| step type | requirements | statement |
0 | instantiation | 1, 2, 3, 4* | ⊢ |
| : , : , : |
1 | reference | 356 | ⊢ |
2 | instantiation | 356, 5, 6 | ⊢ |
| : , : , : |
3 | instantiation | 7, 384, 366, 8 | ⊢ |
| : , : , : , : |
4 | instantiation | 291, 9, 10 | ⊢ |
| : , : , : |
5 | instantiation | 356, 11, 12 | ⊢ |
| : , : , : |
6 | instantiation | 13, 338, 339, 14*, 15*, 16* | ⊢ |
| : , : , : , : |
7 | theorem | | ⊢ |
| proveit.numbers.summation.sum_split_first |
8 | instantiation | 356, 17, 18 | ⊢ |
| : , : , : |
9 | instantiation | 142, 19 | ⊢ |
| : , : , : |
10 | instantiation | 148, 402, 412, 331, 20, 332, 69, 21, 92, 22* | ⊢ |
| : , : , : , : , : , : |
11 | instantiation | 23, 24, 25 | ⊢ |
| : , : , : |
12 | instantiation | 26, 365, 404, 378, 27*, 28* | ⊢ |
| : , : , : , : , : |
13 | theorem | | ⊢ |
| proveit.numbers.summation.index_negate |
14 | instantiation | 176, 29 | ⊢ |
| : |
15 | instantiation | 30, 31, 370, 32* | ⊢ |
| : , : |
16 | instantiation | 33, 34, 402, 162* | , ⊢ |
| : , : |
17 | instantiation | 35, 343, 36, 380, 37, 392 | ⊢ |
| : , : , : |
18 | instantiation | 291, 38, 39 | ⊢ |
| : , : , : |
19 | instantiation | 291, 40, 41 | ⊢ |
| : , : , : |
20 | instantiation | 346 | ⊢ |
| : , : |
21 | instantiation | 42, 348, 180 | ⊢ |
| : , : |
22 | instantiation | 291, 43, 44 | ⊢ |
| : , : , : |
23 | theorem | | ⊢ |
| proveit.numbers.ordering.transitivity_less_eq_less_eq |
24 | instantiation | 47, 94, 45, 48, 46, 51 | ⊢ |
| : , : , : |
25 | instantiation | 47, 94, 48, 49, 50, 51 | ⊢ |
| : , : , : |
26 | theorem | | ⊢ |
| proveit.numbers.summation.index_shift |
27 | instantiation | 291, 52, 53 | ⊢ |
| : , : , : |
28 | instantiation | 291, 54, 55 | , ⊢ |
| : , : , : |
29 | instantiation | 410, 379, 56 | ⊢ |
| : , : , : |
30 | theorem | | ⊢ |
| proveit.numbers.negation.distribute_neg_through_binary_sum |
31 | instantiation | 410, 379, 57 | ⊢ |
| : , : , : |
32 | instantiation | 176, 61 | ⊢ |
| : |
33 | theorem | | ⊢ |
| proveit.numbers.exponentiation.even_pow_is_even_fn |
34 | instantiation | 410, 379, 276 | , ⊢ |
| : , : , : |
35 | theorem | | ⊢ |
| proveit.numbers.ordering.less_eq_add_right_strong |
36 | instantiation | 410, 388, 58 | ⊢ |
| : , : , : |
37 | instantiation | 318, 399, 400, 401 | ⊢ |
| : , : , : |
38 | instantiation | 118, 331, 412, 402, 332, 59, 61, 124, 370 | ⊢ |
| : , : , : , : , : , : |
39 | instantiation | 90, 402, 412, 331, 60, 332, 61, 124, 370, 62* | ⊢ |
| : , : , : , : , : , : |
40 | instantiation | 118, 402, 412, 331, 63, 332, 180, 92 | ⊢ |
| : , : , : , : , : , : |
41 | instantiation | 291, 64, 65 | ⊢ |
| : , : , : |
42 | theorem | | ⊢ |
| proveit.numbers.multiplication.mult_complex_closure_bin |
43 | instantiation | 311, 402, 412, 331, 66, 332, 69, 348, 180 | ⊢ |
| : , : , : , : , : , : |
44 | instantiation | 67, 331, 412, 402, 332, 68, 69, 348, 180, 70* | ⊢ |
| : , : , : , : , : , : |
45 | instantiation | 283, 72, 75 | ⊢ |
| : , : |
46 | instantiation | 71, 75, 72, 74, 73 | ⊢ |
| : , : , : |
47 | theorem | | ⊢ |
| proveit.numbers.multiplication.weak_bound_via_right_factor_bound |
48 | instantiation | 283, 74, 75 | ⊢ |
| : , : |
49 | instantiation | 283, 74, 76 | ⊢ |
| : , : |
50 | instantiation | 229, 74, 75, 76, 77 | ⊢ |
| : , : , : |
51 | instantiation | 287, 78 | ⊢ |
| : , : |
52 | instantiation | 118, 331, 412, 402, 332, 79, 80, 370, 312 | ⊢ |
| : , : , : , : , : , : |
53 | instantiation | 120, 370, 80, 122 | ⊢ |
| : , : , : |
54 | instantiation | 142, 81 | ⊢ |
| : , : , : |
55 | instantiation | 291, 82, 83 | , ⊢ |
| : , : , : |
56 | instantiation | 410, 388, 84 | ⊢ |
| : , : , : |
57 | instantiation | 410, 388, 85 | ⊢ |
| : , : , : |
58 | instantiation | 410, 396, 400 | ⊢ |
| : , : , : |
59 | instantiation | 346 | ⊢ |
| : , : |
60 | instantiation | 346 | ⊢ |
| : , : |
61 | instantiation | 410, 379, 86 | ⊢ |
| : , : , : |
62 | instantiation | 356, 87, 88 | ⊢ |
| : , : , : |
63 | instantiation | 346 | ⊢ |
| : , : |
64 | instantiation | 89, 402, 331, 332, 180, 92 | ⊢ |
| : , : , : , : , : , : , : |
65 | instantiation | 90, 331, 412, 402, 332, 91, 180, 92, 93* | ⊢ |
| : , : , : , : , : , : |
66 | instantiation | 346 | ⊢ |
| : , : |
67 | theorem | | ⊢ |
| proveit.numbers.multiplication.association |
68 | instantiation | 346 | ⊢ |
| : , : |
69 | instantiation | 410, 379, 94 | ⊢ |
| : , : , : |
70 | instantiation | 95, 370, 348, 96, 97, 98*, 99* | ⊢ |
| : , : , : , : |
71 | theorem | | ⊢ |
| proveit.numbers.addition.weak_bound_via_left_term_bound |
72 | modus ponens | 100, 101 | ⊢ |
73 | modus ponens | 102, 103 | ⊢ |
74 | modus ponens | 104, 105 | ⊢ |
75 | modus ponens | 106, 107 | ⊢ |
76 | modus ponens | 108, 109 | ⊢ |
77 | modus ponens | 110, 111 | ⊢ |
78 | instantiation | 112, 152 | ⊢ |
| : |
79 | instantiation | 346 | ⊢ |
| : , : |
80 | instantiation | 410, 379, 343 | ⊢ |
| : , : , : |
81 | instantiation | 113, 317, 114, 115, 116, 117 | ⊢ |
| : , : , : |
82 | instantiation | 118, 331, 412, 402, 332, 119, 121, 370, 312 | , ⊢ |
| : , : , : , : , : , : |
83 | instantiation | 120, 370, 121, 122 | , ⊢ |
| : , : , : |
84 | instantiation | 410, 396, 365 | ⊢ |
| : , : , : |
85 | instantiation | 410, 396, 354 | ⊢ |
| : , : , : |
86 | instantiation | 373, 374, 407 | ⊢ |
| : , : , : |
87 | instantiation | 123, 370, 348, 128 | ⊢ |
| : , : , : |
88 | instantiation | 369, 370, 124 | ⊢ |
| : , : |
89 | theorem | | ⊢ |
| proveit.numbers.addition.leftward_commutation |
90 | theorem | | ⊢ |
| proveit.numbers.addition.association |
91 | instantiation | 346 | ⊢ |
| : , : |
92 | instantiation | 410, 379, 125 | ⊢ |
| : , : , : |
93 | instantiation | 126, 127, 128* | ⊢ |
| : , : |
94 | instantiation | 410, 388, 129 | ⊢ |
| : , : , : |
95 | theorem | | ⊢ |
| proveit.numbers.division.prod_of_fracs |
96 | instantiation | 410, 187, 130 | ⊢ |
| : , : , : |
97 | instantiation | 410, 187, 131 | ⊢ |
| : , : , : |
98 | instantiation | 132, 348 | ⊢ |
| : |
99 | instantiation | 291, 133, 134 | ⊢ |
| : , : , : |
100 | instantiation | 239 | ⊢ |
| : , : , : |
101 | generalization | 135 | ⊢ |
102 | instantiation | 140 | ⊢ |
| : , : , : |
103 | generalization | 136 | ⊢ |
104 | instantiation | 239 | ⊢ |
| : , : , : |
105 | generalization | 137 | ⊢ |
106 | instantiation | 239 | ⊢ |
| : , : , : |
107 | generalization | 138 | ⊢ |
108 | instantiation | 239 | ⊢ |
| : , : , : |
109 | generalization | 139 | ⊢ |
110 | instantiation | 140 | ⊢ |
| : , : , : |
111 | generalization | 141 | ⊢ |
112 | theorem | | ⊢ |
| proveit.numbers.number_sets.rational_numbers.positive_if_in_rational_pos |
113 | theorem | | ⊢ |
| proveit.core_expr_types.tuples.tuple_eq_via_elem_eq |
114 | instantiation | 346 | ⊢ |
| : , : |
115 | instantiation | 346 | ⊢ |
| : , : |
116 | instantiation | 142, 143 | ⊢ |
| : , : , : |
117 | instantiation | 212 | ⊢ |
| : |
118 | theorem | | ⊢ |
| proveit.numbers.addition.disassociation |
119 | instantiation | 346 | ⊢ |
| : , : |
120 | theorem | | ⊢ |
| proveit.numbers.addition.subtraction.add_cancel_triple_23 |
121 | instantiation | 410, 379, 144 | , ⊢ |
| : , : , : |
122 | instantiation | 212 | ⊢ |
| : |
123 | theorem | | ⊢ |
| proveit.numbers.addition.subtraction.subtract_from_add_reversed |
124 | instantiation | 410, 379, 145 | ⊢ |
| : , : , : |
125 | instantiation | 256, 380, 146, 147 | ⊢ |
| : , : |
126 | theorem | | ⊢ |
| proveit.logic.equality.equals_reversal |
127 | instantiation | 148, 331, 412, 402, 332, 149, 370, 180, 150* | ⊢ |
| : , : , : , : , : , : |
128 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.add_1_1 |
129 | instantiation | 410, 151, 152 | ⊢ |
| : , : , : |
130 | instantiation | 410, 208, 153 | ⊢ |
| : , : , : |
131 | instantiation | 410, 208, 154 | ⊢ |
| : , : , : |
132 | theorem | | ⊢ |
| proveit.numbers.division.frac_one_denom |
133 | instantiation | 155, 412, 156, 157, 158, 159 | ⊢ |
| : , : , : , : |
134 | instantiation | 160, 161, 370, 162*, 163* | ⊢ |
| : , : , : |
135 | instantiation | 256, 380, 164, 165 | , ⊢ |
| : , : |
136 | instantiation | 166, 167, 213, 209, 168 | , ⊢ |
| : , : , : |
137 | instantiation | 256, 380, 169, 170 | , ⊢ |
| : , : |
138 | instantiation | 256, 380, 171, 172 | , ⊢ |
| : , : |
139 | instantiation | 256, 380, 173, 174 | , ⊢ |
| : , : |
140 | theorem | | ⊢ |
| proveit.numbers.summation.weak_summation_from_summands_bound |
141 | instantiation | 287, 175 | , ⊢ |
| : , : |
142 | axiom | | ⊢ |
| proveit.logic.equality.substitution |
143 | instantiation | 176, 370 | ⊢ |
| : |
144 | instantiation | 410, 388, 177 | , ⊢ |
| : , : , : |
145 | instantiation | 410, 388, 178 | ⊢ |
| : , : , : |
146 | instantiation | 275, 343, 412 | ⊢ |
| : , : |
147 | instantiation | 277, 179, 279 | ⊢ |
| : , : |
148 | theorem | | ⊢ |
| proveit.numbers.multiplication.distribute_through_sum |
149 | instantiation | 346 | ⊢ |
| : , : |
150 | instantiation | 185, 180 | ⊢ |
| : |
151 | theorem | | ⊢ |
| proveit.numbers.number_sets.rational_numbers.rational_pos_within_rational |
152 | instantiation | 181, 216, 182 | ⊢ |
| : , : |
153 | instantiation | 410, 296, 183 | ⊢ |
| : , : , : |
154 | instantiation | 410, 296, 184 | ⊢ |
| : , : , : |
155 | axiom | | ⊢ |
| proveit.core_expr_types.operations.operands_substitution |
156 | instantiation | 346 | ⊢ |
| : , : |
157 | instantiation | 346 | ⊢ |
| : , : |
158 | instantiation | 185, 348 | ⊢ |
| : |
159 | instantiation | 310, 186 | ⊢ |
| : |
160 | theorem | | ⊢ |
| proveit.numbers.division.frac_cancel_left |
161 | instantiation | 410, 187, 188 | ⊢ |
| : , : , : |
162 | instantiation | 310, 348 | ⊢ |
| : |
163 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.mult_2_2 |
164 | instantiation | 275, 242, 412 | , ⊢ |
| : , : |
165 | instantiation | 196, 189 | , ⊢ |
| : |
166 | theorem | | ⊢ |
| proveit.numbers.division.weak_div_from_denom_bound__all_pos |
167 | instantiation | 410, 190, 191 | ⊢ |
| : , : , : |
168 | instantiation | 192, 359, 242, 263, 193, 194 | , ⊢ |
| : , : , : |
169 | instantiation | 275, 263, 412 | , ⊢ |
| : , : |
170 | instantiation | 196, 195 | , ⊢ |
| : |
171 | instantiation | 275, 265, 412 | , ⊢ |
| : , : |
172 | instantiation | 196, 197 | , ⊢ |
| : |
173 | instantiation | 275, 220, 412 | , ⊢ |
| : , : |
174 | instantiation | 198, 236 | , ⊢ |
| : |
175 | instantiation | 199, 200, 201, 215, 202 | , ⊢ |
| : , : , : |
176 | theorem | | ⊢ |
| proveit.numbers.negation.double_negation |
177 | instantiation | 410, 396, 203 | , ⊢ |
| : , : , : |
178 | instantiation | 410, 396, 405 | ⊢ |
| : , : , : |
179 | instantiation | 410, 296, 204 | ⊢ |
| : , : , : |
180 | instantiation | 410, 379, 205 | ⊢ |
| : , : , : |
181 | theorem | | ⊢ |
| proveit.numbers.division.div_rational_pos_closure |
182 | instantiation | 410, 235, 206 | ⊢ |
| : , : , : |
183 | instantiation | 410, 316, 206 | ⊢ |
| : , : , : |
184 | instantiation | 410, 316, 395 | ⊢ |
| : , : , : |
185 | theorem | | ⊢ |
| proveit.numbers.multiplication.elim_one_left |
186 | instantiation | 410, 379, 207 | ⊢ |
| : , : , : |
187 | theorem | | ⊢ |
| proveit.numbers.number_sets.complex_numbers.real_nonzero_within_complex_nonzero |
188 | instantiation | 410, 208, 279 | ⊢ |
| : , : , : |
189 | instantiation | 410, 214, 209 | , ⊢ |
| : , : , : |
190 | theorem | | ⊢ |
| proveit.numbers.number_sets.real_numbers.rational_nonneg_within_real_nonneg |
191 | instantiation | 410, 210, 402 | ⊢ |
| : , : , : |
192 | theorem | | ⊢ |
| proveit.numbers.exponentiation.exp_even_neg_base_lesseq |
193 | instantiation | 237, 211, 280 | , ⊢ |
| : , : |
194 | instantiation | 212 | ⊢ |
| : |
195 | instantiation | 410, 214, 213 | , ⊢ |
| : , : , : |
196 | theorem | | ⊢ |
| proveit.numbers.number_sets.real_numbers.nonzero_if_in_real_nonzero |
197 | instantiation | 410, 214, 215 | , ⊢ |
| : , : , : |
198 | theorem | | ⊢ |
| proveit.numbers.number_sets.natural_numbers.nonzero_if_is_nat_pos |
199 | theorem | | ⊢ |
| proveit.numbers.division.strong_div_from_denom_bound__all_pos |
200 | instantiation | 410, 217, 216 | ⊢ |
| : , : , : |
201 | instantiation | 410, 217, 218 | , ⊢ |
| : , : , : |
202 | instantiation | 219, 359, 220, 265, 221, 222 | , ⊢ |
| : , : , : |
203 | instantiation | 410, 223, 224 | , ⊢ |
| : , : , : |
204 | instantiation | 410, 316, 377 | ⊢ |
| : , : , : |
205 | modus ponens | 225, 226 | ⊢ |
206 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.posnat4 |
207 | instantiation | 410, 388, 227 | ⊢ |
| : , : , : |
208 | theorem | | ⊢ |
| proveit.numbers.number_sets.real_numbers.rational_nonzero_within_real_nonzero |
209 | instantiation | 233, 242, 228 | , ⊢ |
| : |
210 | theorem | | ⊢ |
| proveit.numbers.number_sets.rational_numbers.nat_within_rational_nonneg |
211 | instantiation | 229, 263, 285, 342, 230, 231* | , ⊢ |
| : , : , : |
212 | axiom | | ⊢ |
| proveit.logic.equality.equals_reflexivity |
213 | instantiation | 233, 263, 232 | , ⊢ |
| : |
214 | theorem | | ⊢ |
| proveit.numbers.number_sets.real_numbers.real_pos_within_real_nonzero |
215 | instantiation | 233, 265, 234 | , ⊢ |
| : |
216 | instantiation | 410, 235, 395 | ⊢ |
| : , : , : |
217 | theorem | | ⊢ |
| proveit.numbers.number_sets.real_numbers.rational_pos_within_real_pos |
218 | instantiation | 410, 235, 236 | , ⊢ |
| : , : , : |
219 | theorem | | ⊢ |
| proveit.numbers.exponentiation.exp_pos_less |
220 | instantiation | 283, 284, 271 | , ⊢ |
| : , : |
221 | instantiation | 237, 269, 238 | , ⊢ |
| : , : |
222 | instantiation | 363, 317 | ⊢ |
| : |
223 | instantiation | 397, 384, 366 | ⊢ |
| : , : |
224 | assumption | | ⊢ |
225 | instantiation | 239 | ⊢ |
| : , : , : |
226 | generalization | 240 | ⊢ |
227 | instantiation | 410, 396, 241 | ⊢ |
| : , : , : |
228 | instantiation | 264, 242, 342, 243 | , ⊢ |
| : , : |
229 | theorem | | ⊢ |
| proveit.numbers.addition.weak_bound_via_right_term_bound |
230 | instantiation | 244, 271, 342, 305, 281, 245, 274*, 246* | ⊢ |
| : , : , : |
231 | instantiation | 368, 247 | , ⊢ |
| : |
232 | instantiation | 248, 302, 249, 280 | , ⊢ |
| : , : |
233 | theorem | | ⊢ |
| proveit.numbers.exponentiation.sqrd_pos_closure |
234 | instantiation | 250, 251 | , ⊢ |
| : , : |
235 | theorem | | ⊢ |
| proveit.numbers.number_sets.rational_numbers.nat_pos_within_rational_pos |
236 | instantiation | 252, 253, 412 | , ⊢ |
| : , : |
237 | theorem | | ⊢ |
| proveit.logic.booleans.conjunction.and_if_both |
238 | instantiation | 254, 284, 271, 285, 255 | , ⊢ |
| : , : , : |
239 | theorem | | ⊢ |
| proveit.numbers.summation.summation_real_closure |
240 | instantiation | 256, 380, 257, 258 | , ⊢ |
| : , : |
241 | instantiation | 410, 411, 259 | ⊢ |
| : , : , : |
242 | instantiation | 283, 263, 285 | , ⊢ |
| : , : |
243 | instantiation | 260, 261 | , ⊢ |
| : , : |
244 | theorem | | ⊢ |
| proveit.numbers.multiplication.reversed_weak_bound_via_right_factor_bound |
245 | instantiation | 287, 272 | ⊢ |
| : , : |
246 | instantiation | 262, 312 | ⊢ |
| : |
247 | instantiation | 410, 379, 263 | , ⊢ |
| : , : , : |
248 | theorem | | ⊢ |
| proveit.numbers.ordering.less_is_not_eq_int |
249 | theorem | | ⊢ |
| proveit.numbers.number_sets.integers.zero_is_int |
250 | theorem | | ⊢ |
| proveit.logic.equality.not_equals_symmetry |
251 | instantiation | 264, 342, 265, 266 | , ⊢ |
| : , : |
252 | theorem | | ⊢ |
| proveit.numbers.exponentiation.exp_natpos_closure |
253 | instantiation | 267, 268, 269 | , ⊢ |
| : |
254 | theorem | | ⊢ |
| proveit.numbers.addition.strong_bound_via_right_term_bound |
255 | instantiation | 270, 271, 305, 380, 307, 272, 273*, 274* | ⊢ |
| : , : , : |
256 | theorem | | ⊢ |
| proveit.numbers.division.div_real_closure |
257 | instantiation | 275, 276, 412 | , ⊢ |
| : , : |
258 | instantiation | 277, 278, 279 | , ⊢ |
| : , : |
259 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.nat4 |
260 | theorem | | ⊢ |
| proveit.numbers.addition.subtraction.neg_difference |
261 | instantiation | 391, 280, 281 | , ⊢ |
| : , : , : |
262 | theorem | | ⊢ |
| proveit.numbers.multiplication.mult_zero_right |
263 | instantiation | 410, 388, 282 | , ⊢ |
| : , : , : |
264 | theorem | | ⊢ |
| proveit.numbers.ordering.less_is_not_eq |
265 | instantiation | 283, 284, 285 | , ⊢ |
| : , : |
266 | instantiation | 308, 286 | , ⊢ |
| : , : |
267 | theorem | | ⊢ |
| proveit.numbers.number_sets.integers.nonneg_int_is_natural |
268 | instantiation | 403, 323, 378 | , ⊢ |
| : , : |
269 | instantiation | 287, 288 | , ⊢ |
| : , : |
270 | theorem | | ⊢ |
| proveit.numbers.multiplication.reversed_strong_bound_via_right_factor_bound |
271 | instantiation | 304, 380 | ⊢ |
| : |
272 | instantiation | 319, 387 | ⊢ |
| : |
273 | instantiation | 289, 370, 290* | ⊢ |
| : , : |
274 | instantiation | 291, 292, 293 | ⊢ |
| : , : , : |
275 | theorem | | ⊢ |
| proveit.numbers.exponentiation.exp_real_closure_nat_power |
276 | instantiation | 410, 388, 294 | , ⊢ |
| : , : , : |
277 | theorem | | ⊢ |
| proveit.numbers.exponentiation.exp_rational_non_zero__not_zero |
278 | instantiation | 410, 296, 295 | , ⊢ |
| : , : , : |
279 | instantiation | 410, 296, 297 | ⊢ |
| : , : , : |
280 | instantiation | 298, 299, 300 | , ⊢ |
| : , : , : |
281 | instantiation | 301, 342, 380, 326 | ⊢ |
| : , : , : |
282 | instantiation | 410, 396, 302 | , ⊢ |
| : , : , : |
283 | theorem | | ⊢ |
| proveit.numbers.addition.add_real_closure_bin |
284 | instantiation | 410, 388, 303 | , ⊢ |
| : , : , : |
285 | instantiation | 304, 305 | ⊢ |
| : |
286 | instantiation | 306, 307, 309 | , ⊢ |
| : , : , : |
287 | theorem | | ⊢ |
| proveit.numbers.ordering.relax_less |
288 | instantiation | 308, 309 | , ⊢ |
| : , : |
289 | theorem | | ⊢ |
| proveit.numbers.multiplication.mult_neg_left |
290 | instantiation | 310, 370 | ⊢ |
| : |
291 | axiom | | ⊢ |
| proveit.logic.equality.equals_transitivity |
292 | instantiation | 311, 402, 412, 331, 333, 332, 312, 334, 335 | ⊢ |
| : , : , : , : , : , : |
293 | instantiation | 313, 331, 412, 332, 333, 370, 334, 335, 314* | ⊢ |
| : , : , : , : , : |
294 | instantiation | 410, 396, 336 | , ⊢ |
| : , : , : |
295 | instantiation | 410, 316, 315 | , ⊢ |
| : , : , : |
296 | theorem | | ⊢ |
| proveit.numbers.number_sets.rational_numbers.nonzero_int_within_rational_nonzero |
297 | instantiation | 410, 316, 317 | ⊢ |
| : , : , : |
298 | theorem | | ⊢ |
| proveit.numbers.ordering.transitivity_less_eq_less |
299 | instantiation | 318, 338, 339, 322 | , ⊢ |
| : , : , : |
300 | instantiation | 319, 320 | ⊢ |
| : |
301 | theorem | | ⊢ |
| proveit.numbers.number_sets.real_numbers.interval_co_lower_bound |
302 | instantiation | 410, 321, 322 | , ⊢ |
| : , : , : |
303 | instantiation | 410, 396, 323 | , ⊢ |
| : , : , : |
304 | theorem | | ⊢ |
| proveit.numbers.negation.real_closure |
305 | instantiation | 324, 342, 380, 326 | ⊢ |
| : , : , : |
306 | axiom | | ⊢ |
| proveit.numbers.ordering.transitivity_less_less |
307 | instantiation | 325, 342, 380, 326 | ⊢ |
| : , : , : |
308 | theorem | | ⊢ |
| proveit.numbers.addition.subtraction.pos_difference |
309 | instantiation | 391, 327, 328 | , ⊢ |
| : , : , : |
310 | theorem | | ⊢ |
| proveit.numbers.multiplication.elim_one_right |
311 | theorem | | ⊢ |
| proveit.numbers.multiplication.disassociation |
312 | instantiation | 329, 370 | ⊢ |
| : |
313 | theorem | | ⊢ |
| proveit.numbers.multiplication.mult_neg_any |
314 | instantiation | 330, 331, 412, 332, 333, 334, 335 | ⊢ |
| : , : , : , : |
315 | instantiation | 383, 336, 337 | , ⊢ |
| : |
316 | theorem | | ⊢ |
| proveit.numbers.number_sets.integers.nat_pos_within_nonzero_int |
317 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.posnat2 |
318 | theorem | | ⊢ |
| proveit.numbers.number_sets.integers.interval_upper_bound |
319 | theorem | | ⊢ |
| proveit.numbers.number_sets.integers.negative_if_in_neg_int |
320 | instantiation | 394, 364 | ⊢ |
| : |
321 | instantiation | 397, 338, 339 | ⊢ |
| : , : |
322 | assumption | | ⊢ |
323 | instantiation | 410, 340, 345 | , ⊢ |
| : , : , : |
324 | theorem | | ⊢ |
| proveit.numbers.number_sets.real_numbers.all_in_interval_co__is__real |
325 | theorem | | ⊢ |
| proveit.numbers.number_sets.real_numbers.interval_co_upper_bound |
326 | theorem | | ⊢ |
| proveit.physics.quantum.QPE._scaled_delta_b_floor_in_interval |
327 | instantiation | 341, 380, 342, 343, 385, 344* | ⊢ |
| : , : , : |
328 | instantiation | 398, 365, 404, 345 | , ⊢ |
| : , : , : |
329 | theorem | | ⊢ |
| proveit.numbers.negation.complex_closure |
330 | theorem | | ⊢ |
| proveit.numbers.multiplication.elim_one_any |
331 | axiom | | ⊢ |
| proveit.numbers.number_sets.natural_numbers.zero_in_nats |
332 | theorem | | ⊢ |
| proveit.core_expr_types.tuples.tuple_len_0_typical_eq |
333 | instantiation | 346 | ⊢ |
| : , : |
334 | instantiation | 347, 348, 349 | ⊢ |
| : , : |
335 | instantiation | 410, 379, 350 | ⊢ |
| : , : , : |
336 | instantiation | 410, 351, 367 | , ⊢ |
| : , : , : |
337 | instantiation | 391, 352, 353 | , ⊢ |
| : , : , : |
338 | instantiation | 403, 354, 399 | ⊢ |
| : , : |
339 | instantiation | 408, 365 | ⊢ |
| : |
340 | instantiation | 397, 365, 404 | ⊢ |
| : , : |
341 | theorem | | ⊢ |
| proveit.numbers.addition.strong_bound_via_left_term_bound |
342 | theorem | | ⊢ |
| proveit.numbers.number_sets.real_numbers.zero_is_real |
343 | instantiation | 410, 388, 355 | ⊢ |
| : , : , : |
344 | instantiation | 356, 357, 358 | ⊢ |
| : , : , : |
345 | assumption | | ⊢ |
346 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.tuple_len_2_typical_eq |
347 | theorem | | ⊢ |
| proveit.numbers.exponentiation.exp_complex_closure |
348 | instantiation | 410, 379, 359 | ⊢ |
| : , : , : |
349 | instantiation | 410, 379, 360 | ⊢ |
| : , : , : |
350 | instantiation | 361, 362 | ⊢ |
| : |
351 | instantiation | 397, 365, 366 | ⊢ |
| : , : |
352 | instantiation | 363, 364 | ⊢ |
| : |
353 | instantiation | 398, 365, 366, 367 | , ⊢ |
| : , : , : |
354 | instantiation | 408, 404 | ⊢ |
| : |
355 | instantiation | 410, 396, 384 | ⊢ |
| : , : , : |
356 | theorem | | ⊢ |
| proveit.logic.equality.sub_right_side_into |
357 | instantiation | 368, 370 | ⊢ |
| : |
358 | instantiation | 369, 370, 371 | ⊢ |
| : , : |
359 | instantiation | 410, 388, 372 | ⊢ |
| : , : , : |
360 | instantiation | 373, 374, 375 | ⊢ |
| : , : , : |
361 | theorem | | ⊢ |
| proveit.physics.quantum.QPE._delta_b_is_real |
362 | theorem | | ⊢ |
| proveit.physics.quantum.QPE._best_floor_is_int |
363 | theorem | | ⊢ |
| proveit.numbers.number_sets.natural_numbers.natural_pos_is_pos |
364 | instantiation | 376, 377, 395 | ⊢ |
| : , : |
365 | instantiation | 403, 384, 399 | ⊢ |
| : , : |
366 | instantiation | 403, 404, 378 | ⊢ |
| : , : |
367 | assumption | | ⊢ |
368 | theorem | | ⊢ |
| proveit.numbers.addition.elim_zero_right |
369 | theorem | | ⊢ |
| proveit.numbers.addition.commutation |
370 | instantiation | 410, 379, 380 | ⊢ |
| : , : , : |
371 | theorem | | ⊢ |
| proveit.numbers.number_sets.complex_numbers.zero_is_complex |
372 | instantiation | 410, 396, 409 | ⊢ |
| : , : , : |
373 | theorem | | ⊢ |
| proveit.logic.sets.inclusion.unfold_subset_eq |
374 | instantiation | 381, 382 | ⊢ |
| : , : |
375 | axiom | | ⊢ |
| proveit.physics.quantum.QPE._t_in_natural_pos |
376 | theorem | | ⊢ |
| proveit.numbers.addition.add_nat_pos_closure_bin |
377 | instantiation | 383, 384, 385 | ⊢ |
| : |
378 | instantiation | 410, 386, 387 | ⊢ |
| : , : , : |
379 | theorem | | ⊢ |
| proveit.numbers.number_sets.complex_numbers.real_within_complex |
380 | instantiation | 410, 388, 389 | ⊢ |
| : , : , : |
381 | theorem | | ⊢ |
| proveit.logic.sets.inclusion.relax_proper_subset |
382 | theorem | | ⊢ |
| proveit.numbers.number_sets.real_numbers.nat_pos_within_real |
383 | theorem | | ⊢ |
| proveit.numbers.number_sets.integers.pos_int_is_natural_pos |
384 | instantiation | 410, 390, 401 | ⊢ |
| : , : , : |
385 | instantiation | 391, 392, 393 | ⊢ |
| : , : , : |
386 | theorem | | ⊢ |
| proveit.numbers.number_sets.integers.neg_int_within_int |
387 | instantiation | 394, 395 | ⊢ |
| : |
388 | theorem | | ⊢ |
| proveit.numbers.number_sets.real_numbers.rational_within_real |
389 | instantiation | 410, 396, 399 | ⊢ |
| : , : , : |
390 | instantiation | 397, 399, 400 | ⊢ |
| : , : |
391 | theorem | | ⊢ |
| proveit.numbers.ordering.transitivity_less_less_eq |
392 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.less_0_1 |
393 | instantiation | 398, 399, 400, 401 | ⊢ |
| : , : , : |
394 | theorem | | ⊢ |
| proveit.numbers.negation.int_neg_closure |
395 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.posnat1 |
396 | theorem | | ⊢ |
| proveit.numbers.number_sets.rational_numbers.int_within_rational |
397 | theorem | | ⊢ |
| proveit.numbers.number_sets.integers.int_interval_within_int |
398 | theorem | | ⊢ |
| proveit.numbers.number_sets.integers.interval_lower_bound |
399 | instantiation | 410, 411, 402 | ⊢ |
| : , : , : |
400 | instantiation | 403, 404, 405 | ⊢ |
| : , : |
401 | assumption | | ⊢ |
402 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.nat1 |
403 | theorem | | ⊢ |
| proveit.numbers.addition.add_int_closure_bin |
404 | instantiation | 410, 406, 407 | ⊢ |
| : , : , : |
405 | instantiation | 408, 409 | ⊢ |
| : |
406 | theorem | | ⊢ |
| proveit.numbers.number_sets.integers.nat_pos_within_int |
407 | theorem | | ⊢ |
| proveit.physics.quantum.QPE._two_pow_t_minus_one_is_nat_pos |
408 | theorem | | ⊢ |
| proveit.numbers.negation.int_closure |
409 | instantiation | 410, 411, 412 | ⊢ |
| : , : , : |
410 | theorem | | ⊢ |
| proveit.logic.sets.inclusion.superset_membership_from_proper_subset |
411 | theorem | | ⊢ |
| proveit.numbers.number_sets.integers.nat_within_int |
412 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.nat2 |
*equality replacement requirements |