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