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