | ⊢ |
| proveit.logic.booleans.conjunction.and_if_both |
8 | instantiation | 12, 10, 11 | , ⊢ |
| : , : , : |
9 | instantiation | 12, 13, 14 | , ⊢ |
| : , : , : |
10 | instantiation | 17, 15, 16 | , ⊢ |
| : , : , : |
11 | instantiation | 20, 186 | ⊢ |
| : |
12 | theorem | | ⊢ |
| proveit.logic.equality.sub_left_side_into |
13 | instantiation | 17, 18, 19 | , ⊢ |
| : , : , : |
14 | instantiation | 20, 151 | ⊢ |
| : |
15 | instantiation | 56, 102, 21, 57, 22, 23* | ⊢ |
| : , : , : |
16 | instantiation | 24, 57, 102, 54, 25 | , ⊢ |
| : , : , : |
17 | theorem | | ⊢ |
| proveit.numbers.ordering.transitivity_less_eq_less |
18 | instantiation | 26, 27, 28, 29* | , ⊢ |
| : , : , : |
19 | instantiation | 30, 180, 222, 31, 181, 32, 206 | ⊢ |
| : , : , : , : , : |
20 | theorem | | ⊢ |
| proveit.numbers.addition.elim_zero_left |
21 | instantiation | 205, 51 | ⊢ |
| : |
22 | instantiation | 75, 77, 51, 33 | ⊢ |
| : , : |
23 | instantiation | 34, 104, 35, 151, 36 | ⊢ |
| : , : , : |
24 | theorem | | ⊢ |
| proveit.numbers.addition.strong_bound_via_left_term_bound |
25 | instantiation | 37, 102, 117, 74 | ⊢ |
| : , : , : |
26 | theorem | | ⊢ |
| proveit.logic.equality.sub_right_side_into |
27 | instantiation | 38, 39, 40 | , ⊢ |
| : , : , : |
28 | instantiation | 41, 208, 42, 43, 151, 93, 128, 44* | ⊢ |
| : , : , : |
29 | instantiation | 167, 45, 46 | ⊢ |
| : , : , : |
30 | theorem | | ⊢ |
| proveit.numbers.addition.term_as_strong_upper_bound |
31 | instantiation | 116, 47 | ⊢ |
| : |
32 | instantiation | 48, 49 | ⊢ |
| : |
33 | instantiation | 97, 127, 99, 110, 50, 101 | ⊢ |
| : , : , : |
34 | theorem | | ⊢ |
| proveit.numbers.addition.subtraction.negated_add |
35 | instantiation | 220, 196, 51 | ⊢ |
| : , : , : |
36 | instantiation | 167, 52, 87 | ⊢ |
| : , : , : |
37 | theorem | | ⊢ |
| proveit.numbers.number_sets.real_numbers.interval_oc_lower_bound |
38 | theorem | | ⊢ |
| proveit.numbers.ordering.transitivity_less_eq_less_eq |
39 | instantiation | 53, 57, 54, 117, 55 | , ⊢ |
| : , : , : |
40 | instantiation | 56, 117, 57, 58, 59 | ⊢ |
| : , : , : |
41 | theorem | | ⊢ |
| proveit.numbers.division.distribute_frac_through_sum |
42 | instantiation | 194 | ⊢ |
| : , : |
43 | instantiation | 220, 196, 60 | ⊢ |
| : , : , : |
44 | instantiation | 61, 92, 93, 128, 71* | ⊢ |
| : , : |
45 | instantiation | 153, 62 | ⊢ |
| : , : , : |
46 | instantiation | 167, 63, 64 | ⊢ |
| : , : , : |
47 | instantiation | 65, 222, 180, 181, 66 | ⊢ |
| : , : , : , : , : |
48 | theorem | | ⊢ |
| proveit.numbers.negation.real_neg_closure |
49 | instantiation | 67, 68, 69, 128 | ⊢ |
| : , : |
50 | instantiation | 70, 160, 191, 143 | ⊢ |
| : , : , : |
51 | instantiation | 126, 110, 127, 128 | ⊢ |
| : , : |
52 | instantiation | 153, 71 | ⊢ |
| : , : , : |
53 | theorem | | ⊢ |
| proveit.numbers.addition.weak_bound_via_left_term_bound |
54 | instantiation | 72, 102, 117, 74 | ⊢ |
| : , : , : |
55 | instantiation | 73, 102, 117, 74 | ⊢ |
| : , : , : |
56 | theorem | | ⊢ |
| proveit.numbers.addition.weak_bound_via_right_term_bound |
57 | instantiation | 205, 77 | ⊢ |
| : |
58 | instantiation | 205, 76 | ⊢ |
| : |
59 | instantiation | 75, 76, 77, 78 | ⊢ |
| : , : |
60 | instantiation | 220, 213, 79 | ⊢ |
| : , : , : |
61 | theorem | | ⊢ |
| proveit.numbers.division.neg_frac_neg_numerator |
62 | instantiation | 80, 81, 106, 82* | ⊢ |
| : , : |
63 | instantiation | 179, 222, 215, 180, 83, 181, 104, 86 | ⊢ |
| : , : , : , : , : , : |
64 | instantiation | 84, 180, 215, 222, 181, 85, 104, 86, 87* | ⊢ |
| : , : , : , : , : , : |
65 | theorem | | ⊢ |
| proveit.numbers.addition.add_nat_pos_from_nonneg |
66 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.less_0_1 |
67 | theorem | | ⊢ |
| proveit.numbers.division.div_real_pos_closure |
68 | instantiation | 220, 89, 88 | ⊢ |
| : , : , : |
69 | instantiation | 220, 89, 90 | ⊢ |
| : , : , : |
70 | theorem | | ⊢ |
| proveit.numbers.number_sets.integers.interval_upper_bound |
71 | instantiation | 91, 92, 93, 128, 94* | ⊢ |
| : , : |
72 | theorem | | ⊢ |
| proveit.numbers.number_sets.real_numbers.all_in_interval_oc__is__real |
73 | theorem | | ⊢ |
| proveit.numbers.number_sets.real_numbers.interval_oc_upper_bound |
74 | instantiation | 95, 96 | ⊢ |
| : |
75 | theorem | | ⊢ |
| proveit.numbers.negation.negated_weak_bound |
76 | instantiation | 126, 98, 127, 128 | ⊢ |
| : , : |
77 | instantiation | 126, 99, 127, 128 | ⊢ |
| : , : |
78 | instantiation | 97, 127, 98, 99, 100, 101 | ⊢ |
| : , : , : |
79 | instantiation | 220, 218, 174 | ⊢ |
| : , : , : |
80 | theorem | | ⊢ |
| proveit.numbers.negation.distribute_neg_through_binary_sum |
81 | instantiation | 220, 196, 102 | ⊢ |
| : , : , : |
82 | instantiation | 103, 104 | ⊢ |
| : |
83 | instantiation | 194 | ⊢ |
| : , : |
84 | theorem | | ⊢ |
| proveit.numbers.addition.association |
85 | instantiation | 194 | ⊢ |
| : , : |
86 | instantiation | 105, 106 | ⊢ |
| : |
87 | instantiation | 107, 219, 209, 108* | ⊢ |
| : , : , : , : |
88 | instantiation | 220, 109, 157 | ⊢ |
| : , : , : |
89 | theorem | | ⊢ |
| proveit.numbers.number_sets.real_numbers.rational_pos_within_real_pos |
90 | instantiation | 220, 109, 144 | ⊢ |
| : , : , : |
91 | theorem | | ⊢ |
| proveit.numbers.division.div_as_mult |
92 | instantiation | 220, 196, 110 | ⊢ |
| : , : , : |
93 | instantiation | 220, 196, 127 | ⊢ |
| : , : , : |
94 | instantiation | 167, 111, 112 | ⊢ |
| : , : , : |
95 | theorem | | ⊢ |
| proveit.physics.quantum.QPE._delta_b_in_interval |
96 | assumption | | ⊢ |
97 | theorem | | ⊢ |
| proveit.numbers.division.weak_div_from_numer_bound__pos_denom |
98 | instantiation | 220, 213, 113 | ⊢ |
| : , : , : |
99 | instantiation | 220, 213, 114 | ⊢ |
| : , : , : |
100 | instantiation | 115, 160, 191, 143 | ⊢ |
| : , : , : |
101 | instantiation | 116, 144 | ⊢ |
| : |
102 | instantiation | 205, 117 | ⊢ |
| : |
103 | theorem | | ⊢ |
| proveit.numbers.negation.double_negation |
104 | instantiation | 220, 196, 117 | ⊢ |
| : , : , : |
105 | theorem | | ⊢ |
| proveit.numbers.negation.complex_closure |
106 | instantiation | 220, 196, 118 | ⊢ |
| : , : , : |
107 | theorem | | ⊢ |
| proveit.numbers.addition.rational_pair_addition |
108 | instantiation | 167, 119, 120 | ⊢ |
| : , : , : |
109 | theorem | | ⊢ |
| proveit.numbers.number_sets.rational_numbers.nat_pos_within_rational_pos |
110 | instantiation | 210, 211, 202 | ⊢ |
| : , : , : |
111 | instantiation | 153, 121 | ⊢ |
| : , : , : |
112 | instantiation | 122, 177, 123, 195, 137, 124* | ⊢ |
| : , : , : |
113 | instantiation | 220, 218, 160 | ⊢ |
| : , : , : |
114 | instantiation | 220, 218, 125 | ⊢ |
| : , : , : |
115 | theorem | | ⊢ |
| proveit.numbers.number_sets.integers.interval_lower_bound |
116 | theorem | | ⊢ |
| proveit.numbers.number_sets.natural_numbers.natural_pos_is_pos |
117 | instantiation | 126, 206, 192, 137 | ⊢ |
| : , : |
118 | instantiation | 126, 206, 127, 128 | ⊢ |
| : , : |
119 | instantiation | 161, 215, 129, 130, 131, 132 | ⊢ |
| : , : , : , : |
120 | instantiation | 133, 134, 135 | ⊢ |
| : |
121 | instantiation | 136, 177, 204, 197, 137, 138* | ⊢ |
| : , : , : |
122 | theorem | | ⊢ |
| proveit.numbers.exponentiation.product_of_real_powers |
123 | instantiation | 139, 204, 197 | ⊢ |
| : , : |
124 | instantiation | 167, 140, 141 | ⊢ |
| : , : , : |
125 | instantiation | 220, 142, 143 | ⊢ |
| : , : , : |
126 | theorem | | ⊢ |
| proveit.numbers.division.div_real_closure |
127 | instantiation | 210, 211, 144 | ⊢ |
| : , : , : |
128 | instantiation | 149, 144 | ⊢ |
| : |
129 | instantiation | 194 | ⊢ |
| : , : |
130 | instantiation | 194 | ⊢ |
| : , : |
131 | instantiation | 167, 145, 146 | ⊢ |
| : , : , : |
132 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.mult_2_2 |
133 | theorem | | ⊢ |
| proveit.numbers.division.frac_cancel_complete |
134 | instantiation | 220, 196, 147 | ⊢ |
| : , : , : |
135 | instantiation | 149, 148 | ⊢ |
| : |
136 | theorem | | ⊢ |
| proveit.numbers.exponentiation.real_power_of_real_power |
137 | instantiation | 149, 208 | ⊢ |
| : |
138 | instantiation | 150, 185, 151, 152* | ⊢ |
| : , : |
139 | theorem | | ⊢ |
| proveit.numbers.addition.add_real_closure_bin |
140 | instantiation | 153, 154 | ⊢ |
| : , : , : |
141 | instantiation | 155, 156, 157, 158* | ⊢ |
| : , : |
142 | instantiation | 159, 160, 191 | ⊢ |
| : , : |
143 | assumption | | ⊢ |
144 | theorem | | ⊢ |
| proveit.physics.quantum.QPE._two_pow_t_is_nat_pos |
145 | instantiation | 161, 215, 162, 163, 164, 165 | ⊢ |
| : , : , : , : |
146 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.add_2_2 |
147 | instantiation | 220, 213, 166 | ⊢ |
| : , : , : |
148 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.posnat4 |
149 | theorem | | ⊢ |
| proveit.numbers.number_sets.natural_numbers.nonzero_if_is_nat_pos |
150 | theorem | | ⊢ |
| proveit.numbers.multiplication.mult_neg_right |
151 | instantiation | 220, 196, 206 | ⊢ |
| : , : , : |
152 | instantiation | 176, 185 | ⊢ |
| : |
153 | axiom | | ⊢ |
| proveit.logic.equality.substitution |
154 | instantiation | 167, 168, 169 | ⊢ |
| : , : , : |
155 | theorem | | ⊢ |
| proveit.numbers.exponentiation.neg_power_as_div |
156 | instantiation | 220, 170, 171 | ⊢ |
| : , : , : |
157 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.posnat1 |
158 | instantiation | 172, 177 | ⊢ |
| : |
159 | theorem | | ⊢ |
| proveit.numbers.number_sets.integers.int_interval_within_int |
160 | instantiation | 173, 174, 219 | ⊢ |
| : , : |
161 | axiom | | ⊢ |
| proveit.core_expr_types.operations.operands_substitution |
162 | instantiation | 194 | ⊢ |
| : , : |
163 | instantiation | 194 | ⊢ |
| : , : |
164 | instantiation | 175, 177 | ⊢ |
| : |
165 | instantiation | 176, 177 | ⊢ |
| : |
166 | instantiation | 220, 218, 178 | ⊢ |
| : , : , : |
167 | axiom | | ⊢ |
| proveit.logic.equality.equals_transitivity |
168 | instantiation | 179, 180, 215, 222, 181, 182, 185, 186, 183 | ⊢ |
| : , : , : , : , : , : |
169 | instantiation | 184, 185, 186, 187 | ⊢ |
| : , : , : |
170 | theorem | | ⊢ |
| proveit.numbers.number_sets.complex_numbers.real_nonzero_within_complex_nonzero |
171 | instantiation | 220, 188, 189 | ⊢ |
| : , : , : |
172 | theorem | | ⊢ |
| proveit.numbers.exponentiation.complex_x_to_first_power_is_x |
173 | theorem | | ⊢ |
| proveit.numbers.addition.add_int_closure_bin |
174 | instantiation | 190, 191 | ⊢ |
| : |
175 | theorem | | ⊢ |
| proveit.numbers.multiplication.elim_one_left |
176 | theorem | | ⊢ |
| proveit.numbers.multiplication.elim_one_right |
177 | instantiation | 220, 196, 192 | ⊢ |
| : , : , : |
178 | instantiation | 220, 221, 193 | ⊢ |
| : , : , : |
179 | theorem | | ⊢ |
| proveit.numbers.addition.disassociation |
180 | axiom | | ⊢ |
| proveit.numbers.number_sets.natural_numbers.zero_in_nats |
181 | theorem | | ⊢ |
| proveit.core_expr_types.tuples.tuple_len_0_typical_eq |
182 | instantiation | 194 | ⊢ |
| : , : |
183 | instantiation | 220, 196, 195 | ⊢ |
| : , : , : |
184 | theorem | | ⊢ |
| proveit.numbers.addition.subtraction.add_cancel_triple_13 |
185 | instantiation | 220, 196, 204 | ⊢ |
| : , : , : |
186 | instantiation | 220, 196, 197 | ⊢ |
| : , : , : |
187 | instantiation | 198 | ⊢ |
| : |
188 | theorem | | ⊢ |
| proveit.numbers.number_sets.real_numbers.rational_nonzero_within_real_nonzero |
189 | instantiation | 220, 199, 200 | ⊢ |
| : , : , : |
190 | theorem | | ⊢ |
| proveit.numbers.negation.int_closure |
191 | instantiation | 220, 201, 202 | ⊢ |
| : , : , : |
192 | instantiation | 220, 213, 203 | ⊢ |
| : , : , : |
193 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.nat4 |
194 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.tuple_len_2_typical_eq |
195 | instantiation | 205, 204 | ⊢ |
| : |
196 | theorem | | ⊢ |
| proveit.numbers.number_sets.complex_numbers.real_within_complex |
197 | instantiation | 205, 206 | ⊢ |
| : |
198 | axiom | | ⊢ |
| proveit.logic.equality.equals_reflexivity |
199 | theorem | | ⊢ |
| proveit.numbers.number_sets.rational_numbers.nonzero_int_within_rational_nonzero |
200 | instantiation | 220, 207, 208 | ⊢ |
| : , : , : |
201 | theorem | | ⊢ |
| proveit.numbers.number_sets.integers.nat_pos_within_int |
202 | theorem | | ⊢ |
| proveit.physics.quantum.QPE._two_pow_t_minus_one_is_nat_pos |
203 | instantiation | 220, 218, 209 | ⊢ |
| : , : , : |
204 | instantiation | 210, 211, 212 | ⊢ |
| : , : , : |
205 | theorem | | ⊢ |
| proveit.numbers.negation.real_closure |
206 | instantiation | 220, 213, 214 | ⊢ |
| : , : , : |
207 | theorem | | ⊢ |
| proveit.numbers.number_sets.integers.nat_pos_within_nonzero_int |
208 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.posnat2 |
209 | instantiation | 220, 221, 215 | ⊢ |
| : , : , : |
210 | theorem | | ⊢ |
| proveit.logic.sets.inclusion.unfold_subset_eq |
211 | instantiation | 216, 217 | ⊢ |
| : , : |
212 | axiom | | ⊢ |
| proveit.physics.quantum.QPE._t_in_natural_pos |
213 | theorem | | ⊢ |
| proveit.numbers.number_sets.real_numbers.rational_within_real |
214 | instantiation | 220, 218, 219 | ⊢ |
| : , : , : |
215 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.nat2 |
216 | theorem | | ⊢ |
| proveit.logic.sets.inclusion.relax_proper_subset |
217 | theorem | | ⊢ |
| proveit.numbers.number_sets.real_numbers.nat_pos_within_real |
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 |