| step type | requirements | statement |
0 | instantiation | 1, 2, 3, 4, 5 | ⊢ |
| : , : , : , : |
1 | theorem | | ⊢ |
| proveit.numbers.number_sets.integers.interval_subset_eq |
2 | instantiation | 252, 80, 249 | ⊢ |
| : , : |
3 | instantiation | 252, 228, 249 | ⊢ |
| : , : |
4 | reference | 253 | ⊢ |
5 | instantiation | 6, 185, 7, 8, 9, 10 | ⊢ |
| : , : |
6 | theorem | | ⊢ |
| proveit.logic.booleans.conjunction.and_if_all |
7 | instantiation | 196 | ⊢ |
| : , : , : |
8 | instantiation | 11, 12, 13 | ⊢ |
| : , : , : |
9 | instantiation | 64, 231, 210, 14, 15, 16* | ⊢ |
| : , : , : |
10 | instantiation | 17, 18, 19 | ⊢ |
| : , : |
11 | theorem | | ⊢ |
| proveit.numbers.ordering.transitivity_less_eq_less_eq |
12 | instantiation | 64, 20, 210, 29, 30, 21*, 22* | ⊢ |
| : , : , : |
13 | instantiation | 64, 94, 23, 24, 25, 26*, 27* | ⊢ |
| : , : , : |
14 | instantiation | 114, 29, 231 | ⊢ |
| : , : |
15 | instantiation | 28, 210, 29, 231, 30, 31 | ⊢ |
| : , : , : |
16 | instantiation | 180, 32, 163, 33 | ⊢ |
| : , : , : , : |
17 | theorem | | ⊢ |
| proveit.numbers.ordering.relax_equal_to_less_eq |
18 | instantiation | 235, 236, 258 | ⊢ |
| : , : , : |
19 | instantiation | 176 | ⊢ |
| : |
20 | instantiation | 34, 185, 35, 36, 231, 115 | ⊢ |
| : , : |
21 | instantiation | 180, 37, 38, 39 | ⊢ |
| : , : , : , : |
22 | instantiation | 192, 40 | ⊢ |
| : , : |
23 | instantiation | 132, 244, 65 | ⊢ |
| : , : |
24 | instantiation | 114, 116, 244 | ⊢ |
| : , : |
25 | instantiation | 41, 42, 43, 260, 44, 45 | ⊢ |
| : , : , : |
26 | instantiation | 192, 46 | ⊢ |
| : , : |
27 | instantiation | 180, 47, 48, 49 | ⊢ |
| : , : , : , : |
28 | theorem | | ⊢ |
| proveit.numbers.ordering.less_eq_add_right |
29 | instantiation | 261, 250, 50 | ⊢ |
| : , : , : |
30 | instantiation | 51, 249, 248, 239 | ⊢ |
| : , : , : |
31 | instantiation | 87, 255 | ⊢ |
| : |
32 | instantiation | 158, 52, 53 | ⊢ |
| : , : , : |
33 | instantiation | 192, 170 | ⊢ |
| : , : |
34 | theorem | | ⊢ |
| proveit.numbers.addition.add_real_closure |
35 | instantiation | 196 | ⊢ |
| : , : , : |
36 | instantiation | 261, 250, 54 | ⊢ |
| : , : , : |
37 | instantiation | 158, 55, 56 | ⊢ |
| : , : , : |
38 | instantiation | 176 | ⊢ |
| : |
39 | instantiation | 192, 57 | ⊢ |
| : , : |
40 | instantiation | 180, 69, 58, 59 | ⊢ |
| : , : , : , : |
41 | theorem | | ⊢ |
| proveit.numbers.ordering.less_add_right_weak_int |
42 | instantiation | 261, 262, 60 | ⊢ |
| : , : , : |
43 | instantiation | 261, 262, 61 | ⊢ |
| : , : , : |
44 | instantiation | 62, 244, 65, 210, 127, 63 | ⊢ |
| : , : , : |
45 | instantiation | 64, 203, 65, 111, 66, 67*, 68* | ⊢ |
| : , : , : |
46 | instantiation | 180, 69, 70, 71 | ⊢ |
| : , : , : , : |
47 | instantiation | 172, 173, 263, 255, 175, 73, 97, 234, 72 | ⊢ |
| : , : , : , : , : , : |
48 | instantiation | 172, 263, 173, 73, 151, 175, 97, 234, 188, 201 | ⊢ |
| : , : , : , : , : , : |
49 | instantiation | 180, 74, 75, 76 | ⊢ |
| : , : , : , : |
50 | instantiation | 261, 256, 248 | ⊢ |
| : , : , : |
51 | theorem | | ⊢ |
| proveit.numbers.number_sets.integers.interval_upper_bound |
52 | instantiation | 194, 77 | ⊢ |
| : , : , : |
53 | instantiation | 158, 78, 79 | ⊢ |
| : , : , : |
54 | instantiation | 261, 256, 80 | ⊢ |
| : , : , : |
55 | instantiation | 194, 138 | ⊢ |
| : , : , : |
56 | instantiation | 158, 81, 82 | ⊢ |
| : , : , : |
57 | instantiation | 194, 157 | ⊢ |
| : , : , : |
58 | instantiation | 200, 188, 201 | ⊢ |
| : , : |
59 | instantiation | 192, 83 | ⊢ |
| : , : |
60 | instantiation | 84, 263, 173 | ⊢ |
| : , : |
61 | instantiation | 84, 263, 85 | ⊢ |
| : , : |
62 | theorem | | ⊢ |
| proveit.numbers.multiplication.strong_bound_via_right_factor_bound |
63 | instantiation | 86, 241 | ⊢ |
| : |
64 | theorem | | ⊢ |
| proveit.numbers.addition.weak_bound_via_left_term_bound |
65 | theorem | | ⊢ |
| proveit.numbers.number_sets.real_numbers.zero_is_real |
66 | instantiation | 87, 185 | ⊢ |
| : |
67 | instantiation | 164, 88, 89 | ⊢ |
| : , : , : |
68 | instantiation | 169, 234, 223, 90, 91 | ⊢ |
| : , : , : |
69 | instantiation | 92, 198, 223 | ⊢ |
| : , : |
70 | instantiation | 176 | ⊢ |
| : |
71 | instantiation | 192, 93 | ⊢ |
| : , : |
72 | instantiation | 261, 243, 94 | ⊢ |
| : , : , : |
73 | instantiation | 189 | ⊢ |
| : , : |
74 | instantiation | 95, 255, 97, 234, 188, 201 | ⊢ |
| : , : , : , : , : , : , : |
75 | instantiation | 141, 173, 263, 175, 96, 154, 97, 188, 234, 201, 98* | ⊢ |
| : , : , : , : , : , : |
76 | instantiation | 141, 255, 263, 173, 154, 175, 198, 234, 201, 155* | ⊢ |
| : , : , : , : , : , : |
77 | instantiation | 158, 99, 100 | ⊢ |
| : , : , : |
78 | instantiation | 172, 173, 263, 255, 175, 101, 197, 201, 223 | ⊢ |
| : , : , : , : , : , : |
79 | instantiation | 102, 223, 197, 103 | ⊢ |
| : , : , : |
80 | instantiation | 259, 253 | ⊢ |
| : |
81 | instantiation | 172, 255, 185, 173, 186, 175, 198, 187, 223, 188 | ⊢ |
| : , : , : , : , : , : |
82 | instantiation | 161, 173, 263, 175, 104, 198, 187, 223, 105 | ⊢ |
| : , : , : , : , : , : , : , : |
83 | instantiation | 158, 106, 107 | ⊢ |
| : , : , : |
84 | theorem | | ⊢ |
| proveit.numbers.multiplication.mult_nat_closure_bin |
85 | instantiation | 108, 228, 109 | ⊢ |
| : |
86 | theorem | | ⊢ |
| proveit.numbers.number_sets.natural_numbers.natural_pos_is_pos |
87 | theorem | | ⊢ |
| proveit.numbers.number_sets.natural_numbers.natural_lower_bound |
88 | instantiation | 110, 201 | ⊢ |
| : |
89 | instantiation | 200, 201, 149 | ⊢ |
| : , : |
90 | instantiation | 261, 243, 111 | ⊢ |
| : , : , : |
91 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.add_2_1 |
92 | theorem | | ⊢ |
| proveit.numbers.negation.distribute_neg_through_binary_sum |
93 | instantiation | 158, 112, 113 | ⊢ |
| : , : , : |
94 | instantiation | 114, 115, 203 | ⊢ |
| : , : |
95 | theorem | | ⊢ |
| proveit.numbers.addition.leftward_commutation |
96 | instantiation | 189 | ⊢ |
| : , : |
97 | instantiation | 261, 243, 116 | ⊢ |
| : , : , : |
98 | instantiation | 158, 117, 118, 119* | ⊢ |
| : , : , : |
99 | instantiation | 194, 137 | ⊢ |
| : , : , : |
100 | instantiation | 158, 120, 121 | ⊢ |
| : , : , : |
101 | instantiation | 189 | ⊢ |
| : , : |
102 | theorem | | ⊢ |
| proveit.numbers.addition.subtraction.add_cancel_triple_32 |
103 | instantiation | 176 | ⊢ |
| : |
104 | instantiation | 189 | ⊢ |
| : , : |
105 | instantiation | 176 | ⊢ |
| : |
106 | instantiation | 158, 122, 123 | ⊢ |
| : , : , : |
107 | instantiation | 158, 124, 125 | ⊢ |
| : , : , : |
108 | theorem | | ⊢ |
| proveit.numbers.number_sets.integers.nonneg_int_is_natural |
109 | instantiation | 126, 127 | ⊢ |
| : , : |
110 | theorem | | ⊢ |
| proveit.numbers.addition.elim_zero_right |
111 | instantiation | 261, 250, 128 | ⊢ |
| : , : , : |
112 | instantiation | 194, 129 | ⊢ |
| : , : , : |
113 | instantiation | 158, 130, 131 | ⊢ |
| : , : , : |
114 | theorem | | ⊢ |
| proveit.numbers.addition.add_real_closure_bin |
115 | instantiation | 212, 210 | ⊢ |
| : |
116 | instantiation | 132, 244, 210 | ⊢ |
| : , : |
117 | instantiation | 194, 133 | ⊢ |
| : , : , : |
118 | instantiation | 192, 134 | ⊢ |
| : , : |
119 | instantiation | 158, 135, 136 | ⊢ |
| : , : , : |
120 | instantiation | 172, 173, 263, 255, 175, 174, 197, 179, 223 | ⊢ |
| : , : , : , : , : , : |
121 | instantiation | 141, 255, 263, 173, 142, 175, 197, 179, 223, 143* | ⊢ |
| : , : , : , : , : , : |
122 | instantiation | 194, 137 | ⊢ |
| : , : , : |
123 | instantiation | 194, 138 | ⊢ |
| : , : , : |
124 | instantiation | 158, 139, 140 | ⊢ |
| : , : , : |
125 | instantiation | 141, 173, 263, 255, 175, 142, 179, 223, 188, 143* | ⊢ |
| : , : , : , : , : , : |
126 | theorem | | ⊢ |
| proveit.numbers.ordering.relax_less |
127 | instantiation | 144, 145, 146 | ⊢ |
| : , : , : |
128 | instantiation | 261, 256, 147 | ⊢ |
| : , : , : |
129 | instantiation | 148, 234 | ⊢ |
| : |
130 | instantiation | 172, 255, 263, 173, 151, 175, 149, 188, 201 | ⊢ |
| : , : , : , : , : , : |
131 | instantiation | 150, 173, 263, 175, 151, 188, 201 | ⊢ |
| : , : , : , : |
132 | theorem | | ⊢ |
| proveit.numbers.multiplication.mult_real_closure_bin |
133 | instantiation | 192, 152 | ⊢ |
| : , : |
134 | instantiation | 153, 173, 263, 255, 175, 154, 234, 201, 198 | ⊢ |
| : , : , : , : , : , : |
135 | instantiation | 194, 155 | ⊢ |
| : , : , : |
136 | instantiation | 156, 198 | ⊢ |
| : |
137 | instantiation | 194, 170 | ⊢ |
| : , : , : |
138 | instantiation | 194, 157 | ⊢ |
| : , : , : |
139 | instantiation | 158, 159, 160 | ⊢ |
| : , : , : |
140 | instantiation | 161, 173, 255, 263, 175, 162, 197, 179, 223, 188, 163 | ⊢ |
| : , : , : , : , : , : , : , : |
141 | theorem | | ⊢ |
| proveit.numbers.addition.association |
142 | instantiation | 189 | ⊢ |
| : , : |
143 | instantiation | 164, 165, 166 | ⊢ |
| : , : , : |
144 | theorem | | ⊢ |
| proveit.numbers.ordering.transitivity_less_less_eq |
145 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.less_0_1 |
146 | instantiation | 167, 249, 248, 239 | ⊢ |
| : , : , : |
147 | instantiation | 261, 262, 185 | ⊢ |
| : , : , : |
148 | theorem | | ⊢ |
| proveit.numbers.multiplication.mult_zero_right |
149 | theorem | | ⊢ |
| proveit.numbers.number_sets.complex_numbers.zero_is_complex |
150 | theorem | | ⊢ |
| proveit.numbers.addition.elim_zero_any |
151 | instantiation | 189 | ⊢ |
| : , : |
152 | instantiation | 168, 198 | ⊢ |
| : |
153 | theorem | | ⊢ |
| proveit.numbers.multiplication.distribute_through_sum |
154 | instantiation | 189 | ⊢ |
| : , : |
155 | instantiation | 169, 223, 234, 178 | ⊢ |
| : , : , : |
156 | theorem | | ⊢ |
| proveit.numbers.multiplication.elim_one_left |
157 | instantiation | 194, 170 | ⊢ |
| : , : , : |
158 | axiom | | ⊢ |
| proveit.logic.equality.equals_transitivity |
159 | instantiation | 172, 173, 263, 255, 175, 174, 197, 179, 171 | ⊢ |
| : , : , : , : , : , : |
160 | instantiation | 172, 263, 185, 173, 174, 186, 175, 197, 179, 187, 223, 188 | ⊢ |
| : , : , : , : , : , : |
161 | theorem | | ⊢ |
| proveit.numbers.addition.subtraction.add_cancel_general |
162 | instantiation | 189 | ⊢ |
| : , : |
163 | instantiation | 176 | ⊢ |
| : |
164 | theorem | | ⊢ |
| proveit.logic.equality.sub_right_side_into |
165 | instantiation | 177, 223, 234, 178 | ⊢ |
| : , : , : |
166 | instantiation | 200, 223, 179 | ⊢ |
| : , : |
167 | theorem | | ⊢ |
| proveit.numbers.number_sets.integers.interval_lower_bound |
168 | theorem | | ⊢ |
| proveit.numbers.negation.mult_neg_one_left |
169 | theorem | | ⊢ |
| proveit.numbers.addition.subtraction.subtract_from_add |
170 | instantiation | 180, 181, 182, 183 | ⊢ |
| : , : , : , : |
171 | instantiation | 184, 185, 186, 187, 223, 188 | ⊢ |
| : , : |
172 | theorem | | ⊢ |
| proveit.numbers.addition.disassociation |
173 | axiom | | ⊢ |
| proveit.numbers.number_sets.natural_numbers.zero_in_nats |
174 | instantiation | 189 | ⊢ |
| : , : |
175 | theorem | | ⊢ |
| proveit.core_expr_types.tuples.tuple_len_0_typical_eq |
176 | axiom | | ⊢ |
| proveit.logic.equality.equals_reflexivity |
177 | theorem | | ⊢ |
| proveit.numbers.addition.subtraction.subtract_from_add_reversed |
178 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.add_1_1 |
179 | instantiation | 261, 243, 190 | ⊢ |
| : , : , : |
180 | theorem | | ⊢ |
| proveit.logic.equality.four_chain_transitivity |
181 | instantiation | 194, 191 | ⊢ |
| : , : , : |
182 | instantiation | 192, 193 | ⊢ |
| : , : |
183 | instantiation | 194, 195 | ⊢ |
| : , : , : |
184 | theorem | | ⊢ |
| proveit.numbers.addition.add_complex_closure |
185 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.nat3 |
186 | instantiation | 196 | ⊢ |
| : , : , : |
187 | instantiation | 211, 197 | ⊢ |
| : |
188 | instantiation | 211, 198 | ⊢ |
| : |
189 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.tuple_len_2_typical_eq |
190 | instantiation | 261, 250, 199 | ⊢ |
| : , : , : |
191 | instantiation | 200, 218, 201 | ⊢ |
| : , : |
192 | theorem | | ⊢ |
| proveit.logic.equality.equals_reversal |
193 | instantiation | 202, 234, 203, 227, 225 | ⊢ |
| : , : , : |
194 | axiom | | ⊢ |
| proveit.logic.equality.substitution |
195 | instantiation | 204, 205, 206 | ⊢ |
| : , : |
196 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.tuple_len_3_typical_eq |
197 | instantiation | 207, 208, 209 | ⊢ |
| : , : |
198 | instantiation | 261, 243, 210 | ⊢ |
| : , : , : |
199 | instantiation | 261, 256, 254 | ⊢ |
| : , : , : |
200 | theorem | | ⊢ |
| proveit.numbers.addition.commutation |
201 | instantiation | 211, 223 | ⊢ |
| : |
202 | theorem | | ⊢ |
| proveit.numbers.exponentiation.product_of_real_powers |
203 | instantiation | 212, 231 | ⊢ |
| : |
204 | theorem | | ⊢ |
| proveit.numbers.exponentiation.neg_power_as_div |
205 | instantiation | 261, 213, 214 | ⊢ |
| : , : , : |
206 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.posnat1 |
207 | theorem | | ⊢ |
| proveit.numbers.multiplication.mult_complex_closure_bin |
208 | instantiation | 215, 223, 216, 217 | ⊢ |
| : , : |
209 | instantiation | 222, 234, 218 | ⊢ |
| : , : |
210 | instantiation | 261, 250, 219 | ⊢ |
| : , : , : |
211 | theorem | | ⊢ |
| proveit.numbers.negation.complex_closure |
212 | theorem | | ⊢ |
| proveit.numbers.negation.real_closure |
213 | theorem | | ⊢ |
| proveit.numbers.number_sets.complex_numbers.real_nonzero_within_complex_nonzero |
214 | instantiation | 261, 220, 221 | ⊢ |
| : , : , : |
215 | theorem | | ⊢ |
| proveit.numbers.division.div_complex_closure |
216 | instantiation | 222, 234, 223 | ⊢ |
| : , : |
217 | instantiation | 224, 225, 226 | ⊢ |
| : , : , : |
218 | instantiation | 261, 243, 227 | ⊢ |
| : , : , : |
219 | instantiation | 261, 256, 228 | ⊢ |
| : , : , : |
220 | theorem | | ⊢ |
| proveit.numbers.number_sets.real_numbers.rational_nonzero_within_real_nonzero |
221 | instantiation | 261, 229, 230 | ⊢ |
| : , : , : |
222 | theorem | | ⊢ |
| proveit.numbers.exponentiation.exp_complex_closure |
223 | instantiation | 261, 243, 231 | ⊢ |
| : , : , : |
224 | theorem | | ⊢ |
| proveit.logic.equality.sub_left_side_into |
225 | instantiation | 232, 241 | ⊢ |
| : |
226 | instantiation | 233, 234 | ⊢ |
| : |
227 | instantiation | 235, 236, 237 | ⊢ |
| : , : , : |
228 | instantiation | 261, 238, 239 | ⊢ |
| : , : , : |
229 | theorem | | ⊢ |
| proveit.numbers.number_sets.rational_numbers.nonzero_int_within_rational_nonzero |
230 | instantiation | 261, 240, 241 | ⊢ |
| : , : , : |
231 | instantiation | 261, 250, 242 | ⊢ |
| : , : , : |
232 | theorem | | ⊢ |
| proveit.numbers.number_sets.natural_numbers.nonzero_if_is_nat_pos |
233 | theorem | | ⊢ |
| proveit.numbers.exponentiation.complex_x_to_first_power_is_x |
234 | instantiation | 261, 243, 244 | ⊢ |
| : , : , : |
235 | theorem | | ⊢ |
| proveit.logic.sets.inclusion.unfold_subset_eq |
236 | instantiation | 245, 246 | ⊢ |
| : , : |
237 | axiom | | ⊢ |
| proveit.physics.quantum.QPE._t_in_natural_pos |
238 | instantiation | 247, 249, 248 | ⊢ |
| : , : |
239 | assumption | | ⊢ |
240 | theorem | | ⊢ |
| proveit.numbers.number_sets.integers.nat_pos_within_nonzero_int |
241 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.posnat2 |
242 | instantiation | 261, 256, 249 | ⊢ |
| : , : , : |
243 | theorem | | ⊢ |
| proveit.numbers.number_sets.complex_numbers.real_within_complex |
244 | instantiation | 261, 250, 251 | ⊢ |
| : , : , : |
245 | theorem | | ⊢ |
| proveit.logic.sets.inclusion.relax_proper_subset |
246 | theorem | | ⊢ |
| proveit.numbers.number_sets.real_numbers.nat_pos_within_real |
247 | theorem | | ⊢ |
| proveit.numbers.number_sets.integers.int_interval_within_int |
248 | instantiation | 252, 253, 254 | ⊢ |
| : , : |
249 | instantiation | 261, 262, 255 | ⊢ |
| : , : , : |
250 | theorem | | ⊢ |
| proveit.numbers.number_sets.real_numbers.rational_within_real |
251 | instantiation | 261, 256, 260 | ⊢ |
| : , : , : |
252 | theorem | | ⊢ |
| proveit.numbers.addition.add_int_closure_bin |
253 | instantiation | 261, 257, 258 | ⊢ |
| : , : , : |
254 | instantiation | 259, 260 | ⊢ |
| : |
255 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.nat1 |
256 | theorem | | ⊢ |
| proveit.numbers.number_sets.rational_numbers.int_within_rational |
257 | theorem | | ⊢ |
| proveit.numbers.number_sets.integers.nat_pos_within_int |
258 | theorem | | ⊢ |
| proveit.physics.quantum.QPE._two_pow_t_minus_one_is_nat_pos |
259 | theorem | | ⊢ |
| proveit.numbers.negation.int_closure |
260 | instantiation | 261, 262, 263 | ⊢ |
| : , : , : |
261 | theorem | | ⊢ |
| proveit.logic.sets.inclusion.superset_membership_from_proper_subset |
262 | theorem | | ⊢ |
| proveit.numbers.number_sets.integers.nat_within_int |
263 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.nat2 |
*equality replacement requirements |