| step type | requirements | statement |
0 | instantiation | 1, 2 | ⊢ |
| : , : |
1 | theorem | | ⊢ |
| proveit.numbers.addition.subtraction.nonneg_difference |
2 | instantiation | 40, 44, 150, 3, 4, 5*, 6* | ⊢ |
| : , : , : |
3 | instantiation | 64, 8, 150 | ⊢ |
| : , : |
4 | instantiation | 7, 150, 8, 9, 123 | ⊢ |
| : , : , : |
5 | instantiation | 126, 10, 11 | ⊢ |
| : , : , : |
6 | instantiation | 126, 12, 13 | ⊢ |
| : , : , : |
7 | theorem | | ⊢ |
| proveit.numbers.ordering.less_eq_add_right |
8 | instantiation | 64, 66, 110 | ⊢ |
| : , : |
9 | instantiation | 24, 14, 15 | ⊢ |
| : , : , : |
10 | instantiation | 82, 204, 175, 83, 30, 84, 139, 88, 31 | ⊢ |
| : , : , : , : , : , : |
11 | instantiation | 87, 139, 88, 49 | ⊢ |
| : , : , : |
12 | instantiation | 96, 16 | ⊢ |
| : , : , : |
13 | instantiation | 17, 18, 19, 20 | ⊢ |
| : , : , : , : |
14 | instantiation | 21, 201, 38, 22, 23* | ⊢ |
| : , : |
15 | instantiation | 24, 25, 26 | ⊢ |
| : , : , : |
16 | instantiation | 82, 83, 175, 204, 84, 48, 51, 86, 139 | ⊢ |
| : , : , : , : , : , : |
17 | theorem | | ⊢ |
| proveit.logic.equality.four_chain_transitivity |
18 | instantiation | 82, 83, 28, 204, 84, 29, 51, 86, 139, 27 | ⊢ |
| : , : , : , : , : , : |
19 | instantiation | 82, 28, 175, 83, 29, 30, 84, 51, 86, 139, 88, 31 | ⊢ |
| : , : , : , : , : , : |
20 | instantiation | 126, 32, 33 | ⊢ |
| : , : , : |
21 | theorem | | ⊢ |
| proveit.numbers.rounding.ceil_of_real_above_int |
22 | instantiation | 34, 184, 60, 35, 176, 36* | ⊢ |
| : , : , : |
23 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.add_1_1 |
24 | theorem | | ⊢ |
| proveit.numbers.ordering.transitivity_less_eq_less_eq |
25 | instantiation | 37, 38, 157, 39 | ⊢ |
| : , : |
26 | instantiation | 40, 110, 41, 66, 42, 43* | ⊢ |
| : , : , : |
27 | instantiation | 202, 161, 44 | ⊢ |
| : , : , : |
28 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.nat3 |
29 | instantiation | 45 | ⊢ |
| : , : , : |
30 | instantiation | 151 | ⊢ |
| : , : |
31 | instantiation | 46, 139 | ⊢ |
| : |
32 | instantiation | 47, 175, 204, 83, 48, 84, 51, 86, 139, 88, 49 | ⊢ |
| : , : , : , : , : , : , : , : |
33 | instantiation | 50, 88, 51, 90 | ⊢ |
| : , : , : |
34 | theorem | | ⊢ |
| proveit.numbers.logarithms.log_increasing_less |
35 | instantiation | 52, 150, 53, 54, 55, 56*, 57* | ⊢ |
| : , : , : |
36 | instantiation | 58, 184 | ⊢ |
| : |
37 | theorem | | ⊢ |
| proveit.numbers.rounding.ceil_increasing_less_eq |
38 | instantiation | 162, 184, 60, 164 | ⊢ |
| : , : |
39 | instantiation | 59, 184, 60, 163, 61, 176 | ⊢ |
| : , : , : |
40 | theorem | | ⊢ |
| proveit.numbers.addition.weak_bound_via_left_term_bound |
41 | instantiation | 64, 131, 111 | ⊢ |
| : , : |
42 | axiom | | ⊢ |
| proveit.physics.quantum.QPE._t_req |
43 | instantiation | 126, 62, 63 | ⊢ |
| : , : , : |
44 | instantiation | 64, 131, 65 | ⊢ |
| : , : |
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 | 151 | ⊢ |
| : , : |
49 | instantiation | 112 | ⊢ |
| : |
50 | theorem | | ⊢ |
| proveit.numbers.addition.subtraction.add_cancel_triple_32 |
51 | instantiation | 202, 161, 66 | ⊢ |
| : , : , : |
52 | theorem | | ⊢ |
| proveit.numbers.addition.strong_bound_via_left_term_bound |
53 | instantiation | 67, 133, 195 | ⊢ |
| : , : |
54 | instantiation | 202, 198, 68 | ⊢ |
| : , : , : |
55 | instantiation | 69, 133, 195, 196, 70, 71 | ⊢ |
| : , : , : |
56 | instantiation | 126, 72, 73 | ⊢ |
| : , : , : |
57 | instantiation | 126, 74, 75 | ⊢ |
| : , : , : |
58 | theorem | | ⊢ |
| proveit.numbers.logarithms.log_eq_1 |
59 | theorem | | ⊢ |
| proveit.numbers.logarithms.log_increasing_less_eq |
60 | instantiation | 171, 76, 184, 101 | ⊢ |
| : , : |
61 | instantiation | 77, 150, 78, 79, 80, 81* | ⊢ |
| : , : , : |
62 | instantiation | 82, 83, 175, 204, 84, 85, 88, 89, 86 | ⊢ |
| : , : , : , : , : , : |
63 | instantiation | 87, 88, 89, 90 | ⊢ |
| : , : , : |
64 | theorem | | ⊢ |
| proveit.numbers.addition.add_real_closure_bin |
65 | instantiation | 130, 150 | ⊢ |
| : |
66 | instantiation | 145, 146, 91 | ⊢ |
| : , : , : |
67 | theorem | | ⊢ |
| proveit.numbers.multiplication.mult_real_closure_bin |
68 | instantiation | 92, 149, 199 | ⊢ |
| : , : |
69 | theorem | | ⊢ |
| proveit.numbers.multiplication.strong_bound_via_right_factor_bound |
70 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.less_0_1 |
71 | instantiation | 93, 159 | ⊢ |
| : |
72 | instantiation | 96, 94 | ⊢ |
| : , : , : |
73 | instantiation | 95, 139 | ⊢ |
| : |
74 | instantiation | 96, 97 | ⊢ |
| : , : , : |
75 | instantiation | 106, 201, 166, 107*, 98*, 124* | ⊢ |
| : , : , : , : |
76 | instantiation | 202, 186, 99 | ⊢ |
| : , : , : |
77 | theorem | | ⊢ |
| proveit.numbers.addition.weak_bound_via_right_term_bound |
78 | instantiation | 100, 196, 150, 101 | ⊢ |
| : , : |
79 | instantiation | 202, 102, 168 | ⊢ |
| : , : , : |
80 | instantiation | 103, 104, 182, 184, 105 | ⊢ |
| : , : , : |
81 | instantiation | 106, 166, 201, 107*, 108*, 109* | ⊢ |
| : , : , : , : |
82 | theorem | | ⊢ |
| proveit.numbers.addition.disassociation |
83 | axiom | | ⊢ |
| proveit.numbers.number_sets.natural_numbers.zero_in_nats |
84 | theorem | | ⊢ |
| proveit.core_expr_types.tuples.tuple_len_0_typical_eq |
85 | instantiation | 151 | ⊢ |
| : , : |
86 | instantiation | 202, 161, 110 | ⊢ |
| : , : , : |
87 | theorem | | ⊢ |
| proveit.numbers.addition.subtraction.add_cancel_triple_13 |
88 | instantiation | 202, 161, 131 | ⊢ |
| : , : , : |
89 | instantiation | 202, 161, 111 | ⊢ |
| : , : , : |
90 | instantiation | 112 | ⊢ |
| : |
91 | axiom | | ⊢ |
| proveit.physics.quantum.QPE._t_in_natural_pos |
92 | theorem | | ⊢ |
| proveit.numbers.multiplication.mult_rational_closure_bin |
93 | theorem | | ⊢ |
| proveit.numbers.number_sets.rational_numbers.positive_if_in_rational_pos |
94 | instantiation | 113, 114 | ⊢ |
| : |
95 | theorem | | ⊢ |
| proveit.numbers.addition.elim_zero_left |
96 | axiom | | ⊢ |
| proveit.logic.equality.substitution |
97 | instantiation | 152, 114 | ⊢ |
| : |
98 | instantiation | 126, 115, 116 | ⊢ |
| : , : , : |
99 | instantiation | 202, 191, 117 | ⊢ |
| : , : , : |
100 | theorem | | ⊢ |
| proveit.numbers.division.div_real_closure |
101 | instantiation | 118, 192 | ⊢ |
| : |
102 | theorem | | ⊢ |
| proveit.numbers.number_sets.real_numbers.real_pos_within_real |
103 | theorem | | ⊢ |
| proveit.numbers.division.weak_div_from_denom_bound__all_pos |
104 | instantiation | 202, 119, 120 | ⊢ |
| : , : , : |
105 | instantiation | 121, 150, 189, 196, 122, 123, 124* | ⊢ |
| : , : , : |
106 | theorem | | ⊢ |
| proveit.numbers.addition.rational_pair_addition |
107 | instantiation | 125, 139 | ⊢ |
| : |
108 | instantiation | 126, 127, 128 | ⊢ |
| : , : , : |
109 | instantiation | 129, 139 | ⊢ |
| : |
110 | instantiation | 130, 131 | ⊢ |
| : |
111 | instantiation | 202, 198, 132 | ⊢ |
| : , : , : |
112 | axiom | | ⊢ |
| proveit.logic.equality.equals_reflexivity |
113 | theorem | | ⊢ |
| proveit.numbers.multiplication.mult_zero_right |
114 | instantiation | 202, 161, 133 | ⊢ |
| : , : , : |
115 | instantiation | 140, 175, 134, 135, 144, 143 | ⊢ |
| : , : , : , : |
116 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.add_1_4 |
117 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.posnat5 |
118 | theorem | | ⊢ |
| proveit.numbers.number_sets.natural_numbers.nonzero_if_is_nat_pos |
119 | theorem | | ⊢ |
| proveit.numbers.number_sets.real_numbers.rational_nonneg_within_real_nonneg |
120 | instantiation | 202, 136, 204 | ⊢ |
| : , : , : |
121 | theorem | | ⊢ |
| proveit.numbers.multiplication.weak_bound_via_right_factor_bound |
122 | instantiation | 137, 195, 196, 197 | ⊢ |
| : , : , : |
123 | instantiation | 138, 175 | ⊢ |
| : |
124 | instantiation | 152, 139 | ⊢ |
| : |
125 | theorem | | ⊢ |
| proveit.numbers.division.frac_one_denom |
126 | axiom | | ⊢ |
| proveit.logic.equality.equals_transitivity |
127 | instantiation | 140, 175, 141, 142, 143, 144 | ⊢ |
| : , : , : , : |
128 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.add_4_1 |
129 | theorem | | ⊢ |
| proveit.numbers.multiplication.elim_one_left |
130 | theorem | | ⊢ |
| proveit.numbers.negation.real_closure |
131 | instantiation | 145, 146, 147 | ⊢ |
| : , : , : |
132 | instantiation | 202, 200, 148 | ⊢ |
| : , : , : |
133 | instantiation | 202, 198, 149 | ⊢ |
| : , : , : |
134 | instantiation | 151 | ⊢ |
| : , : |
135 | instantiation | 151 | ⊢ |
| : , : |
136 | theorem | | ⊢ |
| proveit.numbers.number_sets.rational_numbers.nat_within_rational_nonneg |
137 | theorem | | ⊢ |
| proveit.numbers.number_sets.real_numbers.interval_oc_upper_bound |
138 | theorem | | ⊢ |
| proveit.numbers.number_sets.natural_numbers.natural_lower_bound |
139 | instantiation | 202, 161, 150 | ⊢ |
| : , : , : |
140 | axiom | | ⊢ |
| proveit.core_expr_types.operations.operands_substitution |
141 | instantiation | 151 | ⊢ |
| : , : |
142 | instantiation | 151 | ⊢ |
| : , : |
143 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.mult_2_2 |
144 | instantiation | 152, 153 | ⊢ |
| : |
145 | theorem | | ⊢ |
| proveit.logic.sets.inclusion.unfold_subset_eq |
146 | instantiation | 154, 155 | ⊢ |
| : , : |
147 | axiom | | ⊢ |
| proveit.physics.quantum.QPE._n_in_natural_pos |
148 | instantiation | 156, 157 | ⊢ |
| : |
149 | instantiation | 202, 158, 159 | ⊢ |
| : , : , : |
150 | instantiation | 202, 198, 160 | ⊢ |
| : , : , : |
151 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.tuple_len_2_typical_eq |
152 | theorem | | ⊢ |
| proveit.numbers.multiplication.elim_one_right |
153 | instantiation | 202, 161, 196 | ⊢ |
| : , : , : |
154 | theorem | | ⊢ |
| proveit.logic.sets.inclusion.relax_proper_subset |
155 | theorem | | ⊢ |
| proveit.numbers.number_sets.real_numbers.nat_pos_within_real |
156 | axiom | | ⊢ |
| proveit.numbers.rounding.ceil_is_an_int |
157 | instantiation | 162, 184, 163, 164 | ⊢ |
| : , : |
158 | theorem | | ⊢ |
| proveit.numbers.number_sets.rational_numbers.rational_pos_within_rational |
159 | instantiation | 165, 177, 187 | ⊢ |
| : , : |
160 | instantiation | 202, 200, 166 | ⊢ |
| : , : , : |
161 | theorem | | ⊢ |
| proveit.numbers.number_sets.complex_numbers.real_within_complex |
162 | theorem | | ⊢ |
| proveit.numbers.logarithms.log_real_pos_real_closure |
163 | instantiation | 167, 184, 168 | ⊢ |
| : , : |
164 | instantiation | 169, 170 | ⊢ |
| : , : |
165 | theorem | | ⊢ |
| proveit.numbers.division.div_rational_pos_closure |
166 | instantiation | 202, 203, 175 | ⊢ |
| : , : , : |
167 | theorem | | ⊢ |
| proveit.numbers.addition.add_real_pos_closure_bin |
168 | instantiation | 171, 172, 182, 173 | ⊢ |
| : , : |
169 | theorem | | ⊢ |
| proveit.logic.equality.not_equals_symmetry |
170 | instantiation | 174, 204, 175, 176 | ⊢ |
| : , : |
171 | theorem | | ⊢ |
| proveit.numbers.division.div_real_pos_closure |
172 | instantiation | 202, 186, 177 | ⊢ |
| : , : , : |
173 | instantiation | 178, 179 | ⊢ |
| : |
174 | theorem | | ⊢ |
| proveit.numbers.ordering.less_is_not_eq_nat |
175 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.nat2 |
176 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.less_1_2 |
177 | instantiation | 202, 191, 180 | ⊢ |
| : , : , : |
178 | theorem | | ⊢ |
| proveit.numbers.number_sets.real_numbers.nonzero_if_in_real_nonzero |
179 | instantiation | 202, 181, 182 | ⊢ |
| : , : , : |
180 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.posnat1 |
181 | theorem | | ⊢ |
| proveit.numbers.number_sets.real_numbers.real_pos_within_real_nonzero |
182 | instantiation | 183, 184, 185 | ⊢ |
| : , : |
183 | theorem | | ⊢ |
| proveit.numbers.multiplication.mult_real_pos_closure_bin |
184 | instantiation | 202, 186, 187 | ⊢ |
| : , : , : |
185 | instantiation | 188, 189, 190 | ⊢ |
| : |
186 | theorem | | ⊢ |
| proveit.numbers.number_sets.real_numbers.rational_pos_within_real_pos |
187 | instantiation | 202, 191, 192 | ⊢ |
| : , : , : |
188 | theorem | | ⊢ |
| proveit.numbers.number_sets.real_numbers.pos_real_is_real_pos |
189 | instantiation | 193, 195, 196, 197 | ⊢ |
| : , : , : |
190 | instantiation | 194, 195, 196, 197 | ⊢ |
| : , : , : |
191 | theorem | | ⊢ |
| proveit.numbers.number_sets.rational_numbers.nat_pos_within_rational_pos |
192 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.posnat2 |
193 | theorem | | ⊢ |
| proveit.numbers.number_sets.real_numbers.all_in_interval_oc__is__real |
194 | theorem | | ⊢ |
| proveit.numbers.number_sets.real_numbers.interval_oc_lower_bound |
195 | theorem | | ⊢ |
| proveit.numbers.number_sets.real_numbers.zero_is_real |
196 | instantiation | 202, 198, 199 | ⊢ |
| : , : , : |
197 | axiom | | ⊢ |
| proveit.physics.quantum.QPE._eps_in_interval |
198 | theorem | | ⊢ |
| proveit.numbers.number_sets.real_numbers.rational_within_real |
199 | instantiation | 202, 200, 201 | ⊢ |
| : , : , : |
200 | theorem | | ⊢ |
| proveit.numbers.number_sets.rational_numbers.int_within_rational |
201 | instantiation | 202, 203, 204 | ⊢ |
| : , : , : |
202 | theorem | | ⊢ |
| proveit.logic.sets.inclusion.superset_membership_from_proper_subset |
203 | theorem | | ⊢ |
| proveit.numbers.number_sets.integers.nat_within_int |
204 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.nat1 |
*equality replacement requirements |