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