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