| step type | requirements | statement |
0 | instantiation | 1, 2, 3 | ⊢ |
| : , : |
1 | theorem | | ⊢ |
| proveit.numbers.exponentiation.exp_real_closure_nat_power |
2 | reference | 163 | ⊢ |
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 | 215, 12, 104 | ⊢ |
| : , : , : |
9 | instantiation | 215, 13, 14 | ⊢ |
| : , : , : |
10 | theorem | | ⊢ |
| proveit.numbers.addition.subtraction.nonneg_difference |
11 | instantiation | 53, 57, 163, 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, 160 | ⊢ |
| : |
15 | instantiation | 77, 21, 163 | ⊢ |
| : , : |
16 | instantiation | 20, 163, 21, 22, 136 | ⊢ |
| : , : , : |
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 | 77, 79, 123 | ⊢ |
| : , : |
22 | instantiation | 37, 27, 28 | ⊢ |
| : , : , : |
23 | instantiation | 95, 217, 188, 96, 43, 97, 152, 101, 44 | ⊢ |
| : , : , : , : , : , : |
24 | instantiation | 100, 152, 101, 62 | ⊢ |
| : , : , : |
25 | instantiation | 109, 29 | ⊢ |
| : , : , : |
26 | instantiation | 30, 31, 32, 33 | ⊢ |
| : , : , : , : |
27 | instantiation | 34, 214, 51, 35, 36* | ⊢ |
| : , : |
28 | instantiation | 37, 38, 39 | ⊢ |
| : , : , : |
29 | instantiation | 95, 96, 188, 217, 97, 61, 64, 99, 152 | ⊢ |
| : , : , : , : , : , : |
30 | theorem | | ⊢ |
| proveit.logic.equality.four_chain_transitivity |
31 | instantiation | 95, 96, 41, 217, 97, 42, 64, 99, 152, 40 | ⊢ |
| : , : , : , : , : , : |
32 | instantiation | 95, 41, 188, 96, 42, 43, 97, 64, 99, 152, 101, 44 | ⊢ |
| : , : , : , : , : , : |
33 | instantiation | 139, 45, 46 | ⊢ |
| : , : , : |
34 | theorem | | ⊢ |
| proveit.numbers.rounding.ceil_of_real_above_int |
35 | instantiation | 47, 197, 73, 48, 189, 49* | ⊢ |
| : , : , : |
36 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.add_1_1 |
37 | theorem | | ⊢ |
| proveit.numbers.ordering.transitivity_less_eq_less_eq |
38 | instantiation | 50, 51, 170, 52 | ⊢ |
| : , : |
39 | instantiation | 53, 123, 54, 79, 55, 56* | ⊢ |
| : , : , : |
40 | instantiation | 215, 174, 57 | ⊢ |
| : , : , : |
41 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.nat3 |
42 | instantiation | 58 | ⊢ |
| : , : , : |
43 | instantiation | 164 | ⊢ |
| : , : |
44 | instantiation | 59, 152 | ⊢ |
| : |
45 | instantiation | 60, 188, 217, 96, 61, 97, 64, 99, 152, 101, 62 | ⊢ |
| : , : , : , : , : , : , : , : |
46 | instantiation | 63, 101, 64, 103 | ⊢ |
| : , : , : |
47 | theorem | | ⊢ |
| proveit.numbers.logarithms.log_increasing_less |
48 | instantiation | 65, 163, 66, 67, 68, 69*, 70* | ⊢ |
| : , : , : |
49 | instantiation | 71, 197 | ⊢ |
| : |
50 | theorem | | ⊢ |
| proveit.numbers.rounding.ceil_increasing_less_eq |
51 | instantiation | 175, 197, 73, 177 | ⊢ |
| : , : |
52 | instantiation | 72, 197, 73, 176, 74, 189 | ⊢ |
| : , : , : |
53 | theorem | | ⊢ |
| proveit.numbers.addition.weak_bound_via_left_term_bound |
54 | instantiation | 77, 144, 124 | ⊢ |
| : , : |
55 | axiom | | ⊢ |
| proveit.physics.quantum.QPE._t_req |
56 | instantiation | 139, 75, 76 | ⊢ |
| : , : , : |
57 | instantiation | 77, 144, 78 | ⊢ |
| : , : |
58 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.tuple_len_3_typical_eq |
59 | theorem | | ⊢ |
| proveit.numbers.negation.complex_closure |
60 | theorem | | ⊢ |
| proveit.numbers.addition.subtraction.add_cancel_general |
61 | instantiation | 164 | ⊢ |
| : , : |
62 | instantiation | 125 | ⊢ |
| : |
63 | theorem | | ⊢ |
| proveit.numbers.addition.subtraction.add_cancel_triple_32 |
64 | instantiation | 215, 174, 79 | ⊢ |
| : , : , : |
65 | theorem | | ⊢ |
| proveit.numbers.addition.strong_bound_via_left_term_bound |
66 | instantiation | 80, 146, 208 | ⊢ |
| : , : |
67 | instantiation | 215, 211, 81 | ⊢ |
| : , : , : |
68 | instantiation | 82, 146, 208, 209, 83, 84 | ⊢ |
| : , : , : |
69 | instantiation | 139, 85, 86 | ⊢ |
| : , : , : |
70 | instantiation | 139, 87, 88 | ⊢ |
| : , : , : |
71 | theorem | | ⊢ |
| proveit.numbers.logarithms.log_eq_1 |
72 | theorem | | ⊢ |
| proveit.numbers.logarithms.log_increasing_less_eq |
73 | instantiation | 184, 89, 197, 114 | ⊢ |
| : , : |
74 | instantiation | 90, 163, 91, 92, 93, 94* | ⊢ |
| : , : , : |
75 | instantiation | 95, 96, 188, 217, 97, 98, 101, 102, 99 | ⊢ |
| : , : , : , : , : , : |
76 | instantiation | 100, 101, 102, 103 | ⊢ |
| : , : , : |
77 | theorem | | ⊢ |
| proveit.numbers.addition.add_real_closure_bin |
78 | instantiation | 143, 163 | ⊢ |
| : |
79 | instantiation | 158, 159, 104 | ⊢ |
| : , : , : |
80 | theorem | | ⊢ |
| proveit.numbers.multiplication.mult_real_closure_bin |
81 | instantiation | 105, 162, 212 | ⊢ |
| : , : |
82 | theorem | | ⊢ |
| proveit.numbers.multiplication.strong_bound_via_right_factor_bound |
83 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.less_0_1 |
84 | instantiation | 106, 172 | ⊢ |
| : |
85 | instantiation | 109, 107 | ⊢ |
| : , : , : |
86 | instantiation | 108, 152 | ⊢ |
| : |
87 | instantiation | 109, 110 | ⊢ |
| : , : , : |
88 | instantiation | 119, 214, 179, 120*, 111*, 137* | ⊢ |
| : , : , : , : |
89 | instantiation | 215, 199, 112 | ⊢ |
| : , : , : |
90 | theorem | | ⊢ |
| proveit.numbers.addition.weak_bound_via_right_term_bound |
91 | instantiation | 113, 209, 163, 114 | ⊢ |
| : , : |
92 | instantiation | 215, 115, 181 | ⊢ |
| : , : , : |
93 | instantiation | 116, 117, 195, 197, 118 | ⊢ |
| : , : , : |
94 | instantiation | 119, 179, 214, 120*, 121*, 122* | ⊢ |
| : , : , : , : |
95 | theorem | | ⊢ |
| proveit.numbers.addition.disassociation |
96 | axiom | | ⊢ |
| proveit.numbers.number_sets.natural_numbers.zero_in_nats |
97 | theorem | | ⊢ |
| proveit.core_expr_types.tuples.tuple_len_0_typical_eq |
98 | instantiation | 164 | ⊢ |
| : , : |
99 | instantiation | 215, 174, 123 | ⊢ |
| : , : , : |
100 | theorem | | ⊢ |
| proveit.numbers.addition.subtraction.add_cancel_triple_13 |
101 | instantiation | 215, 174, 144 | ⊢ |
| : , : , : |
102 | instantiation | 215, 174, 124 | ⊢ |
| : , : , : |
103 | instantiation | 125 | ⊢ |
| : |
104 | axiom | | ⊢ |
| proveit.physics.quantum.QPE._t_in_natural_pos |
105 | theorem | | ⊢ |
| proveit.numbers.multiplication.mult_rational_closure_bin |
106 | theorem | | ⊢ |
| proveit.numbers.number_sets.rational_numbers.positive_if_in_rational_pos |
107 | instantiation | 126, 127 | ⊢ |
| : |
108 | theorem | | ⊢ |
| proveit.numbers.addition.elim_zero_left |
109 | axiom | | ⊢ |
| proveit.logic.equality.substitution |
110 | instantiation | 165, 127 | ⊢ |
| : |
111 | instantiation | 139, 128, 129 | ⊢ |
| : , : , : |
112 | instantiation | 215, 204, 130 | ⊢ |
| : , : , : |
113 | theorem | | ⊢ |
| proveit.numbers.division.div_real_closure |
114 | instantiation | 131, 205 | ⊢ |
| : |
115 | theorem | | ⊢ |
| proveit.numbers.number_sets.real_numbers.real_pos_within_real |
116 | theorem | | ⊢ |
| proveit.numbers.division.weak_div_from_denom_bound__all_pos |
117 | instantiation | 215, 132, 133 | ⊢ |
| : , : , : |
118 | instantiation | 134, 163, 202, 209, 135, 136, 137* | ⊢ |
| : , : , : |
119 | theorem | | ⊢ |
| proveit.numbers.addition.rational_pair_addition |
120 | instantiation | 138, 152 | ⊢ |
| : |
121 | instantiation | 139, 140, 141 | ⊢ |
| : , : , : |
122 | instantiation | 142, 152 | ⊢ |
| : |
123 | instantiation | 143, 144 | ⊢ |
| : |
124 | instantiation | 215, 211, 145 | ⊢ |
| : , : , : |
125 | axiom | | ⊢ |
| proveit.logic.equality.equals_reflexivity |
126 | theorem | | ⊢ |
| proveit.numbers.multiplication.mult_zero_right |
127 | instantiation | 215, 174, 146 | ⊢ |
| : , : , : |
128 | instantiation | 153, 188, 147, 148, 157, 156 | ⊢ |
| : , : , : , : |
129 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.add_1_4 |
130 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.posnat5 |
131 | theorem | | ⊢ |
| proveit.numbers.number_sets.natural_numbers.nonzero_if_is_nat_pos |
132 | theorem | | ⊢ |
| proveit.numbers.number_sets.real_numbers.rational_nonneg_within_real_nonneg |
133 | instantiation | 215, 149, 217 | ⊢ |
| : , : , : |
134 | theorem | | ⊢ |
| proveit.numbers.multiplication.weak_bound_via_right_factor_bound |
135 | instantiation | 150, 208, 209, 210 | ⊢ |
| : , : , : |
136 | instantiation | 151, 188 | ⊢ |
| : |
137 | instantiation | 165, 152 | ⊢ |
| : |
138 | theorem | | ⊢ |
| proveit.numbers.division.frac_one_denom |
139 | axiom | | ⊢ |
| proveit.logic.equality.equals_transitivity |
140 | instantiation | 153, 188, 154, 155, 156, 157 | ⊢ |
| : , : , : , : |
141 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.add_4_1 |
142 | theorem | | ⊢ |
| proveit.numbers.multiplication.elim_one_left |
143 | theorem | | ⊢ |
| proveit.numbers.negation.real_closure |
144 | instantiation | 158, 159, 160 | ⊢ |
| : , : , : |
145 | instantiation | 215, 213, 161 | ⊢ |
| : , : , : |
146 | instantiation | 215, 211, 162 | ⊢ |
| : , : , : |
147 | instantiation | 164 | ⊢ |
| : , : |
148 | instantiation | 164 | ⊢ |
| : , : |
149 | theorem | | ⊢ |
| proveit.numbers.number_sets.rational_numbers.nat_within_rational_nonneg |
150 | theorem | | ⊢ |
| proveit.numbers.number_sets.real_numbers.interval_oc_upper_bound |
151 | theorem | | ⊢ |
| proveit.numbers.number_sets.natural_numbers.natural_lower_bound |
152 | instantiation | 215, 174, 163 | ⊢ |
| : , : , : |
153 | axiom | | ⊢ |
| proveit.core_expr_types.operations.operands_substitution |
154 | instantiation | 164 | ⊢ |
| : , : |
155 | instantiation | 164 | ⊢ |
| : , : |
156 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.mult_2_2 |
157 | instantiation | 165, 166 | ⊢ |
| : |
158 | theorem | | ⊢ |
| proveit.logic.sets.inclusion.unfold_subset_eq |
159 | instantiation | 167, 168 | ⊢ |
| : , : |
160 | axiom | | ⊢ |
| proveit.physics.quantum.QPE._n_in_natural_pos |
161 | instantiation | 169, 170 | ⊢ |
| : |
162 | instantiation | 215, 171, 172 | ⊢ |
| : , : , : |
163 | instantiation | 215, 211, 173 | ⊢ |
| : , : , : |
164 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.tuple_len_2_typical_eq |
165 | theorem | | ⊢ |
| proveit.numbers.multiplication.elim_one_right |
166 | instantiation | 215, 174, 209 | ⊢ |
| : , : , : |
167 | theorem | | ⊢ |
| proveit.logic.sets.inclusion.relax_proper_subset |
168 | theorem | | ⊢ |
| proveit.numbers.number_sets.real_numbers.nat_pos_within_real |
169 | axiom | | ⊢ |
| proveit.numbers.rounding.ceil_is_an_int |
170 | instantiation | 175, 197, 176, 177 | ⊢ |
| : , : |
171 | theorem | | ⊢ |
| proveit.numbers.number_sets.rational_numbers.rational_pos_within_rational |
172 | instantiation | 178, 190, 200 | ⊢ |
| : , : |
173 | instantiation | 215, 213, 179 | ⊢ |
| : , : , : |
174 | theorem | | ⊢ |
| proveit.numbers.number_sets.complex_numbers.real_within_complex |
175 | theorem | | ⊢ |
| proveit.numbers.logarithms.log_real_pos_real_closure |
176 | instantiation | 180, 197, 181 | ⊢ |
| : , : |
177 | instantiation | 182, 183 | ⊢ |
| : , : |
178 | theorem | | ⊢ |
| proveit.numbers.division.div_rational_pos_closure |
179 | instantiation | 215, 216, 188 | ⊢ |
| : , : , : |
180 | theorem | | ⊢ |
| proveit.numbers.addition.add_real_pos_closure_bin |
181 | instantiation | 184, 185, 195, 186 | ⊢ |
| : , : |
182 | theorem | | ⊢ |
| proveit.logic.equality.not_equals_symmetry |
183 | instantiation | 187, 217, 188, 189 | ⊢ |
| : , : |
184 | theorem | | ⊢ |
| proveit.numbers.division.div_real_pos_closure |
185 | instantiation | 215, 199, 190 | ⊢ |
| : , : , : |
186 | instantiation | 191, 192 | ⊢ |
| : |
187 | theorem | | ⊢ |
| proveit.numbers.ordering.less_is_not_eq_nat |
188 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.nat2 |
189 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.less_1_2 |
190 | instantiation | 215, 204, 193 | ⊢ |
| : , : , : |
191 | theorem | | ⊢ |
| proveit.numbers.number_sets.real_numbers.nonzero_if_in_real_nonzero |
192 | instantiation | 215, 194, 195 | ⊢ |
| : , : , : |
193 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.posnat1 |
194 | theorem | | ⊢ |
| proveit.numbers.number_sets.real_numbers.real_pos_within_real_nonzero |
195 | instantiation | 196, 197, 198 | ⊢ |
| : , : |
196 | theorem | | ⊢ |
| proveit.numbers.multiplication.mult_real_pos_closure_bin |
197 | instantiation | 215, 199, 200 | ⊢ |
| : , : , : |
198 | instantiation | 201, 202, 203 | ⊢ |
| : |
199 | theorem | | ⊢ |
| proveit.numbers.number_sets.real_numbers.rational_pos_within_real_pos |
200 | instantiation | 215, 204, 205 | ⊢ |
| : , : , : |
201 | theorem | | ⊢ |
| proveit.numbers.number_sets.real_numbers.pos_real_is_real_pos |
202 | instantiation | 206, 208, 209, 210 | ⊢ |
| : , : , : |
203 | instantiation | 207, 208, 209, 210 | ⊢ |
| : , : , : |
204 | theorem | | ⊢ |
| proveit.numbers.number_sets.rational_numbers.nat_pos_within_rational_pos |
205 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.posnat2 |
206 | theorem | | ⊢ |
| proveit.numbers.number_sets.real_numbers.all_in_interval_oc__is__real |
207 | theorem | | ⊢ |
| proveit.numbers.number_sets.real_numbers.interval_oc_lower_bound |
208 | theorem | | ⊢ |
| proveit.numbers.number_sets.real_numbers.zero_is_real |
209 | instantiation | 215, 211, 212 | ⊢ |
| : , : , : |
210 | axiom | | ⊢ |
| proveit.physics.quantum.QPE._eps_in_interval |
211 | theorem | | ⊢ |
| proveit.numbers.number_sets.real_numbers.rational_within_real |
212 | instantiation | 215, 213, 214 | ⊢ |
| : , : , : |
213 | theorem | | ⊢ |
| proveit.numbers.number_sets.rational_numbers.int_within_rational |
214 | instantiation | 215, 216, 217 | ⊢ |
| : , : , : |
215 | theorem | | ⊢ |
| proveit.logic.sets.inclusion.superset_membership_from_proper_subset |
216 | theorem | | ⊢ |
| proveit.numbers.number_sets.integers.nat_within_int |
217 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.nat1 |
*equality replacement requirements |