| step type | requirements | statement |
0 | instantiation | 1, 2, 3, 4, 5, 6, 7* | ⊢ |
| : , : , : |
1 | reference | 154 | ⊢ |
2 | instantiation | 342, 338, 8 | ⊢ |
| : , : , : |
3 | instantiation | 305, 21, 119, 106 | ⊢ |
| : , : |
4 | instantiation | 305, 22, 32, 9 | ⊢ |
| : , : |
5 | instantiation | 151, 10, 11 | ⊢ |
| : , : , : |
6 | instantiation | 176, 14 | ⊢ |
| : |
7 | instantiation | 292, 12, 13 | ⊢ |
| : , : , : |
8 | instantiation | 342, 268, 14 | ⊢ |
| : , : , : |
9 | instantiation | 15, 16 | ⊢ |
| : , : |
10 | instantiation | 17, 35, 18, 134, 19 | ⊢ |
| : , : , : |
11 | instantiation | 20, 32, 21, 22, 23, 33 | ⊢ |
| : , : , : |
12 | instantiation | 292, 24, 25 | ⊢ |
| : , : , : |
13 | instantiation | 26, 27, 28, 29 | ⊢ |
| : , : , : , : |
14 | instantiation | 289, 290, 74 | ⊢ |
| : , : |
15 | theorem | | ⊢ |
| proveit.logic.equality.not_equals_symmetry |
16 | instantiation | 30, 155, 32, 33 | ⊢ |
| : , : |
17 | theorem | | ⊢ |
| proveit.numbers.division.strong_div_from_denom_bound__all_pos |
18 | instantiation | 31, 32, 33 | ⊢ |
| : |
19 | instantiation | 34, 134 | ⊢ |
| : |
20 | theorem | | ⊢ |
| proveit.numbers.division.weak_div_from_numer_bound__pos_denom |
21 | instantiation | 342, 258, 35 | ⊢ |
| : , : , : |
22 | instantiation | 36, 37 | ⊢ |
| : |
23 | instantiation | 38, 39, 40, 41* | ⊢ |
| : |
24 | instantiation | 233, 42 | ⊢ |
| : , : , : |
25 | instantiation | 190, 43, 44 | ⊢ |
| : , : , : |
26 | theorem | | ⊢ |
| proveit.logic.equality.four_chain_transitivity |
27 | instantiation | 233, 45 | ⊢ |
| : , : , : |
28 | instantiation | 233, 46 | ⊢ |
| : , : , : |
29 | instantiation | 112, 47, 113, 328 | ⊢ |
| : , : , : |
30 | theorem | | ⊢ |
| proveit.numbers.ordering.less_is_not_eq |
31 | theorem | | ⊢ |
| proveit.numbers.number_sets.real_numbers.pos_real_is_real_pos |
32 | instantiation | 48, 155, 306, 50 | ⊢ |
| : , : , : |
33 | instantiation | 49, 155, 306, 50 | ⊢ |
| : , : , : |
34 | theorem | | ⊢ |
| proveit.trigonometry.sine_linear_bound_by_arg_pos |
35 | instantiation | 51, 144, 145, 52, 53, 259 | ⊢ |
| : , : |
36 | theorem | | ⊢ |
| proveit.trigonometry.real_closure |
37 | instantiation | 190, 54, 55 | ⊢ |
| : , : , : |
38 | theorem | | ⊢ |
| proveit.trigonometry.sine_linear_bound_nonneg |
39 | instantiation | 56, 144, 97, 57, 58, 59 | ⊢ |
| : , : |
40 | instantiation | 167, 60, 61 | ⊢ |
| : , : , : |
41 | instantiation | 292, 62, 63 | ⊢ |
| : , : , : |
42 | instantiation | 292, 64, 65 | ⊢ |
| : , : , : |
43 | instantiation | 190, 66, 67 | ⊢ |
| : , : , : |
44 | instantiation | 292, 68, 69 | ⊢ |
| : , : , : |
45 | instantiation | 196, 328, 209 | ⊢ |
| : , : |
46 | instantiation | 196, 208, 209 | ⊢ |
| : , : |
47 | instantiation | 342, 140, 70 | ⊢ |
| : , : , : |
48 | theorem | | ⊢ |
| proveit.numbers.number_sets.real_numbers.all_in_interval_oc__is__real |
49 | theorem | | ⊢ |
| proveit.numbers.number_sets.real_numbers.interval_oc_lower_bound |
50 | instantiation | 71, 72 | ⊢ |
| : |
51 | theorem | | ⊢ |
| proveit.numbers.multiplication.mult_real_pos_closure |
52 | instantiation | 342, 73, 291 | ⊢ |
| : , : , : |
53 | instantiation | 342, 73, 74 | ⊢ |
| : , : , : |
54 | instantiation | 219, 75, 232 | ⊢ |
| : , : |
55 | instantiation | 194, 250, 344, 337, 251, 76, 255, 208, 209 | ⊢ |
| : , : , : , : , : , : |
56 | theorem | | ⊢ |
| proveit.numbers.multiplication.mult_real_nonneg_closure |
57 | instantiation | 342, 77, 78 | ⊢ |
| : , : , : |
58 | instantiation | 342, 79, 257 | ⊢ |
| : , : , : |
59 | instantiation | 342, 79, 259 | ⊢ |
| : , : , : |
60 | instantiation | 167, 153, 80 | ⊢ |
| : , : , : |
61 | instantiation | 81, 208, 328, 307, 82* | ⊢ |
| : , : |
62 | instantiation | 233, 83 | ⊢ |
| : , : , : |
63 | instantiation | 292, 84, 85 | ⊢ |
| : , : , : |
64 | instantiation | 142, 250, 337, 251, 328, 255, 209 | ⊢ |
| : , : , : , : , : , : , : |
65 | instantiation | 143, 337, 344, 250, 86, 251, 255, 328, 209 | ⊢ |
| : , : , : , : , : , : |
66 | instantiation | 87, 261, 104, 114, 88, 89 | ⊢ |
| : , : , : , : , : |
67 | instantiation | 233, 90 | ⊢ |
| : , : , : |
68 | instantiation | 233, 91 | ⊢ |
| : , : , : |
69 | instantiation | 326, 92 | ⊢ |
| : |
70 | instantiation | 342, 146, 259 | ⊢ |
| : , : , : |
71 | theorem | | ⊢ |
| proveit.trigonometry.sine_pos_interval |
72 | instantiation | 93, 155, 231, 119, 94 | ⊢ |
| : , : , : |
73 | theorem | | ⊢ |
| proveit.numbers.number_sets.real_numbers.rational_pos_within_real_pos |
74 | instantiation | 342, 309, 317 | ⊢ |
| : , : , : |
75 | instantiation | 219, 282, 231 | ⊢ |
| : , : |
76 | instantiation | 325 | ⊢ |
| : , : |
77 | theorem | | ⊢ |
| proveit.numbers.number_sets.real_numbers.rational_nonneg_within_real_nonneg |
78 | instantiation | 342, 95, 298 | ⊢ |
| : , : , : |
79 | theorem | | ⊢ |
| proveit.numbers.number_sets.real_numbers.real_pos_within_real_nonneg |
80 | instantiation | 142, 250, 337, 251, 255, 208, 209 | ⊢ |
| : , : , : , : , : , : , : |
81 | theorem | | ⊢ |
| proveit.numbers.division.div_as_mult |
82 | instantiation | 292, 96, 175 | ⊢ |
| : , : , : |
83 | instantiation | 194, 337, 144, 250, 97, 251, 328, 255, 208, 209 | ⊢ |
| : , : , : , : , : , : |
84 | instantiation | 292, 98, 99 | ⊢ |
| : , : , : |
85 | instantiation | 102, 115 | ⊢ |
| : |
86 | instantiation | 325 | ⊢ |
| : , : |
87 | theorem | | ⊢ |
| proveit.numbers.division.mult_frac_cancel_denom_left |
88 | instantiation | 342, 140, 100 | ⊢ |
| : , : , : |
89 | instantiation | 342, 140, 121 | ⊢ |
| : , : , : |
90 | instantiation | 233, 101 | ⊢ |
| : , : , : |
91 | instantiation | 102, 261 | ⊢ |
| : |
92 | instantiation | 103, 104, 105, 106 | ⊢ |
| : , : |
93 | theorem | | ⊢ |
| proveit.numbers.number_sets.real_numbers.in_IntervalOO |
94 | instantiation | 107, 108, 109 | ⊢ |
| : , : |
95 | theorem | | ⊢ |
| proveit.numbers.number_sets.rational_numbers.nat_within_rational_nonneg |
96 | instantiation | 233, 110 | ⊢ |
| : , : , : |
97 | instantiation | 164 | ⊢ |
| : , : , : |
98 | instantiation | 233, 111 | ⊢ |
| : , : , : |
99 | instantiation | 112, 113, 114, 115, 116* | ⊢ |
| : , : , : |
100 | instantiation | 342, 162, 117 | ⊢ |
| : , : , : |
101 | instantiation | 326, 255 | ⊢ |
| : |
102 | theorem | | ⊢ |
| proveit.numbers.division.frac_one_denom |
103 | theorem | | ⊢ |
| proveit.numbers.division.div_complex_closure |
104 | instantiation | 118, 328, 209 | ⊢ |
| : , : |
105 | instantiation | 342, 334, 119 | ⊢ |
| : , : , : |
106 | instantiation | 120, 121 | ⊢ |
| : |
107 | theorem | | ⊢ |
| proveit.logic.booleans.conjunction.and_if_both |
108 | instantiation | 218, 134 | ⊢ |
| : |
109 | instantiation | 122, 123, 124 | ⊢ |
| : , : , : |
110 | instantiation | 125, 126, 308, 248* | ⊢ |
| : , : |
111 | instantiation | 292, 127, 128 | ⊢ |
| : , : , : |
112 | theorem | | ⊢ |
| proveit.numbers.division.frac_cancel_left |
113 | instantiation | 342, 140, 129 | ⊢ |
| : , : , : |
114 | instantiation | 342, 140, 130 | ⊢ |
| : , : , : |
115 | instantiation | 190, 131, 132 | ⊢ |
| : , : , : |
116 | instantiation | 327, 208 | ⊢ |
| : |
117 | instantiation | 342, 184, 133 | ⊢ |
| : , : , : |
118 | theorem | | ⊢ |
| proveit.numbers.multiplication.mult_complex_closure_bin |
119 | instantiation | 342, 258, 134 | ⊢ |
| : , : , : |
120 | theorem | | ⊢ |
| proveit.numbers.number_sets.real_numbers.nonzero_if_in_real_nonzero |
121 | instantiation | 342, 146, 134 | ⊢ |
| : , : , : |
122 | axiom | | ⊢ |
| proveit.numbers.ordering.transitivity_less_less |
123 | instantiation | 190, 135, 169 | ⊢ |
| : , : , : |
124 | instantiation | 202, 199, 136, 137, 138*, 139* | ⊢ |
| : , : , : |
125 | theorem | | ⊢ |
| proveit.numbers.exponentiation.neg_power_as_div |
126 | instantiation | 342, 140, 141 | ⊢ |
| : , : , : |
127 | instantiation | 142, 250, 344, 337, 251, 149, 328, 255, 208, 209 | ⊢ |
| : , : , : , : , : , : , : |
128 | instantiation | 143, 337, 144, 250, 145, 251, 208, 328, 255, 209 | ⊢ |
| : , : , : , : , : , : |
129 | instantiation | 342, 146, 257 | ⊢ |
| : , : , : |
130 | instantiation | 342, 162, 147 | ⊢ |
| : , : , : |
131 | instantiation | 342, 334, 148 | ⊢ |
| : , : , : |
132 | instantiation | 194, 250, 344, 337, 251, 149, 328, 255, 209 | ⊢ |
| : , : , : , : , : , : |
133 | instantiation | 342, 201, 317 | ⊢ |
| : , : , : |
134 | instantiation | 150, 257, 259 | ⊢ |
| : , : |
135 | instantiation | 151, 152, 153 | ⊢ |
| : , : , : |
136 | instantiation | 219, 220, 155 | ⊢ |
| : , : |
137 | instantiation | 154, 220, 155, 231, 193, 156 | ⊢ |
| : , : , : |
138 | instantiation | 292, 157, 158 | ⊢ |
| : , : , : |
139 | instantiation | 159, 160, 161* | ⊢ |
| : , : |
140 | theorem | | ⊢ |
| proveit.numbers.number_sets.complex_numbers.real_nonzero_within_complex_nonzero |
141 | instantiation | 342, 162, 163 | ⊢ |
| : , : , : |
142 | theorem | | ⊢ |
| proveit.numbers.multiplication.leftward_commutation |
143 | theorem | | ⊢ |
| proveit.numbers.multiplication.association |
144 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.nat3 |
145 | instantiation | 164 | ⊢ |
| : , : , : |
146 | theorem | | ⊢ |
| proveit.numbers.number_sets.real_numbers.real_pos_within_real_nonzero |
147 | instantiation | 342, 184, 165 | ⊢ |
| : , : , : |
148 | instantiation | 219, 166, 232 | ⊢ |
| : , : |
149 | instantiation | 325 | ⊢ |
| : , : |
150 | theorem | | ⊢ |
| proveit.numbers.multiplication.mult_real_pos_closure_bin |
151 | theorem | | ⊢ |
| proveit.numbers.ordering.transitivity_less_less_eq |
152 | instantiation | 167, 168, 169 | ⊢ |
| : , : , : |
153 | instantiation | 170, 231, 171, 287, 172, 173, 174*, 175* | ⊢ |
| : , : , : |
154 | theorem | | ⊢ |
| proveit.numbers.multiplication.strong_bound_via_right_factor_bound |
155 | theorem | | ⊢ |
| proveit.numbers.number_sets.real_numbers.zero_is_real |
156 | instantiation | 176, 269 | ⊢ |
| : |
157 | instantiation | 233, 177 | ⊢ |
| : , : , : |
158 | instantiation | 178, 179 | ⊢ |
| : |
159 | theorem | | ⊢ |
| proveit.logic.equality.equals_reversal |
160 | instantiation | 180, 250, 344, 337, 251, 181, 198, 208 | ⊢ |
| : , : , : , : , : , : |
161 | instantiation | 292, 182, 183 | ⊢ |
| : , : , : |
162 | theorem | | ⊢ |
| proveit.numbers.number_sets.real_numbers.rational_nonzero_within_real_nonzero |
163 | instantiation | 342, 184, 185 | ⊢ |
| : , : , : |
164 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.tuple_len_3_typical_eq |
165 | instantiation | 342, 201, 308 | ⊢ |
| : , : , : |
166 | instantiation | 219, 335, 282 | ⊢ |
| : , : |
167 | theorem | | ⊢ |
| proveit.logic.equality.sub_left_side_into |
168 | instantiation | 186, 337, 257, 259, 187, 188* | ⊢ |
| : , : , : , : , : , : |
169 | instantiation | 233, 189 | ⊢ |
| : , : , : |
170 | theorem | | ⊢ |
| proveit.numbers.multiplication.weak_bound_via_right_factor_bound |
171 | instantiation | 219, 282, 232 | ⊢ |
| : , : |
172 | instantiation | 190, 191, 192 | ⊢ |
| : , : , : |
173 | instantiation | 266, 193 | ⊢ |
| : , : |
174 | instantiation | 194, 337, 344, 250, 195, 251, 208, 255, 209 | ⊢ |
| : , : , : , : , : , : |
175 | instantiation | 196, 208, 198 | ⊢ |
| : , : |
176 | theorem | | ⊢ |
| proveit.numbers.number_sets.rational_numbers.positive_if_in_rational_pos |
177 | instantiation | 197, 198 | ⊢ |
| : |
178 | theorem | | ⊢ |
| proveit.numbers.addition.elim_zero_left |
179 | instantiation | 342, 334, 199 | ⊢ |
| : , : , : |
180 | theorem | | ⊢ |
| proveit.numbers.multiplication.distribute_through_sum |
181 | instantiation | 325 | ⊢ |
| : , : |
182 | instantiation | 233, 200 | ⊢ |
| : , : , : |
183 | instantiation | 326, 208 | ⊢ |
| : |
184 | theorem | | ⊢ |
| proveit.numbers.number_sets.rational_numbers.nonzero_int_within_rational_nonzero |
185 | instantiation | 342, 201, 324 | ⊢ |
| : , : , : |
186 | theorem | | ⊢ |
| proveit.numbers.multiplication.strong_bound_via_factor_bound |
187 | instantiation | 202, 281, 335, 203, 204, 205*, 206* | ⊢ |
| : , : , : |
188 | instantiation | 207, 337, 208, 209 | ⊢ |
| : , : , : , : |
189 | instantiation | 292, 210, 211 | ⊢ |
| : , : , : |
190 | theorem | | ⊢ |
| proveit.logic.equality.sub_right_side_into |
191 | instantiation | 212, 213, 214 | ⊢ |
| : , : |
192 | instantiation | 215, 324, 216, 255, 303, 217* | ⊢ |
| : , : |
193 | instantiation | 218, 257 | ⊢ |
| : |
194 | theorem | | ⊢ |
| proveit.numbers.multiplication.disassociation |
195 | instantiation | 325 | ⊢ |
| : , : |
196 | theorem | | ⊢ |
| proveit.numbers.multiplication.commutation |
197 | theorem | | ⊢ |
| proveit.numbers.multiplication.mult_zero_right |
198 | instantiation | 342, 334, 287 | ⊢ |
| : , : , : |
199 | instantiation | 219, 220, 231 | ⊢ |
| : , : |
200 | instantiation | 221, 333, 341, 222* | ⊢ |
| : , : , : , : |
201 | theorem | | ⊢ |
| proveit.numbers.number_sets.integers.nat_pos_within_nonzero_int |
202 | theorem | | ⊢ |
| proveit.numbers.addition.strong_bound_via_left_term_bound |
203 | instantiation | 342, 338, 223 | ⊢ |
| : , : , : |
204 | instantiation | 224, 335, 282, 306, 225, 226 | ⊢ |
| : , : , : |
205 | instantiation | 227, 261, 328, 228 | ⊢ |
| : , : , : |
206 | instantiation | 292, 229, 230 | ⊢ |
| : , : , : |
207 | theorem | | ⊢ |
| proveit.numbers.multiplication.elim_one_any |
208 | instantiation | 342, 334, 231 | ⊢ |
| : , : , : |
209 | instantiation | 342, 334, 232 | ⊢ |
| : , : , : |
210 | instantiation | 233, 234 | ⊢ |
| : , : , : |
211 | instantiation | 235, 303 | ⊢ |
| : |
212 | theorem | | ⊢ |
| proveit.numbers.absolute_value.weak_upper_bound |
213 | instantiation | 236, 264, 287, 265 | ⊢ |
| : , : , : |
214 | instantiation | 266, 237 | ⊢ |
| : , : |
215 | theorem | | ⊢ |
| proveit.numbers.absolute_value.abs_prod |
216 | instantiation | 325 | ⊢ |
| : , : |
217 | instantiation | 238, 239 | ⊢ |
| : |
218 | theorem | | ⊢ |
| proveit.numbers.number_sets.real_numbers.positive_if_in_real_pos |
219 | theorem | | ⊢ |
| proveit.numbers.multiplication.mult_real_closure_bin |
220 | instantiation | 342, 338, 240 | ⊢ |
| : , : , : |
221 | theorem | | ⊢ |
| proveit.numbers.addition.rational_pair_addition |
222 | instantiation | 292, 241, 242 | ⊢ |
| : , : , : |
223 | instantiation | 342, 340, 243 | ⊢ |
| : , : , : |
224 | theorem | | ⊢ |
| proveit.numbers.ordering.less_eq_add_right_strong |
225 | instantiation | 244, 335, 306, 245, 246, 247, 248* | ⊢ |
| : , : , : |
226 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.less_0_1 |
227 | theorem | | ⊢ |
| proveit.numbers.addition.subtraction.subtract_from_add |
228 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.add_1_1 |
229 | instantiation | 249, 250, 344, 337, 251, 252, 255, 261, 253 | ⊢ |
| : , : , : , : , : , : |
230 | instantiation | 254, 261, 255, 256 | ⊢ |
| : , : , : |
231 | instantiation | 342, 258, 257 | ⊢ |
| : , : , : |
232 | instantiation | 342, 258, 259 | ⊢ |
| : , : , : |
233 | axiom | | ⊢ |
| proveit.logic.equality.substitution |
234 | instantiation | 260, 261, 303, 262* | ⊢ |
| : , : |
235 | theorem | | ⊢ |
| proveit.numbers.absolute_value.abs_even |
236 | theorem | | ⊢ |
| proveit.numbers.number_sets.real_numbers.interval_co_lower_bound |
237 | instantiation | 263, 264, 287, 265 | ⊢ |
| : , : , : |
238 | theorem | | ⊢ |
| proveit.numbers.absolute_value.abs_non_neg_elim |
239 | instantiation | 266, 267 | ⊢ |
| : , : |
240 | instantiation | 342, 268, 269 | ⊢ |
| : , : , : |
241 | instantiation | 310, 344, 270, 271, 272, 273 | ⊢ |
| : , : , : , : |
242 | instantiation | 274, 275, 276 | ⊢ |
| : |
243 | instantiation | 342, 343, 277 | ⊢ |
| : , : , : |
244 | theorem | | ⊢ |
| proveit.numbers.exponentiation.exp_monotonicity_large_base_less_eq |
245 | instantiation | 300, 301, 279 | ⊢ |
| : , : , : |
246 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.less_1_2 |
247 | instantiation | 278, 279 | ⊢ |
| : |
248 | instantiation | 280, 328 | ⊢ |
| : |
249 | theorem | | ⊢ |
| proveit.numbers.addition.disassociation |
250 | axiom | | ⊢ |
| proveit.numbers.number_sets.natural_numbers.zero_in_nats |
251 | theorem | | ⊢ |
| proveit.core_expr_types.tuples.tuple_len_0_typical_eq |
252 | instantiation | 325 | ⊢ |
| : , : |
253 | instantiation | 342, 334, 281 | ⊢ |
| : , : , : |
254 | theorem | | ⊢ |
| proveit.numbers.addition.subtraction.add_cancel_triple_23 |
255 | instantiation | 342, 334, 282 | ⊢ |
| : , : , : |
256 | instantiation | 283 | ⊢ |
| : |
257 | theorem | | ⊢ |
| proveit.numbers.number_sets.real_numbers.pi_is_real_pos |
258 | theorem | | ⊢ |
| proveit.numbers.number_sets.real_numbers.real_pos_within_real |
259 | instantiation | 284, 285 | ⊢ |
| : |
260 | theorem | | ⊢ |
| proveit.numbers.multiplication.mult_neg_left |
261 | instantiation | 342, 334, 306 | ⊢ |
| : , : , : |
262 | instantiation | 326, 303 | ⊢ |
| : |
263 | theorem | | ⊢ |
| proveit.numbers.number_sets.real_numbers.interval_co_upper_bound |
264 | instantiation | 286, 287 | ⊢ |
| : |
265 | theorem | | ⊢ |
| proveit.physics.quantum.QPE._scaled_delta_b_round_in_interval |
266 | theorem | | ⊢ |
| proveit.numbers.ordering.relax_less |
267 | instantiation | 288, 317 | ⊢ |
| : |
268 | theorem | | ⊢ |
| proveit.numbers.number_sets.rational_numbers.rational_pos_within_rational |
269 | instantiation | 289, 290, 291 | ⊢ |
| : , : |
270 | instantiation | 325 | ⊢ |
| : , : |
271 | instantiation | 325 | ⊢ |
| : , : |
272 | instantiation | 292, 293, 294 | ⊢ |
| : , : , : |
273 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.mult_2_2 |
274 | theorem | | ⊢ |
| proveit.numbers.division.frac_cancel_complete |
275 | instantiation | 342, 334, 295 | ⊢ |
| : , : , : |
276 | instantiation | 323, 296 | ⊢ |
| : |
277 | instantiation | 297, 298, 337 | ⊢ |
| : , : |
278 | theorem | | ⊢ |
| proveit.numbers.number_sets.natural_numbers.natural_pos_lower_bound |
279 | axiom | | ⊢ |
| proveit.physics.quantum.QPE._t_in_natural_pos |
280 | theorem | | ⊢ |
| proveit.numbers.exponentiation.complex_x_to_first_power_is_x |
281 | instantiation | 342, 338, 299 | ⊢ |
| : , : , : |
282 | instantiation | 300, 301, 317 | ⊢ |
| : , : , : |
283 | axiom | | ⊢ |
| proveit.logic.equality.equals_reflexivity |
284 | theorem | | ⊢ |
| proveit.numbers.absolute_value.abs_nonzero_closure |
285 | instantiation | 302, 303, 304 | ⊢ |
| : |
286 | theorem | | ⊢ |
| proveit.numbers.negation.real_closure |
287 | instantiation | 305, 306, 335, 307 | ⊢ |
| : , : |
288 | theorem | | ⊢ |
| proveit.numbers.number_sets.natural_numbers.natural_pos_is_pos |
289 | theorem | | ⊢ |
| proveit.numbers.division.div_rational_pos_closure |
290 | instantiation | 342, 309, 308 | ⊢ |
| : , : , : |
291 | instantiation | 342, 309, 324 | ⊢ |
| : , : , : |
292 | axiom | | ⊢ |
| proveit.logic.equality.equals_transitivity |
293 | instantiation | 310, 344, 311, 312, 313, 314 | ⊢ |
| : , : , : , : |
294 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.add_2_2 |
295 | instantiation | 342, 338, 315 | ⊢ |
| : , : , : |
296 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.posnat4 |
297 | theorem | | ⊢ |
| proveit.numbers.addition.add_nat_closure_bin |
298 | instantiation | 342, 316, 317 | ⊢ |
| : , : , : |
299 | instantiation | 342, 340, 318 | ⊢ |
| : , : , : |
300 | theorem | | ⊢ |
| proveit.logic.sets.inclusion.unfold_subset_eq |
301 | instantiation | 319, 320 | ⊢ |
| : , : |
302 | theorem | | ⊢ |
| proveit.numbers.number_sets.complex_numbers.nonzero_complex_is_complex_nonzero |
303 | instantiation | 342, 334, 321 | ⊢ |
| : , : , : |
304 | assumption | | ⊢ |
305 | theorem | | ⊢ |
| proveit.numbers.division.div_real_closure |
306 | instantiation | 342, 338, 322 | ⊢ |
| : , : , : |
307 | instantiation | 323, 324 | ⊢ |
| : |
308 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.posnat1 |
309 | theorem | | ⊢ |
| proveit.numbers.number_sets.rational_numbers.nat_pos_within_rational_pos |
310 | axiom | | ⊢ |
| proveit.core_expr_types.operations.operands_substitution |
311 | instantiation | 325 | ⊢ |
| : , : |
312 | instantiation | 325 | ⊢ |
| : , : |
313 | instantiation | 326, 328 | ⊢ |
| : |
314 | instantiation | 327, 328 | ⊢ |
| : |
315 | instantiation | 342, 340, 329 | ⊢ |
| : , : , : |
316 | theorem | | ⊢ |
| proveit.numbers.number_sets.natural_numbers.nat_pos_within_nat |
317 | theorem | | ⊢ |
| proveit.physics.quantum.QPE._two_pow_t_is_nat_pos |
318 | instantiation | 330, 333 | ⊢ |
| : |
319 | theorem | | ⊢ |
| proveit.logic.sets.inclusion.relax_proper_subset |
320 | theorem | | ⊢ |
| proveit.numbers.number_sets.real_numbers.nat_pos_within_real |
321 | instantiation | 331, 332 | ⊢ |
| : |
322 | instantiation | 342, 340, 333 | ⊢ |
| : , : , : |
323 | theorem | | ⊢ |
| proveit.numbers.number_sets.natural_numbers.nonzero_if_is_nat_pos |
324 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.posnat2 |
325 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.tuple_len_2_typical_eq |
326 | theorem | | ⊢ |
| proveit.numbers.multiplication.elim_one_left |
327 | theorem | | ⊢ |
| proveit.numbers.multiplication.elim_one_right |
328 | instantiation | 342, 334, 335 | ⊢ |
| : , : , : |
329 | instantiation | 342, 343, 336 | ⊢ |
| : , : , : |
330 | theorem | | ⊢ |
| proveit.numbers.negation.int_closure |
331 | theorem | | ⊢ |
| proveit.physics.quantum.QPE._delta_b_is_real |
332 | theorem | | ⊢ |
| proveit.physics.quantum.QPE._best_round_is_int |
333 | instantiation | 342, 343, 337 | ⊢ |
| : , : , : |
334 | theorem | | ⊢ |
| proveit.numbers.number_sets.complex_numbers.real_within_complex |
335 | instantiation | 342, 338, 339 | ⊢ |
| : , : , : |
336 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.nat4 |
337 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.nat1 |
338 | theorem | | ⊢ |
| proveit.numbers.number_sets.real_numbers.rational_within_real |
339 | instantiation | 342, 340, 341 | ⊢ |
| : , : , : |
340 | theorem | | ⊢ |
| proveit.numbers.number_sets.rational_numbers.int_within_rational |
341 | instantiation | 342, 343, 344 | ⊢ |
| : , : , : |
342 | theorem | | ⊢ |
| proveit.logic.sets.inclusion.superset_membership_from_proper_subset |
343 | theorem | | ⊢ |
| proveit.numbers.number_sets.integers.nat_within_int |
344 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.nat2 |
*equality replacement requirements |