| step type | requirements | statement |
0 | instantiation | 1, 2, 3 | ⊢ |
| : , : , : |
1 | reference | 146 | ⊢ |
2 | instantiation | 92, 93, 191, 220, 94, 4, 6, 5, 173 | ⊢ |
| : , : , : , : , : , : |
3 | instantiation | 69, 173, 6, 7 | ⊢ |
| : , : , : |
4 | instantiation | 171 | ⊢ |
| : , : |
5 | instantiation | 65, 173 | ⊢ |
| : |
6 | instantiation | 218, 180, 8 | ⊢ |
| : , : , : |
7 | instantiation | 120 | ⊢ |
| : |
8 | instantiation | 9, 165, 10 | ⊢ |
| : , : |
9 | theorem | | ⊢ |
| proveit.numbers.exponentiation.exp_real_closure_nat_power |
10 | instantiation | 11, 12, 13 | ⊢ |
| : |
11 | theorem | | ⊢ |
| proveit.numbers.number_sets.integers.nonneg_int_is_natural |
12 | instantiation | 14, 15, 16 | ⊢ |
| : , : |
13 | instantiation | 17, 18 | ⊢ |
| : , : |
14 | theorem | | ⊢ |
| proveit.numbers.addition.add_int_closure_bin |
15 | instantiation | 218, 19, 101 | ⊢ |
| : , : , : |
16 | instantiation | 218, 20, 21 | ⊢ |
| : , : , : |
17 | theorem | | ⊢ |
| proveit.numbers.addition.subtraction.nonneg_difference |
18 | instantiation | 59, 63, 165, 22, 23, 24*, 25* | ⊢ |
| : , : , : |
19 | theorem | | ⊢ |
| proveit.numbers.number_sets.integers.nat_pos_within_int |
20 | theorem | | ⊢ |
| proveit.numbers.number_sets.integers.neg_int_within_int |
21 | instantiation | 26, 157 | ⊢ |
| : |
22 | instantiation | 78, 28, 165 | ⊢ |
| : , : |
23 | instantiation | 27, 165, 28, 29, 135 | ⊢ |
| : , : , : |
24 | instantiation | 146, 30, 31 | ⊢ |
| : , : , : |
25 | instantiation | 146, 32, 33 | ⊢ |
| : , : , : |
26 | theorem | | ⊢ |
| proveit.numbers.negation.int_neg_closure |
27 | theorem | | ⊢ |
| proveit.numbers.ordering.less_eq_add_right |
28 | instantiation | 78, 80, 118 | ⊢ |
| : , : |
29 | instantiation | 44, 34, 35 | ⊢ |
| : , : , : |
30 | instantiation | 92, 220, 191, 93, 50, 94, 152, 98, 51 | ⊢ |
| : , : , : , : , : , : |
31 | instantiation | 97, 152, 98, 68 | ⊢ |
| : , : , : |
32 | instantiation | 125, 36 | ⊢ |
| : , : , : |
33 | instantiation | 37, 38, 39, 40 | ⊢ |
| : , : , : , : |
34 | instantiation | 41, 217, 57, 42, 43* | ⊢ |
| : , : |
35 | instantiation | 44, 45, 46 | ⊢ |
| : , : , : |
36 | instantiation | 92, 93, 191, 220, 94, 67, 70, 96, 152 | ⊢ |
| : , : , : , : , : , : |
37 | theorem | | ⊢ |
| proveit.logic.equality.four_chain_transitivity |
38 | instantiation | 92, 93, 48, 220, 94, 49, 70, 96, 152, 47 | ⊢ |
| : , : , : , : , : , : |
39 | instantiation | 92, 48, 191, 93, 49, 50, 94, 70, 96, 152, 98, 51 | ⊢ |
| : , : , : , : , : , : |
40 | instantiation | 146, 52, 53 | ⊢ |
| : , : , : |
41 | theorem | | ⊢ |
| proveit.numbers.rounding.ceil_of_real_above_int |
42 | instantiation | 54, 200, 74, 55 | ⊢ |
| : , : |
43 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.add_1_1 |
44 | theorem | | ⊢ |
| proveit.numbers.ordering.transitivity_less_eq_less_eq |
45 | instantiation | 56, 57, 169, 58 | ⊢ |
| : , : |
46 | instantiation | 59, 118, 60, 80, 61, 62* | ⊢ |
| : , : , : |
47 | instantiation | 218, 180, 63 | ⊢ |
| : , : , : |
48 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.nat3 |
49 | instantiation | 64 | ⊢ |
| : , : , : |
50 | instantiation | 171 | ⊢ |
| : , : |
51 | instantiation | 65, 152 | ⊢ |
| : |
52 | instantiation | 66, 191, 220, 93, 67, 94, 70, 96, 152, 98, 68 | ⊢ |
| : , : , : , : , : , : , : , : |
53 | instantiation | 69, 98, 70, 100 | ⊢ |
| : , : , : |
54 | theorem | | ⊢ |
| proveit.numbers.logarithms.log_base_large_a_greater_one |
55 | instantiation | 71, 192, 72 | ⊢ |
| : , : |
56 | theorem | | ⊢ |
| proveit.numbers.rounding.ceil_increasing_less_eq |
57 | instantiation | 175, 200, 74, 177 | ⊢ |
| : , : |
58 | instantiation | 73, 200, 74, 176, 75, 192 | ⊢ |
| : , : , : |
59 | theorem | | ⊢ |
| proveit.numbers.addition.weak_bound_via_left_term_bound |
60 | instantiation | 78, 141, 119 | ⊢ |
| : , : |
61 | axiom | | ⊢ |
| proveit.physics.quantum.QPE._t_req |
62 | instantiation | 146, 76, 77 | ⊢ |
| : , : , : |
63 | instantiation | 78, 141, 79 | ⊢ |
| : , : |
64 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.tuple_len_3_typical_eq |
65 | theorem | | ⊢ |
| proveit.numbers.negation.complex_closure |
66 | theorem | | ⊢ |
| proveit.numbers.addition.subtraction.add_cancel_general |
67 | instantiation | 171 | ⊢ |
| : , : |
68 | instantiation | 120 | ⊢ |
| : |
69 | theorem | | ⊢ |
| proveit.numbers.addition.subtraction.add_cancel_triple_32 |
70 | instantiation | 218, 180, 80 | ⊢ |
| : , : , : |
71 | theorem | | ⊢ |
| proveit.logic.booleans.conjunction.and_if_both |
72 | instantiation | 81, 165, 82, 83, 84, 85*, 86* | ⊢ |
| : , : , : |
73 | theorem | | ⊢ |
| proveit.numbers.logarithms.log_increasing_less_eq |
74 | instantiation | 218, 202, 87 | ⊢ |
| : , : , : |
75 | instantiation | 88, 165, 159, 89, 90, 91* | ⊢ |
| : , : , : |
76 | instantiation | 92, 93, 191, 220, 94, 95, 98, 99, 96 | ⊢ |
| : , : , : , : , : , : |
77 | instantiation | 97, 98, 99, 100 | ⊢ |
| : , : , : |
78 | theorem | | ⊢ |
| proveit.numbers.addition.add_real_closure_bin |
79 | instantiation | 140, 165 | ⊢ |
| : |
80 | instantiation | 155, 156, 101 | ⊢ |
| : , : , : |
81 | theorem | | ⊢ |
| proveit.numbers.addition.strong_bound_via_left_term_bound |
82 | instantiation | 102, 159, 211 | ⊢ |
| : , : |
83 | instantiation | 218, 214, 103 | ⊢ |
| : , : , : |
84 | instantiation | 104, 159, 211, 212, 105, 106 | ⊢ |
| : , : , : |
85 | instantiation | 146, 107, 108 | ⊢ |
| : , : , : |
86 | instantiation | 146, 109, 110 | ⊢ |
| : , : , : |
87 | instantiation | 186, 111, 203 | ⊢ |
| : , : |
88 | theorem | | ⊢ |
| proveit.numbers.addition.weak_bound_via_right_term_bound |
89 | instantiation | 218, 112, 183 | ⊢ |
| : , : , : |
90 | instantiation | 113, 114, 198, 200, 115 | ⊢ |
| : , : , : |
91 | instantiation | 127, 181, 217, 128*, 116*, 117* | ⊢ |
| : , : , : , : |
92 | theorem | | ⊢ |
| proveit.numbers.addition.disassociation |
93 | axiom | | ⊢ |
| proveit.numbers.number_sets.natural_numbers.zero_in_nats |
94 | theorem | | ⊢ |
| proveit.core_expr_types.tuples.tuple_len_0_typical_eq |
95 | instantiation | 171 | ⊢ |
| : , : |
96 | instantiation | 218, 180, 118 | ⊢ |
| : , : , : |
97 | theorem | | ⊢ |
| proveit.numbers.addition.subtraction.add_cancel_triple_13 |
98 | instantiation | 218, 180, 141 | ⊢ |
| : , : , : |
99 | instantiation | 218, 180, 119 | ⊢ |
| : , : , : |
100 | instantiation | 120 | ⊢ |
| : |
101 | axiom | | ⊢ |
| proveit.physics.quantum.QPE._t_in_natural_pos |
102 | theorem | | ⊢ |
| proveit.numbers.multiplication.mult_real_closure_bin |
103 | instantiation | 121, 170, 215 | ⊢ |
| : , : |
104 | theorem | | ⊢ |
| proveit.numbers.multiplication.strong_bound_via_right_factor_bound |
105 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.less_0_1 |
106 | instantiation | 122, 179 | ⊢ |
| : |
107 | instantiation | 125, 123 | ⊢ |
| : , : , : |
108 | instantiation | 124, 152 | ⊢ |
| : |
109 | instantiation | 125, 126 | ⊢ |
| : , : , : |
110 | instantiation | 127, 217, 181, 128*, 129*, 136* | ⊢ |
| : , : , : , : |
111 | instantiation | 218, 207, 130 | ⊢ |
| : , : , : |
112 | theorem | | ⊢ |
| proveit.numbers.number_sets.real_numbers.real_pos_within_real |
113 | theorem | | ⊢ |
| proveit.numbers.division.weak_div_from_denom_bound__all_pos |
114 | instantiation | 218, 131, 132 | ⊢ |
| : , : , : |
115 | instantiation | 133, 165, 205, 212, 134, 135, 136* | ⊢ |
| : , : , : |
116 | instantiation | 146, 137, 138 | ⊢ |
| : , : , : |
117 | instantiation | 139, 152 | ⊢ |
| : |
118 | instantiation | 140, 141 | ⊢ |
| : |
119 | instantiation | 218, 214, 142 | ⊢ |
| : , : , : |
120 | axiom | | ⊢ |
| proveit.logic.equality.equals_reflexivity |
121 | theorem | | ⊢ |
| proveit.numbers.multiplication.mult_rational_closure_bin |
122 | theorem | | ⊢ |
| proveit.numbers.number_sets.rational_numbers.positive_if_in_rational_pos |
123 | instantiation | 143, 144 | ⊢ |
| : |
124 | theorem | | ⊢ |
| proveit.numbers.addition.elim_zero_left |
125 | axiom | | ⊢ |
| proveit.logic.equality.substitution |
126 | instantiation | 172, 144 | ⊢ |
| : |
127 | theorem | | ⊢ |
| proveit.numbers.addition.rational_pair_addition |
128 | instantiation | 145, 152 | ⊢ |
| : |
129 | instantiation | 146, 147, 148 | ⊢ |
| : , : , : |
130 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.posnat5 |
131 | theorem | | ⊢ |
| proveit.numbers.number_sets.real_numbers.rational_nonneg_within_real_nonneg |
132 | instantiation | 218, 149, 220 | ⊢ |
| : , : , : |
133 | theorem | | ⊢ |
| proveit.numbers.multiplication.weak_bound_via_right_factor_bound |
134 | instantiation | 150, 211, 212, 213 | ⊢ |
| : , : , : |
135 | instantiation | 151, 191 | ⊢ |
| : |
136 | instantiation | 172, 152 | ⊢ |
| : |
137 | instantiation | 160, 191, 153, 154, 164, 163 | ⊢ |
| : , : , : , : |
138 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.add_4_1 |
139 | theorem | | ⊢ |
| proveit.numbers.multiplication.elim_one_left |
140 | theorem | | ⊢ |
| proveit.numbers.negation.real_closure |
141 | instantiation | 155, 156, 157 | ⊢ |
| : , : , : |
142 | instantiation | 218, 216, 158 | ⊢ |
| : , : , : |
143 | theorem | | ⊢ |
| proveit.numbers.multiplication.mult_zero_right |
144 | instantiation | 218, 180, 159 | ⊢ |
| : , : , : |
145 | theorem | | ⊢ |
| proveit.numbers.division.frac_one_denom |
146 | axiom | | ⊢ |
| proveit.logic.equality.equals_transitivity |
147 | instantiation | 160, 191, 161, 162, 163, 164 | ⊢ |
| : , : , : , : |
148 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.add_1_4 |
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 | 218, 180, 165 | ⊢ |
| : , : , : |
153 | instantiation | 171 | ⊢ |
| : , : |
154 | instantiation | 171 | ⊢ |
| : , : |
155 | theorem | | ⊢ |
| proveit.logic.sets.inclusion.unfold_subset_eq |
156 | instantiation | 166, 167 | ⊢ |
| : , : |
157 | axiom | | ⊢ |
| proveit.physics.quantum.QPE._n_in_natural_pos |
158 | instantiation | 168, 169 | ⊢ |
| : |
159 | instantiation | 218, 214, 170 | ⊢ |
| : , : , : |
160 | axiom | | ⊢ |
| proveit.core_expr_types.operations.operands_substitution |
161 | instantiation | 171 | ⊢ |
| : , : |
162 | instantiation | 171 | ⊢ |
| : , : |
163 | instantiation | 172, 173 | ⊢ |
| : |
164 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.mult_2_2 |
165 | instantiation | 218, 214, 174 | ⊢ |
| : , : , : |
166 | theorem | | ⊢ |
| proveit.logic.sets.inclusion.relax_proper_subset |
167 | theorem | | ⊢ |
| proveit.numbers.number_sets.real_numbers.nat_pos_within_real |
168 | axiom | | ⊢ |
| proveit.numbers.rounding.ceil_is_an_int |
169 | instantiation | 175, 200, 176, 177 | ⊢ |
| : , : |
170 | instantiation | 218, 178, 179 | ⊢ |
| : , : , : |
171 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.tuple_len_2_typical_eq |
172 | theorem | | ⊢ |
| proveit.numbers.multiplication.elim_one_right |
173 | instantiation | 218, 180, 212 | ⊢ |
| : , : , : |
174 | instantiation | 218, 216, 181 | ⊢ |
| : , : , : |
175 | theorem | | ⊢ |
| proveit.numbers.logarithms.log_real_pos_real_closure |
176 | instantiation | 182, 200, 183 | ⊢ |
| : , : |
177 | instantiation | 184, 185 | ⊢ |
| : , : |
178 | theorem | | ⊢ |
| proveit.numbers.number_sets.rational_numbers.rational_pos_within_rational |
179 | instantiation | 186, 193, 203 | ⊢ |
| : , : |
180 | theorem | | ⊢ |
| proveit.numbers.number_sets.complex_numbers.real_within_complex |
181 | instantiation | 218, 219, 191 | ⊢ |
| : , : , : |
182 | theorem | | ⊢ |
| proveit.numbers.addition.add_real_pos_closure_bin |
183 | instantiation | 187, 188, 198, 189 | ⊢ |
| : , : |
184 | theorem | | ⊢ |
| proveit.logic.equality.not_equals_symmetry |
185 | instantiation | 190, 220, 191, 192 | ⊢ |
| : , : |
186 | theorem | | ⊢ |
| proveit.numbers.division.div_rational_pos_closure |
187 | theorem | | ⊢ |
| proveit.numbers.division.div_real_pos_closure |
188 | instantiation | 218, 202, 193 | ⊢ |
| : , : , : |
189 | instantiation | 194, 195 | ⊢ |
| : |
190 | theorem | | ⊢ |
| proveit.numbers.ordering.less_is_not_eq_nat |
191 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.nat2 |
192 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.less_1_2 |
193 | instantiation | 218, 207, 196 | ⊢ |
| : , : , : |
194 | theorem | | ⊢ |
| proveit.numbers.number_sets.real_numbers.nonzero_if_in_real_nonzero |
195 | instantiation | 218, 197, 198 | ⊢ |
| : , : , : |
196 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.posnat1 |
197 | theorem | | ⊢ |
| proveit.numbers.number_sets.real_numbers.real_pos_within_real_nonzero |
198 | instantiation | 199, 200, 201 | ⊢ |
| : , : |
199 | theorem | | ⊢ |
| proveit.numbers.multiplication.mult_real_pos_closure_bin |
200 | instantiation | 218, 202, 203 | ⊢ |
| : , : , : |
201 | instantiation | 204, 205, 206 | ⊢ |
| : |
202 | theorem | | ⊢ |
| proveit.numbers.number_sets.real_numbers.rational_pos_within_real_pos |
203 | instantiation | 218, 207, 208 | ⊢ |
| : , : , : |
204 | theorem | | ⊢ |
| proveit.numbers.number_sets.real_numbers.pos_real_is_real_pos |
205 | instantiation | 209, 211, 212, 213 | ⊢ |
| : , : , : |
206 | instantiation | 210, 211, 212, 213 | ⊢ |
| : , : , : |
207 | theorem | | ⊢ |
| proveit.numbers.number_sets.rational_numbers.nat_pos_within_rational_pos |
208 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.posnat2 |
209 | theorem | | ⊢ |
| proveit.numbers.number_sets.real_numbers.all_in_interval_oc__is__real |
210 | theorem | | ⊢ |
| proveit.numbers.number_sets.real_numbers.interval_oc_lower_bound |
211 | theorem | | ⊢ |
| proveit.numbers.number_sets.real_numbers.zero_is_real |
212 | instantiation | 218, 214, 215 | ⊢ |
| : , : , : |
213 | axiom | | ⊢ |
| proveit.physics.quantum.QPE._eps_in_interval |
214 | theorem | | ⊢ |
| proveit.numbers.number_sets.real_numbers.rational_within_real |
215 | instantiation | 218, 216, 217 | ⊢ |
| : , : , : |
216 | theorem | | ⊢ |
| proveit.numbers.number_sets.rational_numbers.int_within_rational |
217 | instantiation | 218, 219, 220 | ⊢ |
| : , : , : |
218 | theorem | | ⊢ |
| proveit.logic.sets.inclusion.superset_membership_from_proper_subset |
219 | theorem | | ⊢ |
| proveit.numbers.number_sets.integers.nat_within_int |
220 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.nat1 |
*equality replacement requirements |