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