| step type | requirements | statement |
0 | instantiation | 1, 2, 3 | ⊢ |
| : , : , : |
1 | conjecture | | ⊢ |
| proveit.numbers.ordering.transitivity_less_less_eq |
2 | instantiation | 4, 570, 5, 6, 7 | ⊢ |
| : , : , : |
3 | instantiation | 466, 8, 9 | ⊢ |
| : , : , : |
4 | conjecture | | ⊢ |
| proveit.numbers.addition.strong_bound_via_right_term_bound |
5 | instantiation | 566, 556 | ⊢ |
| : |
6 | instantiation | 566, 11 | ⊢ |
| : |
7 | instantiation | 10, 11, 556, 12 | ⊢ |
| : , : |
8 | instantiation | 200, 13, 14 | ⊢ |
| : , : , : |
9 | instantiation | 248, 591, 588, 524, 150, 525, 543, 551, 313, 15*, 29* | ⊢ |
| : , : , : , : , : , : |
10 | conjecture | | ⊢ |
| proveit.numbers.negation.negated_strong_bound |
11 | instantiation | 323, 556, 17 | ⊢ |
| : , : |
12 | instantiation | 16, 556, 17, 570, 18, 557, 164* | ⊢ |
| : , : , : |
13 | instantiation | 466, 19, 20 | ⊢ |
| : , : , : |
14 | instantiation | 203, 543, 277, 585 | ⊢ |
| : , : , : |
15 | instantiation | 231, 543, 551 | ⊢ |
| : , : |
16 | conjecture | | ⊢ |
| proveit.numbers.multiplication.strong_bound_via_right_factor_bound |
17 | instantiation | 351, 130, 49, 34 | ⊢ |
| : , : |
18 | instantiation | 21, 49, 130, 22, 23, 24* | ⊢ |
| : , : , : |
19 | instantiation | 466, 25, 26 | ⊢ |
| : , : , : |
20 | instantiation | 248, 591, 588, 524, 27, 525, 543, 171, 313, 28*, 29* | ⊢ |
| : , : , : , : , : , : |
21 | conjecture | | ⊢ |
| proveit.numbers.division.strong_div_from_numer_bound__pos_denom |
22 | instantiation | 200, 30, 31 | ⊢ |
| : , : , : |
23 | instantiation | 87, 74 | ⊢ |
| : |
24 | instantiation | 32, 33, 34 | ⊢ |
| : |
25 | instantiation | 200, 35, 36 | ⊢ |
| : , : , : |
26 | instantiation | 509, 37, 38, 39* | ⊢ |
| : , : , : |
27 | instantiation | 540 | ⊢ |
| : , : |
28 | instantiation | 231, 543, 171 | ⊢ |
| : , : |
29 | instantiation | 466, 40, 41 | ⊢ |
| : , : , : |
30 | instantiation | 405, 130, 569, 42, 43, 44*, 45* | ⊢ |
| : , : , : |
31 | instantiation | 466, 46, 47, 48* | ⊢ |
| : , : , : |
32 | conjecture | | ⊢ |
| proveit.numbers.division.frac_cancel_complete |
33 | instantiation | 589, 560, 49 | ⊢ |
| : , : , : |
34 | instantiation | 495, 50 | ⊢ |
| : |
35 | instantiation | 466, 51, 52 | ⊢ |
| : , : , : |
36 | instantiation | 143, 159, 160, 121 | ⊢ |
| : , : , : |
37 | instantiation | 507, 53 | ⊢ |
| : , : , : |
38 | instantiation | 426, 54 | ⊢ |
| : , : |
39 | instantiation | 509, 55, 242 | ⊢ |
| : , : , : |
40 | instantiation | 466, 56, 57 | ⊢ |
| : , : , : |
41 | instantiation | 411, 58, 59, 60 | ⊢ |
| : , : , : , : |
42 | instantiation | 409, 138, 556 | ⊢ |
| : , : |
43 | instantiation | 466, 61, 62 | ⊢ |
| : , : , : |
44 | instantiation | 509, 63, 64 | ⊢ |
| : , : , : |
45 | instantiation | 411, 65, 66, 67 | ⊢ |
| : , : , : , : |
46 | instantiation | 466, 68, 69 | ⊢ |
| : , : , : |
47 | instantiation | 248, 591, 588, 176, 551, 485, 522, 543, 70*, 71* | ⊢ |
| : , : , : , : , : , : |
48 | instantiation | 509, 72, 73 | ⊢ |
| : , : , : |
49 | instantiation | 341, 262, 588 | ⊢ |
| : , : |
50 | instantiation | 589, 505, 74 | ⊢ |
| : , : , : |
51 | instantiation | 466, 75, 76 | ⊢ |
| : , : , : |
52 | instantiation | 507, 77 | ⊢ |
| : , : , : |
53 | instantiation | 411, 78, 79, 80 | ⊢ |
| : , : , : , : |
54 | instantiation | 81, 543, 82, 309, 83, 163*, 84* | ⊢ |
| : , : , : , : |
55 | instantiation | 507, 467 | ⊢ |
| : , : , : |
56 | instantiation | 308, 522, 310, 309 | ⊢ |
| : , : , : , : , : |
57 | instantiation | 509, 85, 86 | ⊢ |
| : , : , : |
58 | instantiation | 507, 312 | ⊢ |
| : , : , : |
59 | instantiation | 507, 312 | ⊢ |
| : , : , : |
60 | instantiation | 269, 522 | ⊢ |
| : |
61 | instantiation | 87, 88 | ⊢ |
| : |
62 | instantiation | 248, 591, 588, 524, 89, 525, 543, 90, 522, 91*, 164* | ⊢ |
| : , : , : , : , : , : |
63 | instantiation | 451, 591, 588, 524, 96, 525, 92, 98, 522 | ⊢ |
| : , : , : , : , : , : |
64 | instantiation | 93, 524, 588, 525, 96, 98, 522 | ⊢ |
| : , : , : , : |
65 | instantiation | 451, 524, 588, 591, 525, 95, 106, 543, 94 | ⊢ |
| : , : , : , : , : , : |
66 | instantiation | 451, 588, 524, 95, 96, 525, 106, 543, 98, 522 | ⊢ |
| : , : , : , : , : , : |
67 | instantiation | 453, 591, 588, 97, 106, 543, 98, 522, 99* | ⊢ |
| : , : , : , : , : , : |
68 | instantiation | 426, 100 | ⊢ |
| : , : |
69 | instantiation | 248, 591, 588, 524, 176, 525, 245, 485, 522, 101* | ⊢ |
| : , : , : , : , : , : |
70 | instantiation | 509, 102, 103 | ⊢ |
| : , : , : |
71 | instantiation | 523, 591, 551, 543 | ⊢ |
| : , : , : , : |
72 | instantiation | 451, 524, 588, 525, 104, 176, 106, 485, 522 | ⊢ |
| : , : , : , : , : , : |
73 | instantiation | 453, 591, 588, 105, 106, 485, 522, 107* | ⊢ |
| : , : , : , : , : , : |
74 | instantiation | 363, 262, 108 | ⊢ |
| : |
75 | instantiation | 200, 109, 110 | ⊢ |
| : , : , : |
76 | instantiation | 453, 591, 588, 524, 111, 525, 522, 112, 113, 114* | ⊢ |
| : , : , : , : , : , : |
77 | instantiation | 509, 115, 116 | ⊢ |
| : , : , : |
78 | instantiation | 507, 117 | ⊢ |
| : , : , : |
79 | instantiation | 521, 524, 588, 591, 525, 118, 543, 120, 121 | ⊢ |
| : , : , : , : , : , : |
80 | instantiation | 216, 591, 588, 524, 119, 525, 543, 120, 121 | ⊢ |
| : , : , : , : , : , : |
81 | conjecture | | ⊢ |
| proveit.numbers.division.prod_of_fracs |
82 | instantiation | 244, 120, 121 | ⊢ |
| : , : |
83 | instantiation | 190, 123, 122 | ⊢ |
| : |
84 | instantiation | 361, 123 | ⊢ |
| : |
85 | instantiation | 507, 124 | ⊢ |
| : , : , : |
86 | instantiation | 507, 125 | ⊢ |
| : , : , : |
87 | conjecture | | ⊢ |
| proveit.numbers.number_sets.real_numbers.positive_if_in_real_pos |
88 | instantiation | 529, 546, 126 | ⊢ |
| : , : |
89 | instantiation | 540 | ⊢ |
| : , : |
90 | instantiation | 589, 560, 127 | ⊢ |
| : , : , : |
91 | instantiation | 509, 128, 129 | ⊢ |
| : , : , : |
92 | conjecture | | ⊢ |
| proveit.numbers.number_sets.complex_numbers.zero_is_complex |
93 | conjecture | | ⊢ |
| proveit.numbers.addition.elim_zero_any |
94 | instantiation | 589, 560, 130 | ⊢ |
| : , : , : |
95 | instantiation | 540 | ⊢ |
| : , : |
96 | instantiation | 540 | ⊢ |
| : , : |
97 | instantiation | 540 | ⊢ |
| : , : |
98 | instantiation | 589, 560, 169 | ⊢ |
| : , : , : |
99 | instantiation | 426, 131, 132* | ⊢ |
| : , : |
100 | instantiation | 241, 245, 583, 133*, 476* | ⊢ |
| : , : , : |
101 | instantiation | 509, 134, 135 | ⊢ |
| : , : , : |
102 | instantiation | 521, 591, 588, 222, 551, 543 | ⊢ |
| : , : , : , : , : , : |
103 | instantiation | 509, 136, 137 | ⊢ |
| : , : , : |
104 | instantiation | 540 | ⊢ |
| : , : |
105 | instantiation | 540 | ⊢ |
| : , : |
106 | instantiation | 589, 560, 138 | ⊢ |
| : , : , : |
107 | instantiation | 426, 139, 140* | ⊢ |
| : , : |
108 | instantiation | 495, 141 | ⊢ |
| : |
109 | instantiation | 466, 142, 227 | ⊢ |
| : , : , : |
110 | instantiation | 143, 144, 522, 145* | ⊢ |
| : , : , : |
111 | instantiation | 540 | ⊢ |
| : , : |
112 | instantiation | 589, 560, 146 | ⊢ |
| : , : , : |
113 | instantiation | 589, 560, 147 | ⊢ |
| : , : , : |
114 | instantiation | 466, 148, 149 | ⊢ |
| : , : , : |
115 | instantiation | 451, 524, 588, 591, 525, 150, 551, 313, 522 | ⊢ |
| : , : , : , : , : , : |
116 | instantiation | 509, 151, 152 | ⊢ |
| : , : , : |
117 | instantiation | 153, 546, 561, 570, 188, 154, 242* | ⊢ |
| : , : , : , : |
118 | instantiation | 540 | ⊢ |
| : , : |
119 | instantiation | 540 | ⊢ |
| : , : |
120 | instantiation | 542, 543, 155 | ⊢ |
| : , : |
121 | instantiation | 589, 560, 156 | ⊢ |
| : , : , : |
122 | instantiation | 157, 588, 158, 159, 160 | ⊢ |
| : , : |
123 | instantiation | 589, 560, 161 | ⊢ |
| : , : , : |
124 | instantiation | 509, 162, 163 | ⊢ |
| : , : , : |
125 | instantiation | 507, 164 | ⊢ |
| : , : , : |
126 | instantiation | 512, 165, 563 | ⊢ |
| : , : |
127 | instantiation | 589, 552, 165 | ⊢ |
| : , : , : |
128 | instantiation | 521, 591, 588, 524, 166, 525, 543, 218 | ⊢ |
| : , : , : , : , : , : |
129 | instantiation | 509, 167, 168 | ⊢ |
| : , : , : |
130 | instantiation | 409, 169, 570 | ⊢ |
| : , : |
131 | instantiation | 248, 524, 588, 591, 525, 170, 522, 171, 543, 191* | ⊢ |
| : , : , : , : , : , : |
132 | conjecture | | ⊢ |
| proveit.numbers.numerals.decimals.add_1_3 |
133 | instantiation | 550, 245 | ⊢ |
| : |
134 | instantiation | 205, 588, 172, 173, 174, 175 | ⊢ |
| : , : , : , : |
135 | instantiation | 451, 591, 588, 524, 176, 525, 177, 485, 522 | ⊢ |
| : , : , : , : , : , : |
136 | instantiation | 216, 524, 588, 525, 255, 217, 551, 543, 230* | ⊢ |
| : , : , : , : , : , : |
137 | instantiation | 216, 591, 588, 524, 217, 525, 218, 543, 219* | ⊢ |
| : , : , : , : , : , : |
138 | instantiation | 323, 320, 220 | ⊢ |
| : , : |
139 | instantiation | 248, 524, 588, 591, 525, 255, 551, 543 | ⊢ |
| : , : , : , : , : , : |
140 | conjecture | | ⊢ |
| proveit.numbers.numerals.decimals.add_2_2 |
141 | instantiation | 589, 505, 178 | ⊢ |
| : , : , : |
142 | instantiation | 200, 179, 180 | ⊢ |
| : , : , : |
143 | conjecture | | ⊢ |
| proveit.numbers.division.frac_cancel_left |
144 | instantiation | 589, 548, 293 | ⊢ |
| : , : , : |
145 | instantiation | 509, 181, 182 | ⊢ |
| : , : , : |
146 | instantiation | 566, 236 | ⊢ |
| : |
147 | instantiation | 566, 237 | ⊢ |
| : |
148 | instantiation | 426, 183 | ⊢ |
| : , : |
149 | instantiation | 507, 184 | ⊢ |
| : , : , : |
150 | instantiation | 540 | ⊢ |
| : , : |
151 | instantiation | 402, 591, 524, 525, 551, 313, 522 | ⊢ |
| : , : , : , : , : , : , : |
152 | instantiation | 453, 524, 588, 591, 525, 185, 551, 522, 313, 186* | ⊢ |
| : , : , : , : , : , : |
153 | conjecture | | ⊢ |
| proveit.numbers.exponentiation.exp_factored_real |
154 | instantiation | 426, 187 | ⊢ |
| : , : |
155 | instantiation | 589, 560, 188 | ⊢ |
| : , : , : |
156 | instantiation | 409, 195, 335 | ⊢ |
| : , : |
157 | conjecture | | ⊢ |
| proveit.numbers.multiplication.mult_not_eq_zero |
158 | instantiation | 540 | ⊢ |
| : , : |
159 | instantiation | 189, 310, 551 | ⊢ |
| : , : |
160 | instantiation | 190, 240, 259 | ⊢ |
| : |
161 | instantiation | 323, 220, 260 | ⊢ |
| : , : |
162 | instantiation | 507, 191 | ⊢ |
| : , : , : |
163 | instantiation | 350, 543 | ⊢ |
| : |
164 | instantiation | 269, 543 | ⊢ |
| : |
165 | instantiation | 529, 352, 546 | ⊢ |
| : , : |
166 | instantiation | 540 | ⊢ |
| : , : |
167 | instantiation | 509, 192, 193 | ⊢ |
| : , : , : |
168 | instantiation | 231, 194, 218 | ⊢ |
| : , : |
169 | instantiation | 323, 195, 556 | ⊢ |
| : , : |
170 | instantiation | 540 | ⊢ |
| : , : |
171 | instantiation | 589, 560, 195 | ⊢ |
| : , : , : |
172 | instantiation | 540 | ⊢ |
| : , : |
173 | instantiation | 540 | ⊢ |
| : , : |
174 | instantiation | 509, 196, 197 | ⊢ |
| : , : , : |
175 | instantiation | 269, 245 | ⊢ |
| : |
176 | instantiation | 540 | ⊢ |
| : , : |
177 | instantiation | 466, 198, 199 | ⊢ |
| : , : , : |
178 | instantiation | 512, 506, 563 | ⊢ |
| : , : |
179 | instantiation | 200, 201, 202 | ⊢ |
| : , : , : |
180 | instantiation | 203, 551, 204, 585 | ⊢ |
| : , : , : |
181 | instantiation | 205, 588, 206, 207, 208, 209 | ⊢ |
| : , : , : , : |
182 | instantiation | 507, 210 | ⊢ |
| : , : , : |
183 | instantiation | 211, 212, 213 | ⊢ |
| : , : |
184 | instantiation | 426, 214 | ⊢ |
| : , : |
185 | instantiation | 540 | ⊢ |
| : , : |
186 | conjecture | | ⊢ |
| proveit.numbers.numerals.decimals.add_2_1 |
187 | instantiation | 509, 215, 476 | ⊢ |
| : , : , : |
188 | instantiation | 409, 561, 554 | ⊢ |
| : , : |
189 | conjecture | | ⊢ |
| proveit.numbers.exponentiation.exp_complex_nonzero_closure |
190 | conjecture | | ⊢ |
| proveit.numbers.number_sets.complex_numbers.nonzero_complex_is_complex_nonzero |
191 | instantiation | 361, 543 | ⊢ |
| : |
192 | instantiation | 223, 591, 524, 525, 543, 218 | ⊢ |
| : , : , : , : , : , : , : |
193 | instantiation | 216, 524, 588, 591, 525, 217, 543, 218, 219* | ⊢ |
| : , : , : , : , : , : |
194 | instantiation | 589, 560, 220 | ⊢ |
| : , : , : |
195 | instantiation | 589, 579, 221 | ⊢ |
| : , : , : |
196 | instantiation | 521, 591, 588, 524, 222, 525, 245, 551, 543 | ⊢ |
| : , : , : , : , : , : |
197 | instantiation | 223, 524, 591, 525, 245, 551, 543 | ⊢ |
| : , : , : , : , : , : , : |
198 | instantiation | 244, 224, 543 | ⊢ |
| : , : |
199 | instantiation | 521, 524, 588, 591, 525, 225, 551, 245, 543 | ⊢ |
| : , : , : , : , : , : |
200 | theorem | | ⊢ |
| proveit.logic.equality.sub_left_side_into |
201 | instantiation | 466, 226, 227 | ⊢ |
| : , : , : |
202 | instantiation | 411, 228, 229, 230 | ⊢ |
| : , : , : , : |
203 | conjecture | | ⊢ |
| proveit.numbers.exponentiation.posnat_power_of_product |
204 | instantiation | 589, 560, 364 | ⊢ |
| : , : , : |
205 | axiom | | ⊢ |
| proveit.core_expr_types.operations.operands_substitution |
206 | instantiation | 540 | ⊢ |
| : , : |
207 | instantiation | 540 | ⊢ |
| : , : |
208 | instantiation | 231, 277, 522 | ⊢ |
| : , : |
209 | instantiation | 241, 277, 583, 232*, 476* | ⊢ |
| : , : , : |
210 | instantiation | 411, 233, 234, 235 | ⊢ |
| : , : , : , : |
211 | conjecture | | ⊢ |
| proveit.numbers.negation.distribute_neg_through_binary_sum |
212 | instantiation | 589, 560, 236 | ⊢ |
| : , : , : |
213 | instantiation | 589, 560, 237 | ⊢ |
| : , : , : |
214 | instantiation | 238, 585, 239, 277, 522, 240, 259 | ⊢ |
| : , : , : |
215 | instantiation | 507, 467 | ⊢ |
| : , : , : |
216 | conjecture | | ⊢ |
| proveit.numbers.multiplication.association |
217 | instantiation | 540 | ⊢ |
| : , : |
218 | instantiation | 589, 560, 320 | ⊢ |
| : , : , : |
219 | instantiation | 241, 543, 583, 242*, 476* | ⊢ |
| : , : , : |
220 | instantiation | 341, 556, 588 | ⊢ |
| : , : |
221 | instantiation | 589, 586, 243 | ⊢ |
| : , : , : |
222 | instantiation | 540 | ⊢ |
| : , : |
223 | conjecture | | ⊢ |
| proveit.numbers.multiplication.leftward_commutation |
224 | instantiation | 244, 551, 245 | ⊢ |
| : , : |
225 | instantiation | 540 | ⊢ |
| : , : |
226 | instantiation | 386, 246, 247 | ⊢ |
| : , : , : |
227 | instantiation | 248, 591, 588, 524, 249, 525, 551, 522, 404, 250*, 251* | ⊢ |
| : , : , : , : , : , : |
228 | instantiation | 252, 585, 551 | ⊢ |
| : , : |
229 | instantiation | 253, 588, 254, 255, 256 | ⊢ |
| : , : , : , : |
230 | conjecture | | ⊢ |
| proveit.numbers.numerals.decimals.mult_2_2 |
231 | conjecture | | ⊢ |
| proveit.numbers.multiplication.commutation |
232 | instantiation | 550, 277 | ⊢ |
| : |
233 | instantiation | 509, 257, 258 | ⊢ |
| : , : , : |
234 | instantiation | 462 | ⊢ |
| : |
235 | instantiation | 426, 274 | ⊢ |
| : , : |
236 | instantiation | 351, 292, 260, 259 | ⊢ |
| : , : |
237 | instantiation | 351, 570, 260, 259 | ⊢ |
| : , : |
238 | conjecture | | ⊢ |
| proveit.numbers.division.distribute_frac_through_sum |
239 | instantiation | 540 | ⊢ |
| : , : |
240 | instantiation | 589, 560, 260 | ⊢ |
| : , : , : |
241 | conjecture | | ⊢ |
| proveit.numbers.exponentiation.product_of_posnat_powers |
242 | instantiation | 550, 543 | ⊢ |
| : |
243 | instantiation | 589, 590, 261 | ⊢ |
| : , : , : |
244 | conjecture | | ⊢ |
| proveit.numbers.multiplication.mult_complex_closure_bin |
245 | instantiation | 589, 560, 262 | ⊢ |
| : , : , : |
246 | instantiation | 266, 588, 524, 263, 525, 570, 264, 265 | ⊢ |
| : , : , : , : , : , : |
247 | instantiation | 266, 591, 570, 267, 268 | ⊢ |
| : , : , : , : , : , : |
248 | conjecture | | ⊢ |
| proveit.numbers.multiplication.distribute_through_sum |
249 | instantiation | 540 | ⊢ |
| : , : |
250 | instantiation | 269, 551 | ⊢ |
| : |
251 | instantiation | 466, 270, 271 | ⊢ |
| : , : , : |
252 | conjecture | | ⊢ |
| proveit.numbers.exponentiation.exp_nat_pos_expansion |
253 | conjecture | | ⊢ |
| proveit.core_expr_types.operations.operands_substitution_via_tuple |
254 | instantiation | 272, 588 | ⊢ |
| : , : |
255 | instantiation | 540 | ⊢ |
| : , : |
256 | instantiation | 273 | ⊢ |
| : |
257 | instantiation | 507, 274 | ⊢ |
| : , : , : |
258 | instantiation | 361, 275 | ⊢ |
| : |
259 | instantiation | 276, 277, 551, 278 | ⊢ |
| : , : |
260 | instantiation | 341, 292, 588 | ⊢ |
| : , : |
261 | conjecture | | ⊢ |
| proveit.numbers.numerals.decimals.nat3 |
262 | instantiation | 409, 494, 570 | ⊢ |
| : , : |
263 | instantiation | 540 | ⊢ |
| : , : |
264 | instantiation | 566, 284 | ⊢ |
| : |
265 | instantiation | 282, 281, 279, 280 | ⊢ |
| : , : |
266 | conjecture | | ⊢ |
| proveit.numbers.addition.weak_bound_via_term_bound |
267 | instantiation | 566, 281 | ⊢ |
| : |
268 | instantiation | 282, 283, 284, 285 | ⊢ |
| : , : |
269 | conjecture | | ⊢ |
| proveit.numbers.multiplication.elim_one_right |
270 | instantiation | 466, 286, 287 | ⊢ |
| : , : , : |
271 | instantiation | 509, 288, 289 | ⊢ |
| : , : , : |
272 | conjecture | | ⊢ |
| proveit.core_expr_types.tuples.range_from1_len_typical_eq |
273 | conjecture | | ⊢ |
| proveit.numbers.numerals.decimals.reduce_2_repeats |
274 | instantiation | 507, 290 | ⊢ |
| : , : , : |
275 | instantiation | 291, 551, 528 | ⊢ |
| : , : |
276 | conjecture | | ⊢ |
| proveit.numbers.exponentiation.exp_not_eq_zero |
277 | instantiation | 589, 560, 292 | ⊢ |
| : , : , : |
278 | instantiation | 495, 293 | ⊢ |
| : |
279 | instantiation | 351, 570, 294, 295 | ⊢ |
| : , : |
280 | instantiation | 304, 305, 337, 296, 297 | ⊢ |
| : , : , : |
281 | instantiation | 351, 570, 298, 299 | ⊢ |
| : , : |
282 | conjecture | | ⊢ |
| proveit.numbers.negation.negated_weak_bound |
283 | instantiation | 351, 570, 300, 301 | ⊢ |
| : , : |
284 | instantiation | 351, 570, 302, 303 | ⊢ |
| : , : |
285 | instantiation | 304, 305, 345, 306, 307 | ⊢ |
| : , : , : |
286 | instantiation | 308, 522, 538, 309, 310 | ⊢ |
| : , : , : , : , : |
287 | instantiation | 507, 311 | ⊢ |
| : , : , : |
288 | instantiation | 507, 312 | ⊢ |
| : , : , : |
289 | instantiation | 361, 313 | ⊢ |
| : |
290 | instantiation | 484, 522, 543, 519, 314* | ⊢ |
| : , : |
291 | conjecture | | ⊢ |
| proveit.numbers.addition.add_complex_closure_bin |
292 | instantiation | 409, 561, 335 | ⊢ |
| : , : |
293 | instantiation | 589, 505, 315 | ⊢ |
| : , : , : |
294 | instantiation | 323, 320, 317 | ⊢ |
| : , : |
295 | instantiation | 495, 316 | ⊢ |
| : |
296 | instantiation | 589, 576, 342 | ⊢ |
| : , : , : |
297 | instantiation | 329, 320, 317, 321, 318, 319 | ⊢ |
| : , : , : |
298 | instantiation | 323, 320, 321 | ⊢ |
| : , : |
299 | instantiation | 324, 322 | ⊢ |
| : |
300 | instantiation | 323, 561, 418 | ⊢ |
| : , : |
301 | instantiation | 324, 325 | ⊢ |
| : |
302 | instantiation | 589, 552, 345 | ⊢ |
| : , : , : |
303 | instantiation | 495, 326 | ⊢ |
| : |
304 | conjecture | | ⊢ |
| proveit.numbers.division.weak_div_from_denom_bound__all_pos |
305 | instantiation | 589, 327, 328 | ⊢ |
| : , : , : |
306 | instantiation | 589, 576, 344 | ⊢ |
| : , : , : |
307 | instantiation | 329, 561, 364, 418, 356, 330 | ⊢ |
| : , : , : |
308 | conjecture | | ⊢ |
| proveit.numbers.division.mult_frac_cancel_numer_left |
309 | instantiation | 589, 548, 331 | ⊢ |
| : , : , : |
310 | instantiation | 589, 548, 332 | ⊢ |
| : , : , : |
311 | instantiation | 509, 333, 334 | ⊢ |
| : , : , : |
312 | instantiation | 350, 522 | ⊢ |
| : |
313 | instantiation | 589, 560, 335 | ⊢ |
| : , : , : |
314 | instantiation | 361, 528 | ⊢ |
| : |
315 | instantiation | 512, 564, 336 | ⊢ |
| : , : |
316 | instantiation | 589, 505, 337 | ⊢ |
| : , : , : |
317 | instantiation | 341, 364, 588 | ⊢ |
| : , : |
318 | instantiation | 338, 561, 364, 418, 339, 420 | ⊢ |
| : , : , : |
319 | instantiation | 347, 371 | ⊢ |
| : |
320 | instantiation | 589, 579, 340 | ⊢ |
| : , : , : |
321 | instantiation | 341, 418, 588 | ⊢ |
| : , : |
322 | instantiation | 589, 343, 342 | ⊢ |
| : , : , : |
323 | conjecture | | ⊢ |
| proveit.numbers.multiplication.mult_real_closure_bin |
324 | conjecture | | ⊢ |
| proveit.numbers.number_sets.rational_numbers.nonzero_if_in_rational_nonzero |
325 | instantiation | 589, 343, 344 | ⊢ |
| : , : , : |
326 | instantiation | 589, 505, 345 | ⊢ |
| : , : , : |
327 | conjecture | | ⊢ |
| proveit.numbers.number_sets.real_numbers.rational_nonneg_within_real_nonneg |
328 | instantiation | 589, 346, 591 | ⊢ |
| : , : , : |
329 | conjecture | | ⊢ |
| proveit.numbers.multiplication.weak_bound_via_right_factor_bound |
330 | instantiation | 347, 588 | ⊢ |
| : |
331 | instantiation | 589, 558, 348 | ⊢ |
| : , : , : |
332 | instantiation | 589, 505, 546 | ⊢ |
| : , : , : |
333 | instantiation | 507, 349 | ⊢ |
| : , : , : |
334 | instantiation | 350, 551 | ⊢ |
| : |
335 | instantiation | 351, 570, 556, 519 | ⊢ |
| : , : |
336 | instantiation | 562, 563, 546, 519 | ⊢ |
| : , : |
337 | instantiation | 529, 352, 353 | ⊢ |
| : , : |
338 | conjecture | | ⊢ |
| proveit.numbers.exponentiation.exp_pos_lesseq |
339 | instantiation | 354, 355, 356 | ⊢ |
| : , : |
340 | instantiation | 589, 586, 357 | ⊢ |
| : , : , : |
341 | conjecture | | ⊢ |
| proveit.numbers.exponentiation.exp_real_closure_nat_power |
342 | instantiation | 359, 362, 358 | ⊢ |
| : , : |
343 | conjecture | | ⊢ |
| proveit.numbers.number_sets.rational_numbers.rational_pos_within_rational_nonzero |
344 | instantiation | 359, 577, 373 | ⊢ |
| : , : |
345 | instantiation | 529, 564, 385 | ⊢ |
| : , : |
346 | conjecture | | ⊢ |
| proveit.numbers.number_sets.rational_numbers.nat_within_rational_nonneg |
347 | conjecture | | ⊢ |
| proveit.numbers.number_sets.natural_numbers.natural_lower_bound |
348 | instantiation | 589, 572, 360 | ⊢ |
| : , : , : |
349 | instantiation | 361, 551 | ⊢ |
| : |
350 | conjecture | | ⊢ |
| proveit.numbers.division.frac_one_denom |
351 | conjecture | | ⊢ |
| proveit.numbers.division.div_real_closure |
352 | instantiation | 589, 576, 362 | ⊢ |
| : , : , : |
353 | instantiation | 363, 364, 365 | ⊢ |
| : |
354 | theorem | | ⊢ |
| proveit.logic.booleans.conjunction.and_if_both |
355 | instantiation | 366, 367 | ⊢ |
| : |
356 | instantiation | 396, 554, 368, 465, 369, 370* | ⊢ |
| : , : , : |
357 | instantiation | 589, 590, 371 | ⊢ |
| : , : , : |
358 | instantiation | 372, 373, 582 | ⊢ |
| : , : |
359 | conjecture | | ⊢ |
| proveit.numbers.multiplication.mult_rational_pos_closure_bin |
360 | instantiation | 589, 581, 583 | ⊢ |
| : , : , : |
361 | conjecture | | ⊢ |
| proveit.numbers.multiplication.elim_one_left |
362 | instantiation | 589, 584, 374 | ⊢ |
| : , : , : |
363 | conjecture | | ⊢ |
| proveit.numbers.exponentiation.sqrd_pos_closure |
364 | instantiation | 409, 570, 415 | ⊢ |
| : , : |
365 | instantiation | 495, 375 | ⊢ |
| : |
366 | conjecture | | ⊢ |
| proveit.numbers.number_sets.real_numbers.nonneg_if_in_real_nonneg |
367 | instantiation | 589, 376, 385 | ⊢ |
| : , : , : |
368 | instantiation | 589, 552, 457 | ⊢ |
| : , : , : |
369 | instantiation | 377, 561, 443, 378, 532, 379, 380* | ⊢ |
| : , : , : |
370 | instantiation | 509, 381, 382 | ⊢ |
| : , : , : |
371 | conjecture | | ⊢ |
| proveit.numbers.numerals.decimals.nat4 |
372 | conjecture | | ⊢ |
| proveit.numbers.exponentiation.exp_rational_pos_closure |
373 | instantiation | 383, 427, 384 | ⊢ |
| : |
374 | conjecture | | ⊢ |
| proveit.numbers.numerals.decimals.posnat4 |
375 | instantiation | 589, 505, 385 | ⊢ |
| : , : , : |
376 | conjecture | | ⊢ |
| proveit.numbers.number_sets.real_numbers.real_pos_within_real_nonneg |
377 | conjecture | | ⊢ |
| proveit.numbers.exponentiation.exp_monotonicity_large_base_less_eq |
378 | instantiation | 409, 399, 397 | ⊢ |
| : , : |
379 | instantiation | 386, 387, 388 | ⊢ |
| : , : , : |
380 | instantiation | 389, 564, 457, 501 | ⊢ |
| : , : |
381 | instantiation | 451, 524, 588, 591, 525, 390, 551, 404, 544 | ⊢ |
| : , : , : , : , : , : |
382 | instantiation | 509, 391, 392 | ⊢ |
| : , : , : |
383 | conjecture | | ⊢ |
| proveit.numbers.number_sets.rational_numbers.pos_rational_is_rational_pos |
384 | instantiation | 393, 394 | ⊢ |
| : , : |
385 | instantiation | 512, 563, 469 | ⊢ |
| : , : |
386 | conjecture | | ⊢ |
| proveit.numbers.ordering.transitivity_less_eq_less_eq |
387 | instantiation | 395, 443 | ⊢ |
| : |
388 | instantiation | 396, 397, 398, 399, 400, 401* | ⊢ |
| : , : , : |
389 | conjecture | | ⊢ |
| proveit.numbers.exponentiation.exponent_log_with_same_base |
390 | instantiation | 540 | ⊢ |
| : , : |
391 | instantiation | 402, 591, 524, 525, 551, 404, 544 | ⊢ |
| : , : , : , : , : , : , : |
392 | instantiation | 453, 524, 588, 591, 525, 403, 551, 544, 404, 467* | ⊢ |
| : , : , : , : , : , : |
393 | conjecture | | ⊢ |
| proveit.numbers.addition.subtraction.pos_difference |
394 | instantiation | 405, 554, 561, 406, 407, 467*, 408* | ⊢ |
| : , : , : |
395 | conjecture | | ⊢ |
| proveit.numbers.rounding.ceil_x_ge_x |
396 | conjecture | | ⊢ |
| proveit.numbers.addition.weak_bound_via_left_term_bound |
397 | instantiation | 566, 471 | ⊢ |
| : |
398 | instantiation | 409, 471, 410 | ⊢ |
| : , : |
399 | instantiation | 479, 480, 515 | ⊢ |
| : , : , : |
400 | axiom | | ⊢ |
| proveit.physics.quantum.QPE._t_req |
401 | instantiation | 411, 412, 413, 414 | ⊢ |
| : , : , : , : |
402 | conjecture | | ⊢ |
| proveit.numbers.addition.leftward_commutation |
403 | instantiation | 540 | ⊢ |
| : , : |
404 | instantiation | 589, 560, 415 | ⊢ |
| : , : , : |
405 | conjecture | | ⊢ |
| proveit.numbers.addition.strong_bound_via_left_term_bound |
406 | instantiation | 589, 579, 416 | ⊢ |
| : , : , : |
407 | instantiation | 417, 561, 418, 419, 420 | ⊢ |
| : , : , : |
408 | instantiation | 509, 421, 422 | ⊢ |
| : , : , : |
409 | conjecture | | ⊢ |
| proveit.numbers.addition.add_real_closure_bin |
410 | instantiation | 589, 579, 423 | ⊢ |
| : , : , : |
411 | conjecture | | ⊢ |
| proveit.logic.equality.four_chain_transitivity |
412 | instantiation | 509, 424, 425 | ⊢ |
| : , : , : |
413 | instantiation | 462 | ⊢ |
| : |
414 | instantiation | 426, 444 | ⊢ |
| : , : |
415 | instantiation | 589, 552, 469 | ⊢ |
| : , : , : |
416 | instantiation | 436, 427, 574 | ⊢ |
| : , : |
417 | conjecture | | ⊢ |
| proveit.numbers.ordering.less_eq_add_right_strong |
418 | instantiation | 589, 579, 427 | ⊢ |
| : , : , : |
419 | conjecture | | ⊢ |
| proveit.physics.quantum.QPE._e_value_ge_two |
420 | instantiation | 428, 585 | ⊢ |
| : |
421 | instantiation | 507, 429 | ⊢ |
| : , : , : |
422 | instantiation | 509, 430, 431 | ⊢ |
| : , : , : |
423 | instantiation | 589, 586, 432 | ⊢ |
| : , : , : |
424 | instantiation | 507, 433 | ⊢ |
| : , : , : |
425 | instantiation | 509, 434, 435 | ⊢ |
| : , : , : |
426 | theorem | | ⊢ |
| proveit.logic.equality.equals_reversal |
427 | instantiation | 436, 474, 437 | ⊢ |
| : , : |
428 | conjecture | | ⊢ |
| proveit.numbers.number_sets.natural_numbers.natural_pos_is_pos |
429 | instantiation | 509, 438, 439 | ⊢ |
| : , : , : |
430 | instantiation | 451, 524, 588, 591, 525, 440, 455, 522, 544 | ⊢ |
| : , : , : , : , : , : |
431 | instantiation | 441, 522, 455, 442 | ⊢ |
| : , : , : |
432 | instantiation | 490, 443 | ⊢ |
| : |
433 | instantiation | 507, 444 | ⊢ |
| : , : , : |
434 | instantiation | 451, 524, 588, 591, 525, 445, 460, 448, 446 | ⊢ |
| : , : , : , : , : , : |
435 | instantiation | 447, 460, 448, 449 | ⊢ |
| : , : , : |
436 | conjecture | | ⊢ |
| proveit.numbers.addition.add_rational_closure_bin |
437 | instantiation | 589, 586, 450 | ⊢ |
| : , : , : |
438 | instantiation | 451, 524, 588, 591, 525, 452, 455, 544, 551 | ⊢ |
| : , : , : , : , : , : |
439 | instantiation | 453, 591, 588, 524, 454, 525, 455, 544, 551, 456* | ⊢ |
| : , : , : , : , : , : |
440 | instantiation | 540 | ⊢ |
| : , : |
441 | conjecture | | ⊢ |
| proveit.numbers.addition.subtraction.add_cancel_triple_23 |
442 | instantiation | 462 | ⊢ |
| : |
443 | instantiation | 499, 564, 457, 501 | ⊢ |
| : , : |
444 | instantiation | 507, 458 | ⊢ |
| : , : , : |
445 | instantiation | 540 | ⊢ |
| : , : |
446 | instantiation | 459, 460 | ⊢ |
| : |
447 | conjecture | | ⊢ |
| proveit.numbers.addition.subtraction.add_cancel_triple_13 |
448 | instantiation | 589, 560, 461 | ⊢ |
| : , : , : |
449 | instantiation | 462 | ⊢ |
| : |
450 | instantiation | 589, 463, 464 | ⊢ |
| : , : , : |
451 | conjecture | | ⊢ |
| proveit.numbers.addition.disassociation |
452 | instantiation | 540 | ⊢ |
| : , : |
453 | conjecture | | ⊢ |
| proveit.numbers.addition.association |
454 | instantiation | 540 | ⊢ |
| : , : |
455 | instantiation | 589, 560, 465 | ⊢ |
| : , : , : |
456 | instantiation | 466, 467, 468 | ⊢ |
| : , : , : |
457 | instantiation | 512, 564, 469 | ⊢ |
| : , : |
458 | instantiation | 507, 470 | ⊢ |
| : , : , : |
459 | conjecture | | ⊢ |
| proveit.numbers.negation.complex_closure |
460 | instantiation | 589, 560, 471 | ⊢ |
| : , : , : |
461 | instantiation | 589, 579, 472 | ⊢ |
| : , : , : |
462 | axiom | | ⊢ |
| proveit.logic.equality.equals_reflexivity |
463 | conjecture | | ⊢ |
| proveit.numbers.number_sets.integers.neg_int_within_int |
464 | instantiation | 473, 583 | ⊢ |
| : |
465 | instantiation | 589, 579, 474 | ⊢ |
| : , : , : |
466 | theorem | | ⊢ |
| proveit.logic.equality.sub_right_side_into |
467 | instantiation | 475, 522, 551, 476 | ⊢ |
| : , : , : |
468 | instantiation | 477, 551, 544 | ⊢ |
| : , : |
469 | instantiation | 562, 563, 506, 486 | ⊢ |
| : , : |
470 | instantiation | 507, 478 | ⊢ |
| : , : , : |
471 | instantiation | 479, 480, 534 | ⊢ |
| : , : , : |
472 | instantiation | 589, 586, 481 | ⊢ |
| : , : , : |
473 | conjecture | | ⊢ |
| proveit.numbers.negation.int_neg_closure |
474 | instantiation | 589, 482, 483 | ⊢ |
| : , : , : |
475 | conjecture | | ⊢ |
| proveit.numbers.addition.subtraction.subtract_from_add |
476 | conjecture | | ⊢ |
| proveit.numbers.numerals.decimals.add_1_1 |
477 | conjecture | | ⊢ |
| proveit.numbers.addition.commutation |
478 | instantiation | 484, 522, 485, 486, 487* | ⊢ |
| : , : |
479 | theorem | | ⊢ |
| proveit.logic.sets.inclusion.unfold_subset_eq |
480 | instantiation | 488, 489 | ⊢ |
| : , : |
481 | instantiation | 490, 491 | ⊢ |
| : |
482 | conjecture | | ⊢ |
| proveit.numbers.number_sets.rational_numbers.rational_nonzero_within_rational |
483 | instantiation | 492, 559, 493 | ⊢ |
| : , : |
484 | conjecture | | ⊢ |
| proveit.numbers.division.div_as_mult |
485 | instantiation | 589, 560, 494 | ⊢ |
| : , : , : |
486 | instantiation | 495, 496 | ⊢ |
| : |
487 | instantiation | 509, 497, 498 | ⊢ |
| : , : , : |
488 | theorem | | ⊢ |
| proveit.logic.sets.inclusion.relax_proper_subset |
489 | conjecture | | ⊢ |
| proveit.numbers.number_sets.real_numbers.nat_pos_within_real |
490 | axiom | | ⊢ |
| proveit.numbers.rounding.ceil_is_an_int |
491 | instantiation | 499, 564, 500, 501 | ⊢ |
| : , : |
492 | conjecture | | ⊢ |
| proveit.numbers.exponentiation.exp_rational_nonzero_closure |
493 | instantiation | 502, 503, 504 | ⊢ |
| : , : |
494 | instantiation | 589, 552, 506 | ⊢ |
| : , : , : |
495 | conjecture | | ⊢ |
| proveit.numbers.number_sets.real_numbers.nonzero_if_in_real_nonzero |
496 | instantiation | 589, 505, 506 | ⊢ |
| : , : , : |
497 | instantiation | 507, 508 | ⊢ |
| : , : , : |
498 | instantiation | 509, 510, 511 | ⊢ |
| : , : , : |
499 | conjecture | | ⊢ |
| proveit.numbers.logarithms.log_real_pos_real_closure |
500 | instantiation | 512, 564, 513 | ⊢ |
| : , : |
501 | instantiation | 535, 514 | ⊢ |
| : , : |
502 | conjecture | | ⊢ |
| proveit.numbers.addition.add_int_closure_bin |
503 | instantiation | 589, 533, 515 | ⊢ |
| : , : , : |
504 | instantiation | 516, 517 | ⊢ |
| : |
505 | conjecture | | ⊢ |
| proveit.numbers.number_sets.real_numbers.real_pos_within_real_nonzero |
506 | instantiation | 529, 564, 546 | ⊢ |
| : , : |
507 | axiom | | ⊢ |
| proveit.logic.equality.substitution |
508 | instantiation | 518, 551, 543, 554, 565, 519, 520* | ⊢ |
| : , : , : |
509 | axiom | | ⊢ |
| proveit.logic.equality.equals_transitivity |
510 | instantiation | 521, 591, 588, 524, 526, 525, 522, 527, 528 | ⊢ |
| : , : , : , : , : , : |
511 | instantiation | 523, 524, 588, 525, 526, 527, 528 | ⊢ |
| : , : , : , : |
512 | conjecture | | ⊢ |
| proveit.numbers.addition.add_real_pos_closure_bin |
513 | instantiation | 529, 553, 530 | ⊢ |
| : , : |
514 | instantiation | 531, 591, 588, 532 | ⊢ |
| : , : |
515 | axiom | | ⊢ |
| proveit.physics.quantum.QPE._t_in_natural_pos |
516 | conjecture | | ⊢ |
| proveit.numbers.negation.int_closure |
517 | instantiation | 589, 533, 534 | ⊢ |
| : , : , : |
518 | conjecture | | ⊢ |
| proveit.numbers.exponentiation.real_power_of_product |
519 | instantiation | 535, 536 | ⊢ |
| : , : |
520 | instantiation | 537, 538, 583, 539* | ⊢ |
| : , : |
521 | conjecture | | ⊢ |
| proveit.numbers.multiplication.disassociation |
522 | instantiation | 589, 560, 570 | ⊢ |
| : , : , : |
523 | conjecture | | ⊢ |
| proveit.numbers.multiplication.elim_one_any |
524 | axiom | | ⊢ |
| proveit.numbers.number_sets.natural_numbers.zero_in_nats |
525 | conjecture | | ⊢ |
| proveit.core_expr_types.tuples.tuple_len_0_typical_eq |
526 | instantiation | 540 | ⊢ |
| : , : |
527 | instantiation | 589, 560, 541 | ⊢ |
| : , : , : |
528 | instantiation | 542, 543, 544 | ⊢ |
| : , : |
529 | conjecture | | ⊢ |
| proveit.numbers.multiplication.mult_real_pos_closure_bin |
530 | instantiation | 545, 546, 554 | ⊢ |
| : , : |
531 | conjecture | | ⊢ |
| proveit.numbers.ordering.less_is_not_eq_nat |
532 | conjecture | | ⊢ |
| proveit.numbers.numerals.decimals.less_1_2 |
533 | conjecture | | ⊢ |
| proveit.numbers.number_sets.integers.nat_pos_within_int |
534 | axiom | | ⊢ |
| proveit.physics.quantum.QPE._n_in_natural_pos |
535 | theorem | | ⊢ |
| proveit.logic.equality.not_equals_symmetry |
536 | instantiation | 547, 569, 556, 557 | ⊢ |
| : , : |
537 | conjecture | | ⊢ |
| proveit.numbers.exponentiation.neg_power_as_div |
538 | instantiation | 589, 548, 549 | ⊢ |
| : , : , : |
539 | instantiation | 550, 551 | ⊢ |
| : |
540 | conjecture | | ⊢ |
| proveit.numbers.numerals.decimals.tuple_len_2_typical_eq |
541 | instantiation | 589, 552, 553 | ⊢ |
| : , : , : |
542 | conjecture | | ⊢ |
| proveit.numbers.exponentiation.exp_complex_closure |
543 | instantiation | 589, 560, 556 | ⊢ |
| : , : , : |
544 | instantiation | 589, 560, 554 | ⊢ |
| : , : , : |
545 | conjecture | | ⊢ |
| proveit.numbers.exponentiation.exp_real_pos_closure |
546 | instantiation | 555, 556, 557 | ⊢ |
| : |
547 | conjecture | | ⊢ |
| proveit.numbers.ordering.less_is_not_eq |
548 | conjecture | | ⊢ |
| proveit.numbers.number_sets.complex_numbers.real_nonzero_within_complex_nonzero |
549 | instantiation | 589, 558, 559 | ⊢ |
| : , : , : |
550 | conjecture | | ⊢ |
| proveit.numbers.exponentiation.complex_x_to_first_power_is_x |
551 | instantiation | 589, 560, 561 | ⊢ |
| : , : , : |
552 | conjecture | | ⊢ |
| proveit.numbers.number_sets.real_numbers.real_pos_within_real |
553 | instantiation | 562, 563, 564, 565 | ⊢ |
| : , : |
554 | instantiation | 566, 570 | ⊢ |
| : |
555 | conjecture | | ⊢ |
| proveit.numbers.number_sets.real_numbers.pos_real_is_real_pos |
556 | instantiation | 567, 569, 570, 571 | ⊢ |
| : , : , : |
557 | instantiation | 568, 569, 570, 571 | ⊢ |
| : , : , : |
558 | conjecture | | ⊢ |
| proveit.numbers.number_sets.real_numbers.rational_nonzero_within_real_nonzero |
559 | instantiation | 589, 572, 573 | ⊢ |
| : , : , : |
560 | conjecture | | ⊢ |
| proveit.numbers.number_sets.complex_numbers.real_within_complex |
561 | instantiation | 589, 579, 574 | ⊢ |
| : , : , : |
562 | conjecture | | ⊢ |
| proveit.numbers.division.div_real_pos_closure |
563 | instantiation | 589, 576, 575 | ⊢ |
| : , : , : |
564 | instantiation | 589, 576, 577 | ⊢ |
| : , : , : |
565 | instantiation | 578, 585 | ⊢ |
| : |
566 | conjecture | | ⊢ |
| proveit.numbers.negation.real_closure |
567 | conjecture | | ⊢ |
| proveit.numbers.number_sets.real_numbers.all_in_interval_oc__is__real |
568 | conjecture | | ⊢ |
| proveit.numbers.number_sets.real_numbers.interval_oc_lower_bound |
569 | conjecture | | ⊢ |
| proveit.numbers.number_sets.real_numbers.zero_is_real |
570 | instantiation | 589, 579, 580 | ⊢ |
| : , : , : |
571 | axiom | | ⊢ |
| proveit.physics.quantum.QPE._eps_in_interval |
572 | conjecture | | ⊢ |
| proveit.numbers.number_sets.rational_numbers.nonzero_int_within_rational_nonzero |
573 | instantiation | 589, 581, 585 | ⊢ |
| : , : , : |
574 | instantiation | 589, 586, 582 | ⊢ |
| : , : , : |
575 | instantiation | 589, 584, 583 | ⊢ |
| : , : , : |
576 | conjecture | | ⊢ |
| proveit.numbers.number_sets.real_numbers.rational_pos_within_real_pos |
577 | instantiation | 589, 584, 585 | ⊢ |
| : , : , : |
578 | conjecture | | ⊢ |
| proveit.numbers.number_sets.natural_numbers.nonzero_if_is_nat_pos |
579 | conjecture | | ⊢ |
| proveit.numbers.number_sets.real_numbers.rational_within_real |
580 | instantiation | 589, 586, 587 | ⊢ |
| : , : , : |
581 | conjecture | | ⊢ |
| proveit.numbers.number_sets.integers.nat_pos_within_nonzero_int |
582 | instantiation | 589, 590, 588 | ⊢ |
| : , : , : |
583 | conjecture | | ⊢ |
| proveit.numbers.numerals.decimals.posnat1 |
584 | conjecture | | ⊢ |
| proveit.numbers.number_sets.rational_numbers.nat_pos_within_rational_pos |
585 | conjecture | | ⊢ |
| proveit.numbers.numerals.decimals.posnat2 |
586 | conjecture | | ⊢ |
| proveit.numbers.number_sets.rational_numbers.int_within_rational |
587 | instantiation | 589, 590, 591 | ⊢ |
| : , : , : |
588 | conjecture | | ⊢ |
| proveit.numbers.numerals.decimals.nat2 |
589 | theorem | | ⊢ |
| proveit.logic.sets.inclusion.superset_membership_from_proper_subset |
590 | conjecture | | ⊢ |
| proveit.numbers.number_sets.integers.nat_within_int |
591 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.nat1 |
*equality replacement requirements |