| step type | requirements | statement |
0 | generalization | 1 | ⊢ |
1 | instantiation | 2, 12, 3, 4 | ⊢ |
| : , : |
2 | conjecture | | ⊢ |
| proveit.numbers.modular.mod_abs_x_reduce_to_abs_x |
3 | instantiation | 208, 5, 6 | ⊢ |
| : , : , : |
4 | instantiation | 7, 8, 9 | ⊢ |
| : , : , : |
5 | conjecture | | ⊢ |
| proveit.numbers.number_sets.real_numbers.rational_pos_within_real_pos |
6 | instantiation | 208, 10, 168 | ⊢ |
| : , : , : |
7 | theorem | | ⊢ |
| proveit.logic.equality.sub_right_side_into |
8 | instantiation | 11, 12, 13, 86, 14, 15* | ⊢ |
| : , : , : |
9 | instantiation | 131, 121, 16, 17 | ⊢ |
| : , : , : , : |
10 | conjecture | | ⊢ |
| proveit.numbers.number_sets.rational_numbers.nat_pos_within_rational_pos |
11 | conjecture | | ⊢ |
| proveit.numbers.absolute_value.weak_upper_bound_asym_interval |
12 | instantiation | 208, 197, 18 | ⊢ |
| : , : , : |
13 | instantiation | 208, 197, 19 | ⊢ |
| : , : , : |
14 | instantiation | 20, 21, 22 | ⊢ |
| : , : |
15 | instantiation | 115, 23, 24 | ⊢ |
| : , : , : |
16 | instantiation | 146, 25 | ⊢ |
| : , : , : |
17 | instantiation | 144, 26 | ⊢ |
| : , : |
18 | instantiation | 208, 204, 27 | ⊢ |
| : , : , : |
19 | instantiation | 208, 204, 51 | ⊢ |
| : , : , : |
20 | theorem | | ⊢ |
| proveit.logic.booleans.conjunction.and_if_both |
21 | instantiation | 28, 51, 111, 39 | ⊢ |
| : , : , : |
22 | instantiation | 29, 51, 111, 39 | ⊢ |
| : , : , : |
23 | instantiation | 70, 210, 30, 31, 32, 33 | ⊢ |
| : , : , : , : |
24 | instantiation | 115, 34, 35 | ⊢ |
| : , : , : |
25 | instantiation | 146, 167 | ⊢ |
| : , : , : |
26 | instantiation | 36, 138, 179, 166, 37* | ⊢ |
| : , : |
27 | instantiation | 208, 38, 39 | ⊢ |
| : , : , : |
28 | conjecture | | ⊢ |
| proveit.numbers.number_sets.integers.interval_lower_bound |
29 | conjecture | | ⊢ |
| proveit.numbers.number_sets.integers.interval_upper_bound |
30 | instantiation | 135 | ⊢ |
| : , : |
31 | instantiation | 135 | ⊢ |
| : , : |
32 | instantiation | 40, 41, 42* | ⊢ |
| : |
33 | instantiation | 43, 44 | ⊢ |
| : |
34 | instantiation | 45, 94, 86 | ⊢ |
| : , : |
35 | instantiation | 46, 86, 94, 47* | ⊢ |
| : , : |
36 | conjecture | | ⊢ |
| proveit.numbers.division.div_as_mult |
37 | instantiation | 115, 48, 49 | ⊢ |
| : , : , : |
38 | instantiation | 50, 51, 111 | ⊢ |
| : , : |
39 | assumption | | ⊢ |
40 | conjecture | | ⊢ |
| proveit.numbers.absolute_value.abs_neg_elim |
41 | instantiation | 52, 76, 176, 86, 53, 54*, 55* | ⊢ |
| : , : , : |
42 | instantiation | 56, 64, 164, 57* | ⊢ |
| : , : |
43 | conjecture | | ⊢ |
| proveit.numbers.absolute_value.abs_non_neg_elim |
44 | instantiation | 90, 58 | ⊢ |
| : , : |
45 | conjecture | | ⊢ |
| proveit.numbers.ordering.max_bin_args_commute |
46 | axiom | | ⊢ |
| proveit.numbers.ordering.max_def_bin |
47 | instantiation | 115, 59, 60 | ⊢ |
| : , : , : |
48 | instantiation | 146, 61 | ⊢ |
| : , : , : |
49 | instantiation | 62, 138, 63 | ⊢ |
| : , : |
50 | conjecture | | ⊢ |
| proveit.numbers.number_sets.integers.int_interval_within_int |
51 | instantiation | 152, 88, 196 | ⊢ |
| : , : |
52 | conjecture | | ⊢ |
| proveit.numbers.addition.weak_bound_via_left_term_bound |
53 | instantiation | 171, 118 | ⊢ |
| : |
54 | instantiation | 157, 164, 64 | ⊢ |
| : , : |
55 | instantiation | 115, 65, 66 | ⊢ |
| : , : , : |
56 | conjecture | | ⊢ |
| proveit.numbers.negation.distribute_neg_through_binary_sum |
57 | instantiation | 67, 68 | ⊢ |
| : |
58 | instantiation | 69, 118 | ⊢ |
| : |
59 | instantiation | 70, 210, 71, 72, 73, 74 | ⊢ |
| : , : , : , : |
60 | instantiation | 75, 123, 203, 125 | ⊢ |
| : , : , : , : , : |
61 | instantiation | 161, 162, 207, 167* | ⊢ |
| : , : |
62 | conjecture | | ⊢ |
| proveit.numbers.multiplication.commutation |
63 | instantiation | 148, 164, 179, 166 | ⊢ |
| : , : |
64 | instantiation | 208, 188, 76 | ⊢ |
| : , : , : |
65 | instantiation | 115, 77, 78 | ⊢ |
| : , : , : |
66 | instantiation | 79, 127, 104 | ⊢ |
| : , : |
67 | conjecture | | ⊢ |
| proveit.numbers.negation.double_negation |
68 | instantiation | 208, 188, 86 | ⊢ |
| : , : , : |
69 | conjecture | | ⊢ |
| proveit.numbers.number_sets.natural_numbers.natural_pos_is_pos |
70 | axiom | | ⊢ |
| proveit.core_expr_types.operations.operands_substitution |
71 | instantiation | 135 | ⊢ |
| : , : |
72 | instantiation | 135 | ⊢ |
| : , : |
73 | instantiation | 80, 87 | ⊢ |
| : , : |
74 | instantiation | 81, 82 | ⊢ |
| : , : |
75 | axiom | | ⊢ |
| proveit.core_expr_types.conditionals.true_case_reduction |
76 | instantiation | 208, 197, 83 | ⊢ |
| : , : , : |
77 | instantiation | 146, 121 | ⊢ |
| : , : , : |
78 | instantiation | 146, 84 | ⊢ |
| : , : , : |
79 | conjecture | | ⊢ |
| proveit.numbers.addition.subtraction.add_cancel_basic |
80 | conjecture | | ⊢ |
| proveit.core_expr_types.conditionals.satisfied_condition_reduction |
81 | conjecture | | ⊢ |
| proveit.core_expr_types.conditionals.dissatisfied_condition_reduction |
82 | instantiation | 85, 94, 86, 87 | ⊢ |
| : , : |
83 | instantiation | 208, 204, 88 | ⊢ |
| : , : , : |
84 | instantiation | 146, 121 | ⊢ |
| : , : , : |
85 | conjecture | | ⊢ |
| proveit.numbers.ordering.not_less_from_less_eq |
86 | instantiation | 208, 197, 89 | ⊢ |
| : , : , : |
87 | instantiation | 90, 91 | ⊢ |
| : , : |
88 | instantiation | 92, 111 | ⊢ |
| : |
89 | instantiation | 208, 204, 111 | ⊢ |
| : , : , : |
90 | conjecture | | ⊢ |
| proveit.numbers.ordering.relax_less |
91 | instantiation | 93, 94, 95, 176, 96, 97*, 98* | ⊢ |
| : , : , : |
92 | conjecture | | ⊢ |
| proveit.numbers.negation.int_closure |
93 | conjecture | | ⊢ |
| proveit.numbers.addition.strong_bound_via_left_term_bound |
94 | instantiation | 208, 197, 99 | ⊢ |
| : , : , : |
95 | conjecture | | ⊢ |
| proveit.numbers.number_sets.real_numbers.zero_is_real |
96 | conjecture | | ⊢ |
| proveit.numbers.numerals.decimals.less_0_1 |
97 | instantiation | 131, 100, 101, 102 | ⊢ |
| : , : , : , : |
98 | instantiation | 131, 103, 104, 105 | ⊢ |
| : , : , : , : |
99 | instantiation | 208, 204, 106 | ⊢ |
| : , : , : |
100 | instantiation | 115, 107, 108 | ⊢ |
| : , : , : |
101 | instantiation | 139 | ⊢ |
| : |
102 | instantiation | 144, 114 | ⊢ |
| : , : |
103 | instantiation | 115, 109, 110 | ⊢ |
| : , : , : |
104 | instantiation | 139 | ⊢ |
| : |
105 | instantiation | 144, 121 | ⊢ |
| : , : |
106 | instantiation | 152, 111, 154 | ⊢ |
| : , : |
107 | instantiation | 146, 114 | ⊢ |
| : , : , : |
108 | instantiation | 115, 112, 113 | ⊢ |
| : , : , : |
109 | instantiation | 146, 114 | ⊢ |
| : , : , : |
110 | instantiation | 115, 116, 117 | ⊢ |
| : , : , : |
111 | instantiation | 208, 169, 118 | ⊢ |
| : , : , : |
112 | instantiation | 122, 203, 210, 123, 124, 125, 119, 127, 159 | ⊢ |
| : , : , : , : , : , : |
113 | instantiation | 120, 123, 210, 125, 124, 127, 159 | ⊢ |
| : , : , : , : |
114 | instantiation | 146, 121 | ⊢ |
| : , : , : |
115 | axiom | | ⊢ |
| proveit.logic.equality.equals_transitivity |
116 | instantiation | 122, 203, 210, 123, 124, 125, 164, 127, 159 | ⊢ |
| : , : , : , : , : , : |
117 | instantiation | 126, 164, 127, 128 | ⊢ |
| : , : , : |
118 | instantiation | 129, 210, 130 | ⊢ |
| : , : |
119 | conjecture | | ⊢ |
| proveit.numbers.number_sets.complex_numbers.zero_is_complex |
120 | conjecture | | ⊢ |
| proveit.numbers.addition.elim_zero_any |
121 | instantiation | 131, 132, 133, 134 | ⊢ |
| : , : , : , : |
122 | conjecture | | ⊢ |
| proveit.numbers.addition.disassociation |
123 | axiom | | ⊢ |
| proveit.numbers.number_sets.natural_numbers.zero_in_nats |
124 | instantiation | 135 | ⊢ |
| : , : |
125 | conjecture | | ⊢ |
| proveit.core_expr_types.tuples.tuple_len_0_typical_eq |
126 | conjecture | | ⊢ |
| proveit.numbers.addition.subtraction.add_cancel_triple_13 |
127 | instantiation | 136, 137, 138 | ⊢ |
| : , : |
128 | instantiation | 139 | ⊢ |
| : |
129 | conjecture | | ⊢ |
| proveit.numbers.exponentiation.exp_natpos_closure |
130 | instantiation | 140, 141, 142 | ⊢ |
| : |
131 | conjecture | | ⊢ |
| proveit.logic.equality.four_chain_transitivity |
132 | instantiation | 146, 143 | ⊢ |
| : , : , : |
133 | instantiation | 144, 145 | ⊢ |
| : , : |
134 | instantiation | 146, 147 | ⊢ |
| : , : , : |
135 | conjecture | | ⊢ |
| proveit.numbers.numerals.decimals.tuple_len_2_typical_eq |
136 | conjecture | | ⊢ |
| proveit.numbers.multiplication.mult_complex_closure_bin |
137 | instantiation | 148, 164, 149, 150 | ⊢ |
| : , : |
138 | instantiation | 208, 188, 151 | ⊢ |
| : , : , : |
139 | axiom | | ⊢ |
| proveit.logic.equality.equals_reflexivity |
140 | conjecture | | ⊢ |
| proveit.numbers.number_sets.integers.nonneg_int_is_natural |
141 | instantiation | 152, 153, 154 | ⊢ |
| : , : |
142 | instantiation | 155, 156 | ⊢ |
| : , : |
143 | instantiation | 157, 158, 159 | ⊢ |
| : , : |
144 | theorem | | ⊢ |
| proveit.logic.equality.equals_reversal |
145 | instantiation | 160, 179, 173, 172, 166 | ⊢ |
| : , : , : |
146 | axiom | | ⊢ |
| proveit.logic.equality.substitution |
147 | instantiation | 161, 162, 207 | ⊢ |
| : , : |
148 | conjecture | | ⊢ |
| proveit.numbers.division.div_complex_closure |
149 | instantiation | 163, 179, 164 | ⊢ |
| : , : |
150 | instantiation | 165, 166, 167 | ⊢ |
| : , : , : |
151 | instantiation | 180, 181, 168 | ⊢ |
| : , : , : |
152 | conjecture | | ⊢ |
| proveit.numbers.addition.add_int_closure_bin |
153 | instantiation | 208, 169, 182 | ⊢ |
| : , : , : |
154 | instantiation | 208, 170, 200 | ⊢ |
| : , : , : |
155 | conjecture | | ⊢ |
| proveit.numbers.addition.subtraction.nonneg_difference |
156 | instantiation | 171, 182 | ⊢ |
| : |
157 | conjecture | | ⊢ |
| proveit.numbers.addition.commutation |
158 | instantiation | 208, 188, 172 | ⊢ |
| : , : , : |
159 | instantiation | 208, 188, 173 | ⊢ |
| : , : , : |
160 | conjecture | | ⊢ |
| proveit.numbers.exponentiation.product_of_real_powers |
161 | conjecture | | ⊢ |
| proveit.numbers.exponentiation.neg_power_as_div |
162 | instantiation | 208, 174, 175 | ⊢ |
| : , : , : |
163 | conjecture | | ⊢ |
| proveit.numbers.exponentiation.exp_complex_closure |
164 | instantiation | 208, 188, 176 | ⊢ |
| : , : , : |
165 | theorem | | ⊢ |
| proveit.logic.equality.sub_left_side_into |
166 | instantiation | 177, 202 | ⊢ |
| : |
167 | instantiation | 178, 179 | ⊢ |
| : |
168 | conjecture | | ⊢ |
| proveit.physics.quantum.QPE._two_pow_t_is_nat_pos |
169 | conjecture | | ⊢ |
| proveit.numbers.number_sets.integers.nat_pos_within_int |
170 | conjecture | | ⊢ |
| proveit.numbers.number_sets.integers.neg_int_within_int |
171 | conjecture | | ⊢ |
| proveit.numbers.number_sets.natural_numbers.natural_pos_lower_bound |
172 | instantiation | 180, 181, 182 | ⊢ |
| : , : , : |
173 | instantiation | 208, 183, 184 | ⊢ |
| : , : , : |
174 | conjecture | | ⊢ |
| proveit.numbers.number_sets.complex_numbers.real_nonzero_within_complex_nonzero |
175 | instantiation | 208, 185, 186 | ⊢ |
| : , : , : |
176 | instantiation | 208, 197, 187 | ⊢ |
| : , : , : |
177 | conjecture | | ⊢ |
| proveit.numbers.number_sets.natural_numbers.nonzero_if_is_nat_pos |
178 | conjecture | | ⊢ |
| proveit.numbers.exponentiation.complex_x_to_first_power_is_x |
179 | instantiation | 208, 188, 189 | ⊢ |
| : , : , : |
180 | theorem | | ⊢ |
| proveit.logic.sets.inclusion.unfold_subset_eq |
181 | instantiation | 190, 191 | ⊢ |
| : , : |
182 | axiom | | ⊢ |
| proveit.physics.quantum.QPE._t_in_natural_pos |
183 | conjecture | | ⊢ |
| proveit.numbers.number_sets.real_numbers.real_neg_within_real |
184 | instantiation | 208, 192, 193 | ⊢ |
| : , : , : |
185 | conjecture | | ⊢ |
| proveit.numbers.number_sets.real_numbers.rational_nonzero_within_real_nonzero |
186 | instantiation | 208, 194, 195 | ⊢ |
| : , : , : |
187 | instantiation | 208, 204, 196 | ⊢ |
| : , : , : |
188 | conjecture | | ⊢ |
| proveit.numbers.number_sets.complex_numbers.real_within_complex |
189 | instantiation | 208, 197, 198 | ⊢ |
| : , : , : |
190 | theorem | | ⊢ |
| proveit.logic.sets.inclusion.relax_proper_subset |
191 | conjecture | | ⊢ |
| proveit.numbers.number_sets.real_numbers.nat_pos_within_real |
192 | conjecture | | ⊢ |
| proveit.numbers.number_sets.real_numbers.rational_neg_within_real_neg |
193 | instantiation | 208, 199, 200 | ⊢ |
| : , : , : |
194 | conjecture | | ⊢ |
| proveit.numbers.number_sets.rational_numbers.nonzero_int_within_rational_nonzero |
195 | instantiation | 208, 201, 202 | ⊢ |
| : , : , : |
196 | instantiation | 208, 209, 203 | ⊢ |
| : , : , : |
197 | conjecture | | ⊢ |
| proveit.numbers.number_sets.real_numbers.rational_within_real |
198 | instantiation | 208, 204, 205 | ⊢ |
| : , : , : |
199 | conjecture | | ⊢ |
| proveit.numbers.number_sets.rational_numbers.neg_int_within_rational_neg |
200 | instantiation | 206, 207 | ⊢ |
| : |
201 | conjecture | | ⊢ |
| proveit.numbers.number_sets.integers.nat_pos_within_nonzero_int |
202 | conjecture | | ⊢ |
| proveit.numbers.numerals.decimals.posnat2 |
203 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.nat1 |
204 | conjecture | | ⊢ |
| proveit.numbers.number_sets.rational_numbers.int_within_rational |
205 | instantiation | 208, 209, 210 | ⊢ |
| : , : , : |
206 | conjecture | | ⊢ |
| proveit.numbers.negation.int_neg_closure |
207 | conjecture | | ⊢ |
| proveit.numbers.numerals.decimals.posnat1 |
208 | theorem | | ⊢ |
| proveit.logic.sets.inclusion.superset_membership_from_proper_subset |
209 | conjecture | | ⊢ |
| proveit.numbers.number_sets.integers.nat_within_int |
210 | conjecture | | ⊢ |
| proveit.numbers.numerals.decimals.nat2 |
*equality replacement requirements |