| step type | requirements | statement |
0 | instantiation | 1, 2, 3, 4, 5* | ⊢ |
| : , : |
1 | theorem | | ⊢ |
| proveit.numbers.absolute_value.abs_frac |
2 | instantiation | 7, 358, 6 | ⊢ |
| : , : |
3 | instantiation | 7, 358, 8 | ⊢ |
| : , : |
4 | instantiation | 9, 10 | ⊢ |
| : , : |
5 | instantiation | 394, 11, 12 | ⊢ |
| : , : , : |
6 | instantiation | 159, 13 | ⊢ |
| : |
7 | theorem | | ⊢ |
| proveit.numbers.addition.add_complex_closure_bin |
8 | instantiation | 159, 14 | ⊢ |
| : |
9 | theorem | | ⊢ |
| proveit.numbers.addition.subtraction.nonzero_difference_if_different |
10 | instantiation | 53, 15 | ⊢ |
| : , : |
11 | instantiation | 416, 452, 16, 17, 18, 19 | ⊢ |
| : , : , : , : |
12 | instantiation | 121, 311, 20, 21 | ⊢ |
| : , : , : |
13 | instantiation | 257, 70, 22 | ⊢ |
| : , : |
14 | instantiation | 257, 70, 23 | ⊢ |
| : , : |
15 | instantiation | 239, 24, 25 | ⊢ |
| : , : , : |
16 | instantiation | 433 | ⊢ |
| : , : |
17 | instantiation | 433 | ⊢ |
| : , : |
18 | instantiation | 29, 220, 26, 30*, 27*, 28* | ⊢ |
| : , : |
19 | instantiation | 29, 220, 41, 30*, 31*, 32* | ⊢ |
| : , : |
20 | instantiation | 409, 33, 34 | ⊢ |
| : |
21 | instantiation | 450, 442, 35 | ⊢ |
| : , : , : |
22 | instantiation | 278, 36, 37 | ⊢ |
| : , : , : |
23 | instantiation | 278, 38, 39 | ⊢ |
| : , : , : |
24 | instantiation | 40, 41, 42, 43* | ⊢ |
| : |
25 | instantiation | 402, 44 | ⊢ |
| : , : , : |
26 | instantiation | 278, 192, 172 | ⊢ |
| : , : , : |
27 | instantiation | 224, 45 | ⊢ |
| : , : |
28 | instantiation | 394, 46, 47 | ⊢ |
| : , : , : |
29 | theorem | | ⊢ |
| proveit.trigonometry.complex_unit_circle_chord_length |
30 | instantiation | 394, 48, 49 | ⊢ |
| : , : , : |
31 | instantiation | 224, 50 | ⊢ |
| : , : |
32 | instantiation | 394, 51, 52 | ⊢ |
| : , : , : |
33 | instantiation | 450, 442, 76 | ⊢ |
| : , : , : |
34 | instantiation | 53, 54 | ⊢ |
| : , : |
35 | instantiation | 55, 56 | ⊢ |
| : |
36 | instantiation | 227, 212, 57 | ⊢ |
| : , : |
37 | instantiation | 394, 58, 59 | ⊢ |
| : , : , : |
38 | instantiation | 227, 212, 102 | ⊢ |
| : , : |
39 | instantiation | 394, 60, 61 | ⊢ |
| : , : , : |
40 | theorem | | ⊢ |
| proveit.numbers.exponentiation.unit_complex_polar_num_neq_one |
41 | instantiation | 278, 196, 180 | ⊢ |
| : , : , : |
42 | instantiation | 239, 62, 63 | ⊢ |
| : , : , : |
43 | instantiation | 224, 64 | ⊢ |
| : , : |
44 | instantiation | 208, 452, 445, 347, 213, 348, 436, 294, 132, 410 | ⊢ |
| : , : , : , : , : , : , : |
45 | instantiation | 402, 65 | ⊢ |
| : , : , : |
46 | instantiation | 402, 66 | ⊢ |
| : , : , : |
47 | instantiation | 394, 67, 68 | ⊢ |
| : , : , : |
48 | instantiation | 402, 69 | ⊢ |
| : , : , : |
49 | instantiation | 287, 70 | ⊢ |
| : |
50 | instantiation | 402, 71 | ⊢ |
| : , : , : |
51 | instantiation | 402, 72 | ⊢ |
| : , : , : |
52 | instantiation | 394, 73, 74 | ⊢ |
| : , : , : |
53 | theorem | | ⊢ |
| proveit.logic.equality.not_equals_symmetry |
54 | instantiation | 75, 220, 76, 77 | ⊢ |
| : , : |
55 | theorem | | ⊢ |
| proveit.trigonometry.real_closure |
56 | instantiation | 278, 157, 139 | ⊢ |
| : , : , : |
57 | instantiation | 278, 78, 79 | ⊢ |
| : , : , : |
58 | instantiation | 271, 445, 229, 347, 80, 348, 212, 132, 410, 352 | ⊢ |
| : , : , : , : , : , : |
59 | instantiation | 271, 347, 452, 229, 348, 213, 80, 436, 294, 132, 410, 352 | ⊢ |
| : , : , : , : , : , : |
60 | instantiation | 271, 445, 452, 347, 103, 348, 212, 132, 410 | ⊢ |
| : , : , : , : , : , : |
61 | instantiation | 271, 347, 452, 348, 213, 103, 436, 294, 132, 410 | ⊢ |
| : , : , : , : , : , : |
62 | instantiation | 81, 82, 83, 127, 125 | ⊢ |
| : , : |
63 | instantiation | 281, 84, 359, 85 | ⊢ |
| : , : , : , : |
64 | instantiation | 402, 86 | ⊢ |
| : , : , : |
65 | instantiation | 394, 87, 88 | ⊢ |
| : , : , : |
66 | instantiation | 394, 89, 90 | ⊢ |
| : , : , : |
67 | instantiation | 394, 91, 92 | ⊢ |
| : , : , : |
68 | instantiation | 403, 116 | ⊢ |
| : |
69 | instantiation | 274, 132 | ⊢ |
| : |
70 | instantiation | 450, 442, 93 | ⊢ |
| : , : , : |
71 | instantiation | 394, 94, 112 | ⊢ |
| : , : , : |
72 | instantiation | 394, 95, 96 | ⊢ |
| : , : , : |
73 | instantiation | 394, 97, 98 | ⊢ |
| : , : , : |
74 | instantiation | 403, 122 | ⊢ |
| : |
75 | theorem | | ⊢ |
| proveit.numbers.ordering.less_is_not_eq |
76 | instantiation | 99, 220, 413, 101 | ⊢ |
| : , : , : |
77 | instantiation | 100, 220, 413, 101 | ⊢ |
| : , : , : |
78 | instantiation | 227, 102, 352 | ⊢ |
| : , : |
79 | instantiation | 271, 347, 452, 445, 348, 103, 132, 410, 352 | ⊢ |
| : , : , : , : , : , : |
80 | instantiation | 256 | ⊢ |
| : , : , : |
81 | theorem | | ⊢ |
| proveit.logic.booleans.disjunction.right_if_not_left |
82 | instantiation | 104, 105 | ⊢ |
| : |
83 | instantiation | 106, 107 | ⊢ |
| : , : |
84 | instantiation | 108, 160, 212, 109, 110* | ⊢ |
| : , : |
85 | instantiation | 385 | ⊢ |
| : |
86 | instantiation | 394, 111, 112 | ⊢ |
| : , : , : |
87 | instantiation | 208, 347, 452, 348, 213, 214, 436, 294, 132, 410, 352 | ⊢ |
| : , : , : , : , : , : , : |
88 | instantiation | 228, 445, 444, 347, 134, 348, 132, 436, 294, 410, 352 | ⊢ |
| : , : , : , : , : , : |
89 | instantiation | 402, 113 | ⊢ |
| : , : , : |
90 | instantiation | 327, 151, 114* | ⊢ |
| : |
91 | instantiation | 402, 115 | ⊢ |
| : , : , : |
92 | instantiation | 121, 311, 310, 116, 420* | ⊢ |
| : , : , : |
93 | instantiation | 450, 355, 117 | ⊢ |
| : , : , : |
94 | instantiation | 208, 347, 452, 445, 348, 213, 436, 294, 132, 410 | ⊢ |
| : , : , : , : , : , : , : |
95 | instantiation | 402, 118 | ⊢ |
| : , : , : |
96 | instantiation | 327, 160, 119* | ⊢ |
| : |
97 | instantiation | 402, 120 | ⊢ |
| : , : , : |
98 | instantiation | 121, 311, 310, 122, 420* | ⊢ |
| : , : , : |
99 | theorem | | ⊢ |
| proveit.numbers.number_sets.real_numbers.all_in_interval_oc__is__real |
100 | theorem | | ⊢ |
| proveit.numbers.number_sets.real_numbers.interval_oc_lower_bound |
101 | instantiation | 123, 124 | ⊢ |
| : |
102 | instantiation | 227, 132, 410 | ⊢ |
| : , : |
103 | instantiation | 433 | ⊢ |
| : , : |
104 | axiom | | ⊢ |
| proveit.logic.booleans.negation.operand_is_bool |
105 | instantiation | 126, 125 | ⊢ |
| : |
106 | axiom | | ⊢ |
| proveit.logic.booleans.disjunction.right_in_bool |
107 | instantiation | 126, 127 | ⊢ |
| : |
108 | theorem | | ⊢ |
| proveit.numbers.division.div_as_mult |
109 | instantiation | 128, 452, 213, 311, 129 | ⊢ |
| : , : |
110 | instantiation | 394, 130, 131 | ⊢ |
| : , : , : |
111 | instantiation | 208, 347, 229, 348, 205, 436, 294, 410, 132 | ⊢ |
| : , : , : , : , : , : , : |
112 | instantiation | 228, 445, 229, 347, 205, 348, 132, 436, 294, 410 | ⊢ |
| : , : , : , : , : , : |
113 | instantiation | 250, 133 | ⊢ |
| : |
114 | instantiation | 301, 398, 134, 436, 294, 410, 352, 135* | ⊢ |
| : , : |
115 | instantiation | 394, 136, 137 | ⊢ |
| : , : , : |
116 | instantiation | 278, 138, 139 | ⊢ |
| : , : , : |
117 | theorem | | ⊢ |
| proveit.numbers.number_sets.real_numbers.e_is_real_pos |
118 | instantiation | 250, 140 | ⊢ |
| : |
119 | instantiation | 301, 141, 205, 436, 294, 410, 175*, 176* | ⊢ |
| : , : |
120 | instantiation | 228, 445, 452, 347, 155, 348, 436, 294, 295 | ⊢ |
| : , : , : , : , : , : |
121 | theorem | | ⊢ |
| proveit.numbers.division.frac_cancel_left |
122 | instantiation | 450, 442, 143 | ⊢ |
| : , : , : |
123 | theorem | | ⊢ |
| proveit.trigonometry.sine_pos_interval |
124 | instantiation | 142, 220, 324, 143, 144 | ⊢ |
| : , : , : |
125 | instantiation | 145, 411 | ⊢ |
| : , : |
126 | theorem | | ⊢ |
| proveit.logic.booleans.in_bool_if_true |
127 | instantiation | 146, 147 | ⊢ |
| : |
128 | theorem | | ⊢ |
| proveit.numbers.multiplication.mult_not_eq_zero |
129 | instantiation | 450, 336, 261 | ⊢ |
| : , : , : |
130 | instantiation | 402, 148 | ⊢ |
| : , : , : |
131 | instantiation | 394, 149, 150 | ⊢ |
| : , : , : |
132 | theorem | | ⊢ |
| proveit.numbers.number_sets.complex_numbers.i_is_complex |
133 | instantiation | 159, 151 | ⊢ |
| : |
134 | instantiation | 152 | ⊢ |
| : , : , : , : |
135 | instantiation | 394, 153, 154 | ⊢ |
| : , : , : |
136 | instantiation | 208, 347, 445, 452, 348, 155, 352, 436, 294, 295 | ⊢ |
| : , : , : , : , : , : , : |
137 | instantiation | 228, 445, 229, 347, 156, 348, 436, 352, 294, 295 | ⊢ |
| : , : , : , : , : , : |
138 | instantiation | 450, 442, 157 | ⊢ |
| : , : , : |
139 | instantiation | 271, 347, 452, 445, 348, 158, 352, 294, 295 | ⊢ |
| : , : , : , : , : , : |
140 | instantiation | 159, 160 | ⊢ |
| : |
141 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.posnat3 |
142 | theorem | | ⊢ |
| proveit.numbers.number_sets.real_numbers.in_IntervalOO |
143 | instantiation | 450, 355, 181 | ⊢ |
| : , : , : |
144 | instantiation | 161, 162, 163 | ⊢ |
| : , : |
145 | theorem | | ⊢ |
| proveit.logic.equality.unfold_not_equals |
146 | theorem | | ⊢ |
| proveit.physics.quantum.QPE._delta_b_is_zero_or_non_int |
147 | instantiation | 164, 445, 347, 348 | ⊢ |
| : , : , : , : , : |
148 | instantiation | 165, 436, 294, 383, 414, 235, 166* | ⊢ |
| : , : , : |
149 | instantiation | 394, 167, 168 | ⊢ |
| : , : , : |
150 | instantiation | 394, 169, 170 | ⊢ |
| : , : , : |
151 | instantiation | 278, 171, 172 | ⊢ |
| : , : , : |
152 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.tuple_len_4_typical_eq |
153 | instantiation | 416, 229, 173, 174, 175, 176, 303 | ⊢ |
| : , : , : , : |
154 | instantiation | 208, 347, 229, 348, 177, 436, 294, 295, 352 | ⊢ |
| : , : , : , : , : , : , : |
155 | instantiation | 433 | ⊢ |
| : , : |
156 | instantiation | 256 | ⊢ |
| : , : , : |
157 | instantiation | 305, 178, 325 | ⊢ |
| : , : |
158 | instantiation | 433 | ⊢ |
| : , : |
159 | theorem | | ⊢ |
| proveit.numbers.negation.complex_closure |
160 | instantiation | 278, 179, 180 | ⊢ |
| : , : , : |
161 | theorem | | ⊢ |
| proveit.logic.booleans.conjunction.and_if_both |
162 | instantiation | 304, 181 | ⊢ |
| : |
163 | instantiation | 182, 183, 184 | ⊢ |
| : , : , : |
164 | theorem | | ⊢ |
| proveit.logic.sets.enumeration.in_enumerated_set |
165 | theorem | | ⊢ |
| proveit.numbers.exponentiation.real_power_of_product |
166 | instantiation | 185, 311, 422, 345* | ⊢ |
| : , : |
167 | instantiation | 394, 186, 187 | ⊢ |
| : , : , : |
168 | instantiation | 394, 188, 189 | ⊢ |
| : , : , : |
169 | instantiation | 293, 347, 229, 348, 231, 294, 410, 232 | ⊢ |
| : , : , : , : |
170 | instantiation | 394, 190, 191 | ⊢ |
| : , : , : |
171 | instantiation | 450, 442, 192 | ⊢ |
| : , : , : |
172 | instantiation | 394, 193, 194 | ⊢ |
| : , : , : |
173 | instantiation | 256 | ⊢ |
| : , : , : |
174 | instantiation | 256 | ⊢ |
| : , : , : |
175 | instantiation | 330, 195 | ⊢ |
| : |
176 | instantiation | 330, 245 | ⊢ |
| : |
177 | instantiation | 256 | ⊢ |
| : , : , : |
178 | instantiation | 305, 384, 324 | ⊢ |
| : , : |
179 | instantiation | 450, 442, 196 | ⊢ |
| : , : , : |
180 | instantiation | 271, 347, 452, 445, 348, 213, 436, 294, 410 | ⊢ |
| : , : , : , : , : , : |
181 | instantiation | 197, 354, 356 | ⊢ |
| : , : |
182 | axiom | | ⊢ |
| proveit.numbers.ordering.transitivity_less_less |
183 | instantiation | 278, 198, 241 | ⊢ |
| : , : , : |
184 | instantiation | 288, 276, 199, 200, 201*, 202* | ⊢ |
| : , : , : |
185 | theorem | | ⊢ |
| proveit.numbers.exponentiation.neg_power_as_div |
186 | instantiation | 271, 347, 229, 445, 348, 205, 436, 294, 410, 203 | ⊢ |
| : , : , : , : , : , : |
187 | instantiation | 271, 229, 452, 347, 205, 204, 348, 436, 294, 410, 275, 232 | ⊢ |
| : , : , : , : , : , : |
188 | instantiation | 208, 347, 229, 445, 348, 205, 436, 294, 410, 275, 232 | ⊢ |
| : , : , : , : , : , : , : |
189 | instantiation | 394, 206, 207 | ⊢ |
| : , : , : |
190 | instantiation | 208, 445, 347, 348, 294, 410, 232 | ⊢ |
| : , : , : , : , : , : , : |
191 | instantiation | 228, 347, 452, 445, 348, 209, 294, 232, 410, 210* | ⊢ |
| : , : , : , : , : , : |
192 | instantiation | 305, 238, 211 | ⊢ |
| : , : |
193 | instantiation | 271, 445, 452, 347, 214, 348, 212, 410, 352 | ⊢ |
| : , : , : , : , : , : |
194 | instantiation | 271, 347, 452, 348, 213, 214, 436, 294, 410, 352 | ⊢ |
| : , : , : , : , : , : |
195 | instantiation | 215, 452 | ⊢ |
| : |
196 | instantiation | 305, 238, 429 | ⊢ |
| : , : |
197 | theorem | | ⊢ |
| proveit.numbers.multiplication.mult_real_pos_closure_bin |
198 | instantiation | 216, 217, 218 | ⊢ |
| : , : , : |
199 | instantiation | 305, 306, 220 | ⊢ |
| : , : |
200 | instantiation | 219, 306, 220, 324, 270, 221 | ⊢ |
| : , : , : |
201 | instantiation | 394, 222, 223 | ⊢ |
| : , : , : |
202 | instantiation | 224, 225, 226* | ⊢ |
| : , : |
203 | instantiation | 227, 275, 232 | ⊢ |
| : , : |
204 | instantiation | 433 | ⊢ |
| : , : |
205 | instantiation | 256 | ⊢ |
| : , : , : |
206 | instantiation | 228, 347, 452, 229, 348, 230, 231, 275, 436, 294, 410, 232 | ⊢ |
| : , : , : , : , : , : |
207 | instantiation | 402, 233 | ⊢ |
| : , : , : |
208 | theorem | | ⊢ |
| proveit.numbers.multiplication.leftward_commutation |
209 | instantiation | 433 | ⊢ |
| : , : |
210 | instantiation | 234, 294, 413, 383, 235, 236*, 237* | ⊢ |
| : , : , : |
211 | instantiation | 305, 429, 384 | ⊢ |
| : , : |
212 | instantiation | 450, 442, 238 | ⊢ |
| : , : , : |
213 | instantiation | 433 | ⊢ |
| : , : |
214 | instantiation | 433 | ⊢ |
| : , : |
215 | theorem | | ⊢ |
| proveit.numbers.number_sets.natural_numbers.natural_lower_bound |
216 | theorem | | ⊢ |
| proveit.numbers.ordering.transitivity_less_less_eq |
217 | instantiation | 239, 240, 241 | ⊢ |
| : , : , : |
218 | instantiation | 242, 324, 243, 389, 244, 245, 246*, 247* | ⊢ |
| : , : , : |
219 | theorem | | ⊢ |
| proveit.numbers.multiplication.strong_bound_via_right_factor_bound |
220 | theorem | | ⊢ |
| proveit.numbers.number_sets.real_numbers.zero_is_real |
221 | instantiation | 248, 366 | ⊢ |
| : |
222 | instantiation | 402, 249 | ⊢ |
| : , : , : |
223 | instantiation | 250, 251 | ⊢ |
| : |
224 | theorem | | ⊢ |
| proveit.logic.equality.equals_reversal |
225 | instantiation | 252, 347, 452, 445, 348, 253, 275, 294 | ⊢ |
| : , : , : , : , : , : |
226 | instantiation | 394, 254, 255 | ⊢ |
| : , : , : |
227 | theorem | | ⊢ |
| proveit.numbers.multiplication.mult_complex_closure_bin |
228 | theorem | | ⊢ |
| proveit.numbers.multiplication.association |
229 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.nat3 |
230 | instantiation | 433 | ⊢ |
| : , : |
231 | instantiation | 256 | ⊢ |
| : , : , : |
232 | instantiation | 257, 294, 350 | ⊢ |
| : , : |
233 | instantiation | 278, 258, 259 | ⊢ |
| : , : , : |
234 | theorem | | ⊢ |
| proveit.numbers.exponentiation.product_of_real_powers |
235 | instantiation | 260, 261 | ⊢ |
| : |
236 | instantiation | 382, 294 | ⊢ |
| : |
237 | instantiation | 394, 262, 263 | ⊢ |
| : , : , : |
238 | instantiation | 305, 443, 324 | ⊢ |
| : , : |
239 | theorem | | ⊢ |
| proveit.logic.equality.sub_left_side_into |
240 | instantiation | 264, 445, 354, 356, 265, 266* | ⊢ |
| : , : , : , : , : , : |
241 | instantiation | 402, 267 | ⊢ |
| : , : , : |
242 | theorem | | ⊢ |
| proveit.numbers.multiplication.weak_bound_via_right_factor_bound |
243 | instantiation | 305, 384, 325 | ⊢ |
| : , : |
244 | instantiation | 278, 268, 269 | ⊢ |
| : , : , : |
245 | instantiation | 363, 270 | ⊢ |
| : , : |
246 | instantiation | 271, 445, 452, 347, 272, 348, 294, 352, 295 | ⊢ |
| : , : , : , : , : , : |
247 | instantiation | 273, 294, 275 | ⊢ |
| : , : |
248 | theorem | | ⊢ |
| proveit.numbers.number_sets.rational_numbers.positive_if_in_rational_pos |
249 | instantiation | 274, 275 | ⊢ |
| : |
250 | theorem | | ⊢ |
| proveit.numbers.addition.elim_zero_left |
251 | instantiation | 450, 442, 276 | ⊢ |
| : , : , : |
252 | theorem | | ⊢ |
| proveit.numbers.multiplication.distribute_through_sum |
253 | instantiation | 433 | ⊢ |
| : , : |
254 | instantiation | 402, 277 | ⊢ |
| : , : , : |
255 | instantiation | 434, 294 | ⊢ |
| : |
256 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.tuple_len_3_typical_eq |
257 | theorem | | ⊢ |
| proveit.numbers.exponentiation.exp_complex_closure |
258 | instantiation | 278, 279, 280 | ⊢ |
| : , : , : |
259 | instantiation | 281, 282, 283, 284 | ⊢ |
| : , : , : , : |
260 | theorem | | ⊢ |
| proveit.numbers.number_sets.real_numbers.nonzero_if_in_real_nonzero |
261 | instantiation | 450, 285, 354 | ⊢ |
| : , : , : |
262 | instantiation | 402, 286 | ⊢ |
| : , : , : |
263 | instantiation | 287, 294 | ⊢ |
| : |
264 | theorem | | ⊢ |
| proveit.numbers.multiplication.strong_bound_via_factor_bound |
265 | instantiation | 288, 383, 443, 289, 290, 291*, 292* | ⊢ |
| : , : , : |
266 | instantiation | 293, 445, 294, 295 | ⊢ |
| : , : , : , : |
267 | instantiation | 394, 296, 297 | ⊢ |
| : , : , : |
268 | instantiation | 298, 299, 300 | ⊢ |
| : , : |
269 | instantiation | 301, 432, 302, 352, 410, 303* | ⊢ |
| : , : |
270 | instantiation | 304, 354 | ⊢ |
| : |
271 | theorem | | ⊢ |
| proveit.numbers.multiplication.disassociation |
272 | instantiation | 433 | ⊢ |
| : , : |
273 | theorem | | ⊢ |
| proveit.numbers.multiplication.commutation |
274 | theorem | | ⊢ |
| proveit.numbers.multiplication.mult_zero_right |
275 | instantiation | 450, 442, 389 | ⊢ |
| : , : , : |
276 | instantiation | 305, 306, 324 | ⊢ |
| : , : |
277 | instantiation | 307, 441, 449, 308* | ⊢ |
| : , : , : , : |
278 | theorem | | ⊢ |
| proveit.logic.equality.sub_right_side_into |
279 | instantiation | 309, 358, 310, 311 | ⊢ |
| : , : , : , : , : |
280 | instantiation | 394, 312, 313 | ⊢ |
| : , : , : |
281 | theorem | | ⊢ |
| proveit.logic.equality.four_chain_transitivity |
282 | instantiation | 402, 314 | ⊢ |
| : , : , : |
283 | instantiation | 402, 314 | ⊢ |
| : , : , : |
284 | instantiation | 435, 358 | ⊢ |
| : |
285 | theorem | | ⊢ |
| proveit.numbers.number_sets.real_numbers.real_pos_within_real_nonzero |
286 | instantiation | 315, 358, 353 | ⊢ |
| : , : |
287 | theorem | | ⊢ |
| proveit.numbers.exponentiation.exp_zero_eq_one |
288 | theorem | | ⊢ |
| proveit.numbers.addition.strong_bound_via_left_term_bound |
289 | instantiation | 450, 446, 316 | ⊢ |
| : , : , : |
290 | instantiation | 317, 443, 384, 413, 318, 319 | ⊢ |
| : , : , : |
291 | instantiation | 320, 358, 436, 321 | ⊢ |
| : , : , : |
292 | instantiation | 394, 322, 323 | ⊢ |
| : , : , : |
293 | theorem | | ⊢ |
| proveit.numbers.multiplication.elim_one_any |
294 | instantiation | 450, 442, 324 | ⊢ |
| : , : , : |
295 | instantiation | 450, 442, 325 | ⊢ |
| : , : , : |
296 | instantiation | 402, 326 | ⊢ |
| : , : , : |
297 | instantiation | 327, 410 | ⊢ |
| : |
298 | theorem | | ⊢ |
| proveit.numbers.absolute_value.weak_upper_bound |
299 | instantiation | 328, 361, 389, 362 | ⊢ |
| : , : , : |
300 | instantiation | 363, 329 | ⊢ |
| : , : |
301 | theorem | | ⊢ |
| proveit.numbers.absolute_value.abs_prod |
302 | instantiation | 433 | ⊢ |
| : , : |
303 | instantiation | 330, 331 | ⊢ |
| : |
304 | theorem | | ⊢ |
| proveit.numbers.number_sets.real_numbers.positive_if_in_real_pos |
305 | theorem | | ⊢ |
| proveit.numbers.multiplication.mult_real_closure_bin |
306 | instantiation | 450, 446, 332 | ⊢ |
| : , : , : |
307 | theorem | | ⊢ |
| proveit.numbers.addition.rational_pair_addition |
308 | instantiation | 394, 333, 334 | ⊢ |
| : , : , : |
309 | theorem | | ⊢ |
| proveit.numbers.division.mult_frac_cancel_denom_left |
310 | instantiation | 450, 336, 335 | ⊢ |
| : , : , : |
311 | instantiation | 450, 336, 337 | ⊢ |
| : , : , : |
312 | instantiation | 402, 338 | ⊢ |
| : , : , : |
313 | instantiation | 402, 339 | ⊢ |
| : , : , : |
314 | instantiation | 403, 358 | ⊢ |
| : |
315 | theorem | | ⊢ |
| proveit.numbers.addition.subtraction.add_cancel_basic |
316 | instantiation | 450, 448, 340 | ⊢ |
| : , : , : |
317 | theorem | | ⊢ |
| proveit.numbers.ordering.less_eq_add_right_strong |
318 | instantiation | 341, 443, 413, 342, 343, 344, 345* | ⊢ |
| : , : , : |
319 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.less_0_1 |
320 | theorem | | ⊢ |
| proveit.numbers.addition.subtraction.subtract_from_add |
321 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.add_1_1 |
322 | instantiation | 346, 347, 452, 445, 348, 349, 352, 358, 350 | ⊢ |
| : , : , : , : , : , : |
323 | instantiation | 351, 358, 352, 353 | ⊢ |
| : , : , : |
324 | instantiation | 450, 355, 354 | ⊢ |
| : , : , : |
325 | instantiation | 450, 355, 356 | ⊢ |
| : , : , : |
326 | instantiation | 357, 358, 410, 359* | ⊢ |
| : , : |
327 | theorem | | ⊢ |
| proveit.numbers.absolute_value.abs_even |
328 | theorem | | ⊢ |
| proveit.numbers.number_sets.real_numbers.interval_co_lower_bound |
329 | instantiation | 360, 361, 389, 362 | ⊢ |
| : , : , : |
330 | theorem | | ⊢ |
| proveit.numbers.absolute_value.abs_non_neg_elim |
331 | instantiation | 363, 364 | ⊢ |
| : , : |
332 | instantiation | 450, 365, 366 | ⊢ |
| : , : , : |
333 | instantiation | 416, 452, 367, 368, 369, 370 | ⊢ |
| : , : , : , : |
334 | instantiation | 371, 372, 373 | ⊢ |
| : |
335 | instantiation | 450, 375, 374 | ⊢ |
| : , : , : |
336 | theorem | | ⊢ |
| proveit.numbers.number_sets.complex_numbers.real_nonzero_within_complex_nonzero |
337 | instantiation | 450, 375, 376 | ⊢ |
| : , : , : |
338 | instantiation | 402, 419 | ⊢ |
| : , : , : |
339 | instantiation | 394, 377, 378 | ⊢ |
| : , : , : |
340 | instantiation | 450, 451, 379 | ⊢ |
| : , : , : |
341 | theorem | | ⊢ |
| proveit.numbers.exponentiation.exp_monotonicity_large_base_less_eq |
342 | instantiation | 407, 408, 381 | ⊢ |
| : , : , : |
343 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.less_1_2 |
344 | instantiation | 380, 381 | ⊢ |
| : |
345 | instantiation | 382, 436 | ⊢ |
| : |
346 | theorem | | ⊢ |
| proveit.numbers.addition.disassociation |
347 | axiom | | ⊢ |
| proveit.numbers.number_sets.natural_numbers.zero_in_nats |
348 | theorem | | ⊢ |
| proveit.core_expr_types.tuples.tuple_len_0_typical_eq |
349 | instantiation | 433 | ⊢ |
| : , : |
350 | instantiation | 450, 442, 383 | ⊢ |
| : , : , : |
351 | theorem | | ⊢ |
| proveit.numbers.addition.subtraction.add_cancel_triple_23 |
352 | instantiation | 450, 442, 384 | ⊢ |
| : , : , : |
353 | instantiation | 385 | ⊢ |
| : |
354 | theorem | | ⊢ |
| proveit.numbers.number_sets.real_numbers.pi_is_real_pos |
355 | theorem | | ⊢ |
| proveit.numbers.number_sets.real_numbers.real_pos_within_real |
356 | instantiation | 386, 387 | ⊢ |
| : |
357 | theorem | | ⊢ |
| proveit.numbers.multiplication.mult_neg_left |
358 | instantiation | 450, 442, 413 | ⊢ |
| : , : , : |
359 | instantiation | 434, 410 | ⊢ |
| : |
360 | theorem | | ⊢ |
| proveit.numbers.number_sets.real_numbers.interval_co_upper_bound |
361 | instantiation | 388, 389 | ⊢ |
| : |
362 | theorem | | ⊢ |
| proveit.physics.quantum.QPE._scaled_delta_b_round_in_interval |
363 | theorem | | ⊢ |
| proveit.numbers.ordering.relax_less |
364 | instantiation | 390, 425 | ⊢ |
| : |
365 | theorem | | ⊢ |
| proveit.numbers.number_sets.rational_numbers.rational_pos_within_rational |
366 | instantiation | 391, 392, 393 | ⊢ |
| : , : |
367 | instantiation | 433 | ⊢ |
| : , : |
368 | instantiation | 433 | ⊢ |
| : , : |
369 | instantiation | 394, 395, 396 | ⊢ |
| : , : , : |
370 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.mult_2_2 |
371 | theorem | | ⊢ |
| proveit.numbers.division.frac_cancel_complete |
372 | instantiation | 450, 442, 397 | ⊢ |
| : , : , : |
373 | instantiation | 431, 398 | ⊢ |
| : |
374 | instantiation | 450, 400, 399 | ⊢ |
| : , : , : |
375 | theorem | | ⊢ |
| proveit.numbers.number_sets.real_numbers.rational_nonzero_within_real_nonzero |
376 | instantiation | 450, 400, 401 | ⊢ |
| : , : , : |
377 | instantiation | 402, 420 | ⊢ |
| : , : , : |
378 | instantiation | 403, 436 | ⊢ |
| : |
379 | instantiation | 404, 405, 445 | ⊢ |
| : , : |
380 | theorem | | ⊢ |
| proveit.numbers.number_sets.natural_numbers.natural_pos_lower_bound |
381 | axiom | | ⊢ |
| proveit.physics.quantum.QPE._t_in_natural_pos |
382 | theorem | | ⊢ |
| proveit.numbers.exponentiation.complex_x_to_first_power_is_x |
383 | instantiation | 450, 446, 406 | ⊢ |
| : , : , : |
384 | instantiation | 407, 408, 425 | ⊢ |
| : , : , : |
385 | axiom | | ⊢ |
| proveit.logic.equality.equals_reflexivity |
386 | theorem | | ⊢ |
| proveit.numbers.absolute_value.abs_nonzero_closure |
387 | instantiation | 409, 410, 411 | ⊢ |
| : |
388 | theorem | | ⊢ |
| proveit.numbers.negation.real_closure |
389 | instantiation | 412, 413, 443, 414 | ⊢ |
| : , : |
390 | theorem | | ⊢ |
| proveit.numbers.number_sets.natural_numbers.natural_pos_is_pos |
391 | theorem | | ⊢ |
| proveit.numbers.division.div_rational_pos_closure |
392 | instantiation | 450, 415, 422 | ⊢ |
| : , : , : |
393 | instantiation | 450, 415, 432 | ⊢ |
| : , : , : |
394 | axiom | | ⊢ |
| proveit.logic.equality.equals_transitivity |
395 | instantiation | 416, 452, 417, 418, 419, 420 | ⊢ |
| : , : , : , : |
396 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.add_2_2 |
397 | instantiation | 450, 446, 421 | ⊢ |
| : , : , : |
398 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.posnat4 |
399 | instantiation | 450, 423, 422 | ⊢ |
| : , : , : |
400 | theorem | | ⊢ |
| proveit.numbers.number_sets.rational_numbers.nonzero_int_within_rational_nonzero |
401 | instantiation | 450, 423, 432 | ⊢ |
| : , : , : |
402 | axiom | | ⊢ |
| proveit.logic.equality.substitution |
403 | theorem | | ⊢ |
| proveit.numbers.division.frac_one_denom |
404 | theorem | | ⊢ |
| proveit.numbers.addition.add_nat_closure_bin |
405 | instantiation | 450, 424, 425 | ⊢ |
| : , : , : |
406 | instantiation | 450, 448, 426 | ⊢ |
| : , : , : |
407 | theorem | | ⊢ |
| proveit.logic.sets.inclusion.unfold_subset_eq |
408 | instantiation | 427, 428 | ⊢ |
| : , : |
409 | theorem | | ⊢ |
| proveit.numbers.number_sets.complex_numbers.nonzero_complex_is_complex_nonzero |
410 | instantiation | 450, 442, 429 | ⊢ |
| : , : , : |
411 | assumption | | ⊢ |
412 | theorem | | ⊢ |
| proveit.numbers.division.div_real_closure |
413 | instantiation | 450, 446, 430 | ⊢ |
| : , : , : |
414 | instantiation | 431, 432 | ⊢ |
| : |
415 | theorem | | ⊢ |
| proveit.numbers.number_sets.rational_numbers.nat_pos_within_rational_pos |
416 | axiom | | ⊢ |
| proveit.core_expr_types.operations.operands_substitution |
417 | instantiation | 433 | ⊢ |
| : , : |
418 | instantiation | 433 | ⊢ |
| : , : |
419 | instantiation | 434, 436 | ⊢ |
| : |
420 | instantiation | 435, 436 | ⊢ |
| : |
421 | instantiation | 450, 448, 437 | ⊢ |
| : , : , : |
422 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.posnat1 |
423 | theorem | | ⊢ |
| proveit.numbers.number_sets.integers.nat_pos_within_nonzero_int |
424 | theorem | | ⊢ |
| proveit.numbers.number_sets.natural_numbers.nat_pos_within_nat |
425 | theorem | | ⊢ |
| proveit.physics.quantum.QPE._two_pow_t_is_nat_pos |
426 | instantiation | 438, 441 | ⊢ |
| : |
427 | theorem | | ⊢ |
| proveit.logic.sets.inclusion.relax_proper_subset |
428 | theorem | | ⊢ |
| proveit.numbers.number_sets.real_numbers.nat_pos_within_real |
429 | instantiation | 439, 440 | ⊢ |
| : |
430 | instantiation | 450, 448, 441 | ⊢ |
| : , : , : |
431 | theorem | | ⊢ |
| proveit.numbers.number_sets.natural_numbers.nonzero_if_is_nat_pos |
432 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.posnat2 |
433 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.tuple_len_2_typical_eq |
434 | theorem | | ⊢ |
| proveit.numbers.multiplication.elim_one_left |
435 | theorem | | ⊢ |
| proveit.numbers.multiplication.elim_one_right |
436 | instantiation | 450, 442, 443 | ⊢ |
| : , : , : |
437 | instantiation | 450, 451, 444 | ⊢ |
| : , : , : |
438 | theorem | | ⊢ |
| proveit.numbers.negation.int_closure |
439 | theorem | | ⊢ |
| proveit.physics.quantum.QPE._delta_b_is_real |
440 | theorem | | ⊢ |
| proveit.physics.quantum.QPE._best_round_is_int |
441 | instantiation | 450, 451, 445 | ⊢ |
| : , : , : |
442 | theorem | | ⊢ |
| proveit.numbers.number_sets.complex_numbers.real_within_complex |
443 | instantiation | 450, 446, 447 | ⊢ |
| : , : , : |
444 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.nat4 |
445 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.nat1 |
446 | theorem | | ⊢ |
| proveit.numbers.number_sets.real_numbers.rational_within_real |
447 | instantiation | 450, 448, 449 | ⊢ |
| : , : , : |
448 | theorem | | ⊢ |
| proveit.numbers.number_sets.rational_numbers.int_within_rational |
449 | instantiation | 450, 451, 452 | ⊢ |
| : , : , : |
450 | theorem | | ⊢ |
| proveit.logic.sets.inclusion.superset_membership_from_proper_subset |
451 | theorem | | ⊢ |
| proveit.numbers.number_sets.integers.nat_within_int |
452 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.nat2 |
*equality replacement requirements |