| step type | requirements | statement |
0 | instantiation | 1, 2, 3, 4, 5, 6* | ⊢ |
| : , : , : |
1 | theorem | | ⊢ |
| proveit.numbers.addition.weak_bound_via_right_term_bound |
2 | reference | 42 | ⊢ |
3 | instantiation | 118, 33, 32 | ⊢ |
| : , : |
4 | reference | 171 | ⊢ |
5 | instantiation | 7, 8, 9 | ⊢ |
| : , : , : |
6 | instantiation | 131, 10, 11 | ⊢ |
| : , : , : |
7 | theorem | | ⊢ |
| proveit.numbers.ordering.transitivity_less_eq_less_eq |
8 | instantiation | 75, 12, 13, 14* | ⊢ |
| : , : , : |
9 | instantiation | 85, 15, 16 | ⊢ |
| : , : , : |
10 | instantiation | 143, 193, 188, 144, 17, 146, 19, 20, 18 | ⊢ |
| : , : , : , : , : , : |
11 | instantiation | 148, 19, 20, 21 | ⊢ |
| : , : , : |
12 | instantiation | 22, 43, 55, 26, 23* | ⊢ |
| : , : , : |
13 | instantiation | 30, 62, 89 | ⊢ |
| : , : |
14 | instantiation | 24, 25, 26, 27, 28* | ⊢ |
| : , : |
15 | instantiation | 37, 29 | ⊢ |
| : , : |
16 | instantiation | 30, 31, 88 | ⊢ |
| : , : |
17 | instantiation | 162 | ⊢ |
| : , : |
18 | instantiation | 191, 164, 32 | ⊢ |
| : , : , : |
19 | instantiation | 191, 164, 42 | ⊢ |
| : , : , : |
20 | instantiation | 191, 164, 33 | ⊢ |
| : , : , : |
21 | instantiation | 166 | ⊢ |
| : |
22 | theorem | | ⊢ |
| proveit.numbers.modular.mod_abs_of_difference_bound |
23 | instantiation | 131, 34, 35 | ⊢ |
| : , : , : |
24 | theorem | | ⊢ |
| proveit.numbers.modular.mod_abs_x_reduce_to_abs_x |
25 | instantiation | 118, 100, 74 | ⊢ |
| : , : |
26 | instantiation | 36, 102, 165 | ⊢ |
| : , : |
27 | instantiation | 37, 38 | ⊢ |
| : , : |
28 | instantiation | 39, 40, 41* | ⊢ |
| : |
29 | instantiation | 64, 170, 171, 114 | ⊢ |
| : , : , : |
30 | theorem | | ⊢ |
| proveit.numbers.addition.commutation |
31 | instantiation | 191, 164, 69 | ⊢ |
| : , : , : |
32 | instantiation | 84, 42 | ⊢ |
| : |
33 | instantiation | 54, 43, 160, 56 | ⊢ |
| : , : |
34 | instantiation | 90, 44 | ⊢ |
| : , : , : |
35 | instantiation | 45, 46, 47, 48 | ⊢ |
| : , : , : , : |
36 | theorem | | ⊢ |
| proveit.numbers.exponentiation.exp_real_pos_closure |
37 | theorem | | ⊢ |
| proveit.numbers.ordering.relax_less |
38 | instantiation | 49, 50, 51 | ⊢ |
| : , : , : |
39 | theorem | | ⊢ |
| proveit.numbers.absolute_value.abs_neg_elim |
40 | instantiation | 52, 53 | ⊢ |
| : , : |
41 | instantiation | 57, 89, 88 | ⊢ |
| : , : |
42 | instantiation | 54, 55, 160, 56 | ⊢ |
| : , : |
43 | instantiation | 118, 97, 74 | ⊢ |
| : , : |
44 | instantiation | 57, 83, 89 | ⊢ |
| : , : |
45 | theorem | | ⊢ |
| proveit.logic.equality.four_chain_transitivity |
46 | instantiation | 143, 144, 188, 193, 146, 59, 83, 62, 58 | ⊢ |
| : , : , : , : , : , : |
47 | instantiation | 143, 188, 144, 59, 60, 146, 83, 62, 73, 89 | ⊢ |
| : , : , : , : , : , : |
48 | instantiation | 61, 144, 193, 146, 83, 62, 89, 63 | ⊢ |
| : , : , : , : , : , : , : , : |
49 | theorem | | ⊢ |
| proveit.numbers.ordering.transitivity_less_less_eq |
50 | instantiation | 64, 170, 171, 65 | ⊢ |
| : , : , : |
51 | instantiation | 85, 66, 67 | ⊢ |
| : , : , : |
52 | theorem | | ⊢ |
| proveit.numbers.addition.subtraction.nonpos_difference |
53 | instantiation | 68, 142 | ⊢ |
| : |
54 | theorem | | ⊢ |
| proveit.numbers.modular.mod_abs_real_closure |
55 | instantiation | 118, 97, 69 | ⊢ |
| : , : |
56 | instantiation | 70, 123, 71 | ⊢ |
| : , : |
57 | theorem | | ⊢ |
| proveit.numbers.negation.distribute_neg_through_subtract |
58 | instantiation | 72, 73, 89 | ⊢ |
| : , : |
59 | instantiation | 162 | ⊢ |
| : , : |
60 | instantiation | 162 | ⊢ |
| : , : |
61 | theorem | | ⊢ |
| proveit.numbers.addition.subtraction.add_cancel_general |
62 | instantiation | 191, 164, 74 | ⊢ |
| : , : , : |
63 | instantiation | 166 | ⊢ |
| : |
64 | theorem | | ⊢ |
| proveit.numbers.number_sets.real_numbers.interval_co_upper_bound |
65 | instantiation | 75, 76, 77 | ⊢ |
| : , : , : |
66 | instantiation | 78, 138 | ⊢ |
| : |
67 | instantiation | 131, 79, 80 | ⊢ |
| : , : , : |
68 | theorem | | ⊢ |
| proveit.numbers.rounding.floor_x_le_x |
69 | instantiation | 84, 100 | ⊢ |
| : |
70 | theorem | | ⊢ |
| proveit.numbers.exponentiation.exp_rational_non_zero__not_zero |
71 | instantiation | 191, 136, 81 | ⊢ |
| : , : , : |
72 | theorem | | ⊢ |
| proveit.numbers.addition.add_complex_closure_bin |
73 | instantiation | 82, 83 | ⊢ |
| : |
74 | instantiation | 84, 142 | ⊢ |
| : |
75 | theorem | | ⊢ |
| proveit.logic.equality.sub_right_side_into |
76 | instantiation | 85, 114, 86 | ⊢ |
| : , : , : |
77 | instantiation | 87, 88, 89 | ⊢ |
| : , : |
78 | theorem | | ⊢ |
| proveit.numbers.number_sets.natural_numbers.natural_pos_lower_bound |
79 | instantiation | 90, 91 | ⊢ |
| : , : , : |
80 | instantiation | 92, 93, 94, 111, 95*, 96* | ⊢ |
| : , : , : |
81 | instantiation | 191, 154, 190 | ⊢ |
| : , : , : |
82 | theorem | | ⊢ |
| proveit.numbers.negation.complex_closure |
83 | instantiation | 191, 164, 97 | ⊢ |
| : , : , : |
84 | theorem | | ⊢ |
| proveit.numbers.negation.real_closure |
85 | theorem | | ⊢ |
| proveit.logic.equality.sub_left_side_into |
86 | instantiation | 98, 99 | ⊢ |
| : |
87 | theorem | | ⊢ |
| proveit.numbers.absolute_value.abs_diff_reversal |
88 | instantiation | 191, 164, 142 | ⊢ |
| : , : , : |
89 | instantiation | 191, 164, 100 | ⊢ |
| : , : , : |
90 | axiom | | ⊢ |
| proveit.logic.equality.substitution |
91 | instantiation | 101, 102, 165, 171, 103, 104, 105* | ⊢ |
| : , : , : , : |
92 | theorem | | ⊢ |
| proveit.numbers.division.frac_cancel_left |
93 | instantiation | 191, 107, 106 | ⊢ |
| : , : , : |
94 | instantiation | 191, 107, 108 | ⊢ |
| : , : , : |
95 | instantiation | 109, 122 | ⊢ |
| : |
96 | instantiation | 110, 111 | ⊢ |
| : |
97 | instantiation | 191, 177, 112 | ⊢ |
| : , : , : |
98 | theorem | | ⊢ |
| proveit.numbers.absolute_value.abs_non_neg_elim |
99 | instantiation | 113, 170, 171, 114 | ⊢ |
| : , : , : |
100 | instantiation | 191, 177, 115 | ⊢ |
| : , : , : |
101 | theorem | | ⊢ |
| proveit.numbers.exponentiation.exp_factored_real |
102 | instantiation | 191, 116, 117 | ⊢ |
| : , : , : |
103 | instantiation | 118, 165, 163 | ⊢ |
| : , : |
104 | instantiation | 119, 120 | ⊢ |
| : , : |
105 | instantiation | 121, 122 | ⊢ |
| : |
106 | instantiation | 191, 124, 123 | ⊢ |
| : , : , : |
107 | theorem | | ⊢ |
| proveit.numbers.number_sets.complex_numbers.real_nonzero_within_complex_nonzero |
108 | instantiation | 191, 124, 125 | ⊢ |
| : , : , : |
109 | theorem | | ⊢ |
| proveit.numbers.multiplication.elim_one_right |
110 | theorem | | ⊢ |
| proveit.numbers.division.frac_one_denom |
111 | instantiation | 191, 164, 126 | ⊢ |
| : , : , : |
112 | instantiation | 191, 185, 127 | ⊢ |
| : , : , : |
113 | theorem | | ⊢ |
| proveit.numbers.number_sets.real_numbers.interval_co_lower_bound |
114 | instantiation | 128, 142 | ⊢ |
| : |
115 | instantiation | 191, 185, 129 | ⊢ |
| : , : , : |
116 | theorem | | ⊢ |
| proveit.numbers.number_sets.real_numbers.rational_pos_within_real_pos |
117 | instantiation | 191, 130, 153 | ⊢ |
| : , : , : |
118 | theorem | | ⊢ |
| proveit.numbers.addition.add_real_closure_bin |
119 | theorem | | ⊢ |
| proveit.logic.equality.equals_reversal |
120 | instantiation | 131, 132, 133 | ⊢ |
| : , : , : |
121 | theorem | | ⊢ |
| proveit.numbers.exponentiation.complex_x_to_first_power_is_x |
122 | instantiation | 191, 164, 134 | ⊢ |
| : , : , : |
123 | instantiation | 191, 136, 135 | ⊢ |
| : , : , : |
124 | theorem | | ⊢ |
| proveit.numbers.number_sets.real_numbers.rational_nonzero_within_real_nonzero |
125 | instantiation | 191, 136, 137 | ⊢ |
| : , : , : |
126 | instantiation | 174, 175, 138 | ⊢ |
| : , : , : |
127 | instantiation | 191, 139, 140 | ⊢ |
| : , : , : |
128 | theorem | | ⊢ |
| proveit.numbers.rounding.real_minus_floor_interval |
129 | instantiation | 141, 142 | ⊢ |
| : |
130 | theorem | | ⊢ |
| proveit.numbers.number_sets.rational_numbers.nat_pos_within_rational_pos |
131 | axiom | | ⊢ |
| proveit.logic.equality.equals_transitivity |
132 | instantiation | 143, 193, 188, 144, 145, 146, 149, 150, 147 | ⊢ |
| : , : , : , : , : , : |
133 | instantiation | 148, 149, 150, 151 | ⊢ |
| : , : , : |
134 | instantiation | 191, 177, 152 | ⊢ |
| : , : , : |
135 | instantiation | 191, 154, 153 | ⊢ |
| : , : , : |
136 | theorem | | ⊢ |
| proveit.numbers.number_sets.rational_numbers.nonzero_int_within_rational_nonzero |
137 | instantiation | 191, 154, 155 | ⊢ |
| : , : , : |
138 | theorem | | ⊢ |
| proveit.physics.quantum.QPE._two_pow_t_minus_one_is_nat_pos |
139 | instantiation | 156, 157, 158 | ⊢ |
| : , : |
140 | assumption | | ⊢ |
141 | axiom | | ⊢ |
| proveit.numbers.rounding.floor_is_an_int |
142 | instantiation | 159, 160, 161 | ⊢ |
| : , : |
143 | theorem | | ⊢ |
| proveit.numbers.addition.disassociation |
144 | axiom | | ⊢ |
| proveit.numbers.number_sets.natural_numbers.zero_in_nats |
145 | instantiation | 162 | ⊢ |
| : , : |
146 | theorem | | ⊢ |
| proveit.core_expr_types.tuples.tuple_len_0_typical_eq |
147 | instantiation | 191, 164, 163 | ⊢ |
| : , : , : |
148 | theorem | | ⊢ |
| proveit.numbers.addition.subtraction.add_cancel_triple_13 |
149 | instantiation | 191, 164, 171 | ⊢ |
| : , : , : |
150 | instantiation | 191, 164, 165 | ⊢ |
| : , : , : |
151 | instantiation | 166 | ⊢ |
| : |
152 | instantiation | 191, 185, 183 | ⊢ |
| : , : , : |
153 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.posnat2 |
154 | theorem | | ⊢ |
| proveit.numbers.number_sets.integers.nat_pos_within_nonzero_int |
155 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.posnat1 |
156 | theorem | | ⊢ |
| proveit.numbers.number_sets.integers.int_interval_within_int |
157 | theorem | | ⊢ |
| proveit.numbers.number_sets.integers.zero_is_int |
158 | instantiation | 167, 176, 179 | ⊢ |
| : , : |
159 | theorem | | ⊢ |
| proveit.numbers.multiplication.mult_real_closure_bin |
160 | instantiation | 191, 177, 168 | ⊢ |
| : , : , : |
161 | instantiation | 169, 170, 171, 172 | ⊢ |
| : , : , : |
162 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.tuple_len_2_typical_eq |
163 | instantiation | 191, 177, 173 | ⊢ |
| : , : , : |
164 | theorem | | ⊢ |
| proveit.numbers.number_sets.complex_numbers.real_within_complex |
165 | instantiation | 174, 175, 190 | ⊢ |
| : , : , : |
166 | axiom | | ⊢ |
| proveit.logic.equality.equals_reflexivity |
167 | theorem | | ⊢ |
| proveit.numbers.addition.add_int_closure_bin |
168 | instantiation | 191, 185, 176 | ⊢ |
| : , : , : |
169 | theorem | | ⊢ |
| proveit.numbers.number_sets.real_numbers.all_in_interval_co__is__real |
170 | theorem | | ⊢ |
| proveit.numbers.number_sets.real_numbers.zero_is_real |
171 | instantiation | 191, 177, 178 | ⊢ |
| : , : , : |
172 | axiom | | ⊢ |
| proveit.physics.quantum.QPE._phase_in_interval |
173 | instantiation | 191, 185, 179 | ⊢ |
| : , : , : |
174 | theorem | | ⊢ |
| proveit.logic.sets.inclusion.unfold_subset_eq |
175 | instantiation | 180, 181 | ⊢ |
| : , : |
176 | instantiation | 182, 183, 184 | ⊢ |
| : , : |
177 | theorem | | ⊢ |
| proveit.numbers.number_sets.real_numbers.rational_within_real |
178 | instantiation | 191, 185, 187 | ⊢ |
| : , : , : |
179 | instantiation | 186, 187 | ⊢ |
| : |
180 | theorem | | ⊢ |
| proveit.logic.sets.inclusion.relax_proper_subset |
181 | theorem | | ⊢ |
| proveit.numbers.number_sets.real_numbers.nat_pos_within_real |
182 | theorem | | ⊢ |
| proveit.numbers.exponentiation.exp_int_closure |
183 | instantiation | 191, 192, 188 | ⊢ |
| : , : , : |
184 | instantiation | 191, 189, 190 | ⊢ |
| : , : , : |
185 | theorem | | ⊢ |
| proveit.numbers.number_sets.rational_numbers.int_within_rational |
186 | theorem | | ⊢ |
| proveit.numbers.negation.int_closure |
187 | instantiation | 191, 192, 193 | ⊢ |
| : , : , : |
188 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.nat2 |
189 | theorem | | ⊢ |
| proveit.numbers.number_sets.natural_numbers.nat_pos_within_nat |
190 | axiom | | ⊢ |
| proveit.physics.quantum.QPE._t_in_natural_pos |
191 | theorem | | ⊢ |
| proveit.logic.sets.inclusion.superset_membership_from_proper_subset |
192 | theorem | | ⊢ |
| proveit.numbers.number_sets.integers.nat_within_int |
193 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.nat1 |
*equality replacement requirements |