| step type | requirements | statement |
0 | instantiation | 1, 2, 3, 4, 5 | ⊢ |
| : , : , : |
1 | conjecture | | ⊢ |
| proveit.numbers.number_sets.integers.in_interval |
2 | reference | 316 | ⊢ |
3 | instantiation | 110, 6, 112 | ⊢ |
| : , : |
4 | instantiation | 110, 7, 31 | ⊢ |
| : , : |
5 | instantiation | 170, 8, 9 | ⊢ |
| : , : |
6 | instantiation | 10, 280, 11 | ⊢ |
| : , : |
7 | instantiation | 317, 116, 12 | ⊢ |
| : , : , : |
8 | instantiation | 158, 90, 264, 13, 14, 15*, 16* | ⊢ |
| : , : , : |
9 | instantiation | 17, 18, 19 | ⊢ |
| : , : , : |
10 | conjecture | | ⊢ |
| proveit.numbers.exponentiation.exp_int_closure |
11 | instantiation | 103, 20, 21 | ⊢ |
| : |
12 | instantiation | 59, 290, 67 | ⊢ |
| : , : |
13 | instantiation | 177, 26, 311 | ⊢ |
| : , : |
14 | instantiation | 126, 264, 26, 311, 22, 23 | ⊢ |
| : , : , : |
15 | instantiation | 24, 272, 251, 142 | ⊢ |
| : , : , : |
16 | instantiation | 224, 25 | ⊢ |
| : , : , : |
17 | theorem | | ⊢ |
| proveit.logic.equality.sub_right_side_into |
18 | instantiation | 126, 26, 60, 27, 28, 29* | ⊢ |
| : , : , : |
19 | instantiation | 224, 30 | ⊢ |
| : , : , : |
20 | instantiation | 110, 111, 31 | ⊢ |
| : , : |
21 | instantiation | 113, 32 | ⊢ |
| : , : |
22 | conjecture | | ⊢ |
| proveit.physics.quantum.QPE._e_value_ge_two |
23 | instantiation | 250, 319 | ⊢ |
| : |
24 | conjecture | | ⊢ |
| proveit.numbers.addition.subtraction.subtract_from_add |
25 | instantiation | 245, 33, 34 | ⊢ |
| : , : , : |
26 | instantiation | 177, 57, 90 | ⊢ |
| : , : |
27 | instantiation | 158, 90, 57, 92, 35 | ⊢ |
| : , : , : |
28 | instantiation | 158, 90, 311, 92, 36, 37* | ⊢ |
| : , : , : |
29 | instantiation | 136, 38, 39, 40 | ⊢ |
| : , : , : , : |
30 | instantiation | 224, 41 | ⊢ |
| : , : , : |
31 | instantiation | 317, 117, 42 | ⊢ |
| : , : , : |
32 | instantiation | 47, 200 | ⊢ |
| : |
33 | instantiation | 191, 192, 290, 319, 193, 43, 44, 65, 272 | ⊢ |
| : , : , : , : , : , : |
34 | instantiation | 168, 272, 44, 50 | ⊢ |
| : , : , : |
35 | instantiation | 45, 264, 127, 86, 291, 46 | ⊢ |
| : , : , : |
36 | instantiation | 47, 48 | ⊢ |
| : |
37 | instantiation | 49, 272, 50 | ⊢ |
| : , : |
38 | instantiation | 191, 192, 290, 319, 193, 52, 84, 65, 51 | ⊢ |
| : , : , : , : , : , : |
39 | instantiation | 191, 290, 192, 52, 193, 84, 65 | ⊢ |
| : , : , : , : , : , : |
40 | instantiation | 136, 53, 54, 55 | ⊢ |
| : , : , : , : |
41 | instantiation | 56, 65, 169 | ⊢ |
| : , : |
42 | instantiation | 121, 295 | ⊢ |
| : |
43 | instantiation | 270 | ⊢ |
| : , : |
44 | instantiation | 317, 279, 57 | ⊢ |
| : , : , : |
45 | conjecture | | ⊢ |
| proveit.numbers.exponentiation.exp_monotonicity_large_base_less_eq |
46 | instantiation | 187, 179, 217, 178, 58 | ⊢ |
| : , : , : |
47 | conjecture | | ⊢ |
| proveit.numbers.number_sets.natural_numbers.natural_pos_lower_bound |
48 | instantiation | 59, 290, 99 | ⊢ |
| : , : |
49 | conjecture | | ⊢ |
| proveit.numbers.addition.subtraction.add_cancel_basic |
50 | instantiation | 219 | ⊢ |
| : |
51 | instantiation | 317, 279, 60 | ⊢ |
| : , : , : |
52 | instantiation | 270 | ⊢ |
| : , : |
53 | instantiation | 106, 319, 84, 65 | ⊢ |
| : , : , : , : , : , : , : |
54 | instantiation | 107, 192, 290, 193, 61, 63, 84, 65, 62* | ⊢ |
| : , : , : , : , : , : |
55 | instantiation | 107, 319, 290, 192, 63, 193, 64, 65, 66* | ⊢ |
| : , : , : , : , : , : |
56 | conjecture | | ⊢ |
| proveit.numbers.addition.commutation |
57 | instantiation | 98, 264, 67 | ⊢ |
| : , : |
58 | instantiation | 68, 264, 240, 119 | ⊢ |
| : , : |
59 | conjecture | | ⊢ |
| proveit.numbers.exponentiation.exp_natpos_closure |
60 | instantiation | 177, 92, 90 | ⊢ |
| : , : |
61 | instantiation | 270 | ⊢ |
| : , : |
62 | instantiation | 69, 70, 71* | ⊢ |
| : , : |
63 | instantiation | 270 | ⊢ |
| : , : |
64 | instantiation | 72, 251, 73 | ⊢ |
| : , : |
65 | instantiation | 164, 272 | ⊢ |
| : |
66 | instantiation | 74, 272, 251, 142 | ⊢ |
| : , : , : |
67 | instantiation | 103, 75, 76 | ⊢ |
| : |
68 | conjecture | | ⊢ |
| proveit.numbers.negation.negated_weak_bound |
69 | theorem | | ⊢ |
| proveit.logic.equality.equals_reversal |
70 | instantiation | 77, 192, 290, 319, 193, 78, 272, 84, 79* | ⊢ |
| : , : , : , : , : , : |
71 | instantiation | 245, 80, 81 | ⊢ |
| : , : , : |
72 | conjecture | | ⊢ |
| proveit.numbers.exponentiation.exp_complex_closure |
73 | instantiation | 317, 279, 82 | ⊢ |
| : , : , : |
74 | conjecture | | ⊢ |
| proveit.numbers.addition.subtraction.negated_add |
75 | instantiation | 110, 111, 83 | ⊢ |
| : , : |
76 | instantiation | 113, 120 | ⊢ |
| : , : |
77 | conjecture | | ⊢ |
| proveit.numbers.multiplication.distribute_through_sum |
78 | instantiation | 270 | ⊢ |
| : , : |
79 | instantiation | 238, 84 | ⊢ |
| : |
80 | instantiation | 224, 142 | ⊢ |
| : , : , : |
81 | instantiation | 85, 251, 311, 86, 87, 88*, 89* | ⊢ |
| : , : , : |
82 | instantiation | 177, 90, 179 | ⊢ |
| : , : |
83 | instantiation | 317, 117, 91 | ⊢ |
| : , : , : |
84 | instantiation | 317, 279, 92 | ⊢ |
| : , : , : |
85 | conjecture | | ⊢ |
| proveit.numbers.exponentiation.product_of_real_powers |
86 | instantiation | 317, 313, 93 | ⊢ |
| : , : , : |
87 | instantiation | 94, 307 | ⊢ |
| : |
88 | instantiation | 95, 251 | ⊢ |
| : |
89 | instantiation | 245, 96, 97 | ⊢ |
| : , : , : |
90 | instantiation | 239, 311 | ⊢ |
| : |
91 | instantiation | 121, 256 | ⊢ |
| : |
92 | instantiation | 98, 264, 99 | ⊢ |
| : , : |
93 | instantiation | 317, 315, 104 | ⊢ |
| : , : , : |
94 | conjecture | | ⊢ |
| proveit.numbers.number_sets.natural_numbers.nonzero_if_is_nat_pos |
95 | conjecture | | ⊢ |
| proveit.numbers.exponentiation.complex_x_to_first_power_is_x |
96 | instantiation | 191, 319, 290, 192, 100, 193, 272, 169, 150 | ⊢ |
| : , : , : , : , : , : |
97 | instantiation | 245, 101, 102 | ⊢ |
| : , : , : |
98 | conjecture | | ⊢ |
| proveit.numbers.exponentiation.exp_real_closure_nat_power |
99 | instantiation | 103, 104, 105 | ⊢ |
| : |
100 | instantiation | 270 | ⊢ |
| : , : |
101 | instantiation | 106, 319, 192, 193, 272, 169, 150 | ⊢ |
| : , : , : , : , : , : , : |
102 | instantiation | 107, 192, 290, 319, 193, 108, 272, 150, 169, 109* | ⊢ |
| : , : , : , : , : , : |
103 | conjecture | | ⊢ |
| proveit.numbers.number_sets.integers.nonneg_int_is_natural |
104 | instantiation | 110, 111, 112 | ⊢ |
| : , : |
105 | instantiation | 113, 114 | ⊢ |
| : , : |
106 | conjecture | | ⊢ |
| proveit.numbers.addition.leftward_commutation |
107 | conjecture | | ⊢ |
| proveit.numbers.addition.association |
108 | instantiation | 270 | ⊢ |
| : , : |
109 | instantiation | 115, 272, 251, 142 | ⊢ |
| : , : , : |
110 | conjecture | | ⊢ |
| proveit.numbers.addition.add_int_closure_bin |
111 | instantiation | 317, 116, 200 | ⊢ |
| : , : , : |
112 | instantiation | 317, 117, 118 | ⊢ |
| : , : , : |
113 | conjecture | | ⊢ |
| proveit.numbers.addition.subtraction.nonneg_difference |
114 | instantiation | 143, 119, 120 | ⊢ |
| : , : , : |
115 | conjecture | | ⊢ |
| proveit.numbers.addition.subtraction.subtract_from_add_reversed |
116 | conjecture | | ⊢ |
| proveit.numbers.number_sets.integers.nat_pos_within_int |
117 | conjecture | | ⊢ |
| proveit.numbers.number_sets.integers.neg_int_within_int |
118 | instantiation | 121, 307 | ⊢ |
| : |
119 | axiom | | ⊢ |
| proveit.physics.quantum.QPE._n_ge_two |
120 | instantiation | 158, 162, 264, 122, 123, 124*, 125* | ⊢ |
| : , : , : |
121 | conjecture | | ⊢ |
| proveit.numbers.negation.int_neg_closure |
122 | instantiation | 177, 127, 264 | ⊢ |
| : , : |
123 | instantiation | 126, 264, 127, 128, 234 | ⊢ |
| : , : , : |
124 | instantiation | 245, 129, 130 | ⊢ |
| : , : , : |
125 | instantiation | 245, 131, 132 | ⊢ |
| : , : , : |
126 | conjecture | | ⊢ |
| proveit.numbers.ordering.less_eq_add_right |
127 | instantiation | 177, 179, 217 | ⊢ |
| : , : |
128 | instantiation | 143, 133, 134 | ⊢ |
| : , : , : |
129 | instantiation | 191, 319, 290, 192, 149, 193, 251, 197, 150 | ⊢ |
| : , : , : , : , : , : |
130 | instantiation | 196, 251, 197, 167 | ⊢ |
| : , : , : |
131 | instantiation | 224, 135 | ⊢ |
| : , : , : |
132 | instantiation | 136, 137, 138, 139 | ⊢ |
| : , : , : , : |
133 | instantiation | 140, 316, 156, 141, 142* | ⊢ |
| : , : |
134 | instantiation | 143, 144, 145 | ⊢ |
| : , : , : |
135 | instantiation | 191, 192, 290, 319, 193, 166, 169, 195, 251 | ⊢ |
| : , : , : , : , : , : |
136 | conjecture | | ⊢ |
| proveit.logic.equality.four_chain_transitivity |
137 | instantiation | 191, 192, 147, 319, 193, 148, 169, 195, 251, 146 | ⊢ |
| : , : , : , : , : , : |
138 | instantiation | 191, 147, 290, 192, 148, 149, 193, 169, 195, 251, 197, 150 | ⊢ |
| : , : , : , : , : , : |
139 | instantiation | 245, 151, 152 | ⊢ |
| : , : , : |
140 | conjecture | | ⊢ |
| proveit.numbers.rounding.ceil_of_real_above_int |
141 | instantiation | 153, 299, 173, 154 | ⊢ |
| : , : |
142 | conjecture | | ⊢ |
| proveit.numbers.numerals.decimals.add_1_1 |
143 | conjecture | | ⊢ |
| proveit.numbers.ordering.transitivity_less_eq_less_eq |
144 | instantiation | 155, 156, 268, 157 | ⊢ |
| : , : |
145 | instantiation | 158, 217, 159, 179, 160, 161* | ⊢ |
| : , : , : |
146 | instantiation | 317, 279, 162 | ⊢ |
| : , : , : |
147 | conjecture | | ⊢ |
| proveit.numbers.numerals.decimals.nat3 |
148 | instantiation | 163 | ⊢ |
| : , : , : |
149 | instantiation | 270 | ⊢ |
| : , : |
150 | instantiation | 164, 251 | ⊢ |
| : |
151 | instantiation | 165, 290, 319, 192, 166, 193, 169, 195, 251, 197, 167 | ⊢ |
| : , : , : , : , : , : , : , : |
152 | instantiation | 168, 197, 169, 199 | ⊢ |
| : , : , : |
153 | conjecture | | ⊢ |
| proveit.numbers.logarithms.log_base_large_a_greater_one |
154 | instantiation | 170, 291, 171 | ⊢ |
| : , : |
155 | conjecture | | ⊢ |
| proveit.numbers.rounding.ceil_increasing_less_eq |
156 | instantiation | 274, 299, 173, 276 | ⊢ |
| : , : |
157 | instantiation | 172, 299, 173, 275, 174, 291 | ⊢ |
| : , : , : |
158 | conjecture | | ⊢ |
| proveit.numbers.addition.weak_bound_via_left_term_bound |
159 | instantiation | 177, 240, 218 | ⊢ |
| : , : |
160 | axiom | | ⊢ |
| proveit.physics.quantum.QPE._t_req |
161 | instantiation | 245, 175, 176 | ⊢ |
| : , : , : |
162 | instantiation | 177, 240, 178 | ⊢ |
| : , : |
163 | conjecture | | ⊢ |
| proveit.numbers.numerals.decimals.tuple_len_3_typical_eq |
164 | conjecture | | ⊢ |
| proveit.numbers.negation.complex_closure |
165 | conjecture | | ⊢ |
| proveit.numbers.addition.subtraction.add_cancel_general |
166 | instantiation | 270 | ⊢ |
| : , : |
167 | instantiation | 219 | ⊢ |
| : |
168 | conjecture | | ⊢ |
| proveit.numbers.addition.subtraction.add_cancel_triple_32 |
169 | instantiation | 317, 279, 179 | ⊢ |
| : , : , : |
170 | theorem | | ⊢ |
| proveit.logic.booleans.conjunction.and_if_both |
171 | instantiation | 180, 264, 181, 182, 183, 184*, 185* | ⊢ |
| : , : , : |
172 | conjecture | | ⊢ |
| proveit.numbers.logarithms.log_increasing_less_eq |
173 | instantiation | 317, 301, 186 | ⊢ |
| : , : , : |
174 | instantiation | 187, 264, 258, 188, 189, 190* | ⊢ |
| : , : , : |
175 | instantiation | 191, 192, 290, 319, 193, 194, 197, 198, 195 | ⊢ |
| : , : , : , : , : , : |
176 | instantiation | 196, 197, 198, 199 | ⊢ |
| : , : , : |
177 | conjecture | | ⊢ |
| proveit.numbers.addition.add_real_closure_bin |
178 | instantiation | 239, 264 | ⊢ |
| : |
179 | instantiation | 254, 255, 200 | ⊢ |
| : , : , : |
180 | conjecture | | ⊢ |
| proveit.numbers.addition.strong_bound_via_left_term_bound |
181 | instantiation | 201, 258, 310 | ⊢ |
| : , : |
182 | instantiation | 317, 313, 202 | ⊢ |
| : , : , : |
183 | instantiation | 203, 258, 310, 311, 204, 205 | ⊢ |
| : , : , : |
184 | instantiation | 245, 206, 207 | ⊢ |
| : , : , : |
185 | instantiation | 245, 208, 209 | ⊢ |
| : , : , : |
186 | instantiation | 285, 210, 302 | ⊢ |
| : , : |
187 | conjecture | | ⊢ |
| proveit.numbers.addition.weak_bound_via_right_term_bound |
188 | instantiation | 317, 211, 282 | ⊢ |
| : , : , : |
189 | instantiation | 212, 213, 297, 299, 214 | ⊢ |
| : , : , : |
190 | instantiation | 226, 280, 316, 227*, 215*, 216* | ⊢ |
| : , : , : , : |
191 | conjecture | | ⊢ |
| proveit.numbers.addition.disassociation |
192 | axiom | | ⊢ |
| proveit.numbers.number_sets.natural_numbers.zero_in_nats |
193 | conjecture | | ⊢ |
| proveit.core_expr_types.tuples.tuple_len_0_typical_eq |
194 | instantiation | 270 | ⊢ |
| : , : |
195 | instantiation | 317, 279, 217 | ⊢ |
| : , : , : |
196 | conjecture | | ⊢ |
| proveit.numbers.addition.subtraction.add_cancel_triple_13 |
197 | instantiation | 317, 279, 240 | ⊢ |
| : , : , : |
198 | instantiation | 317, 279, 218 | ⊢ |
| : , : , : |
199 | instantiation | 219 | ⊢ |
| : |
200 | axiom | | ⊢ |
| proveit.physics.quantum.QPE._t_in_natural_pos |
201 | conjecture | | ⊢ |
| proveit.numbers.multiplication.mult_real_closure_bin |
202 | instantiation | 220, 269, 314 | ⊢ |
| : , : |
203 | conjecture | | ⊢ |
| proveit.numbers.multiplication.strong_bound_via_right_factor_bound |
204 | conjecture | | ⊢ |
| proveit.numbers.numerals.decimals.less_0_1 |
205 | instantiation | 221, 278 | ⊢ |
| : |
206 | instantiation | 224, 222 | ⊢ |
| : , : , : |
207 | instantiation | 223, 251 | ⊢ |
| : |
208 | instantiation | 224, 225 | ⊢ |
| : , : , : |
209 | instantiation | 226, 316, 280, 227*, 228*, 235* | ⊢ |
| : , : , : , : |
210 | instantiation | 317, 306, 229 | ⊢ |
| : , : , : |
211 | conjecture | | ⊢ |
| proveit.numbers.number_sets.real_numbers.real_pos_within_real |
212 | conjecture | | ⊢ |
| proveit.numbers.division.weak_div_from_denom_bound__all_pos |
213 | instantiation | 317, 230, 231 | ⊢ |
| : , : , : |
214 | instantiation | 232, 264, 304, 311, 233, 234, 235* | ⊢ |
| : , : , : |
215 | instantiation | 245, 236, 237 | ⊢ |
| : , : , : |
216 | instantiation | 238, 251 | ⊢ |
| : |
217 | instantiation | 239, 240 | ⊢ |
| : |
218 | instantiation | 317, 313, 241 | ⊢ |
| : , : , : |
219 | axiom | | ⊢ |
| proveit.logic.equality.equals_reflexivity |
220 | conjecture | | ⊢ |
| proveit.numbers.multiplication.mult_rational_closure_bin |
221 | conjecture | | ⊢ |
| proveit.numbers.number_sets.rational_numbers.positive_if_in_rational_pos |
222 | instantiation | 242, 243 | ⊢ |
| : |
223 | conjecture | | ⊢ |
| proveit.numbers.addition.elim_zero_left |
224 | axiom | | ⊢ |
| proveit.logic.equality.substitution |
225 | instantiation | 271, 243 | ⊢ |
| : |
226 | conjecture | | ⊢ |
| proveit.numbers.addition.rational_pair_addition |
227 | instantiation | 244, 251 | ⊢ |
| : |
228 | instantiation | 245, 246, 247 | ⊢ |
| : , : , : |
229 | conjecture | | ⊢ |
| proveit.numbers.numerals.decimals.posnat5 |
230 | conjecture | | ⊢ |
| proveit.numbers.number_sets.real_numbers.rational_nonneg_within_real_nonneg |
231 | instantiation | 317, 248, 319 | ⊢ |
| : , : , : |
232 | conjecture | | ⊢ |
| proveit.numbers.multiplication.weak_bound_via_right_factor_bound |
233 | instantiation | 249, 310, 311, 312 | ⊢ |
| : , : , : |
234 | instantiation | 250, 290 | ⊢ |
| : |
235 | instantiation | 271, 251 | ⊢ |
| : |
236 | instantiation | 259, 290, 252, 253, 263, 262 | ⊢ |
| : , : , : , : |
237 | conjecture | | ⊢ |
| proveit.numbers.numerals.decimals.add_4_1 |
238 | conjecture | | ⊢ |
| proveit.numbers.multiplication.elim_one_left |
239 | conjecture | | ⊢ |
| proveit.numbers.negation.real_closure |
240 | instantiation | 254, 255, 256 | ⊢ |
| : , : , : |
241 | instantiation | 317, 315, 257 | ⊢ |
| : , : , : |
242 | conjecture | | ⊢ |
| proveit.numbers.multiplication.mult_zero_right |
243 | instantiation | 317, 279, 258 | ⊢ |
| : , : , : |
244 | conjecture | | ⊢ |
| proveit.numbers.division.frac_one_denom |
245 | axiom | | ⊢ |
| proveit.logic.equality.equals_transitivity |
246 | instantiation | 259, 290, 260, 261, 262, 263 | ⊢ |
| : , : , : , : |
247 | conjecture | | ⊢ |
| proveit.numbers.numerals.decimals.add_1_4 |
248 | conjecture | | ⊢ |
| proveit.numbers.number_sets.rational_numbers.nat_within_rational_nonneg |
249 | conjecture | | ⊢ |
| proveit.numbers.number_sets.real_numbers.interval_oc_upper_bound |
250 | conjecture | | ⊢ |
| proveit.numbers.number_sets.natural_numbers.natural_lower_bound |
251 | instantiation | 317, 279, 264 | ⊢ |
| : , : , : |
252 | instantiation | 270 | ⊢ |
| : , : |
253 | instantiation | 270 | ⊢ |
| : , : |
254 | theorem | | ⊢ |
| proveit.logic.sets.inclusion.unfold_subset_eq |
255 | instantiation | 265, 266 | ⊢ |
| : , : |
256 | axiom | | ⊢ |
| proveit.physics.quantum.QPE._n_in_natural_pos |
257 | instantiation | 267, 268 | ⊢ |
| : |
258 | instantiation | 317, 313, 269 | ⊢ |
| : , : , : |
259 | axiom | | ⊢ |
| proveit.core_expr_types.operations.operands_substitution |
260 | instantiation | 270 | ⊢ |
| : , : |
261 | instantiation | 270 | ⊢ |
| : , : |
262 | instantiation | 271, 272 | ⊢ |
| : |
263 | conjecture | | ⊢ |
| proveit.numbers.numerals.decimals.mult_2_2 |
264 | instantiation | 317, 313, 273 | ⊢ |
| : , : , : |
265 | theorem | | ⊢ |
| proveit.logic.sets.inclusion.relax_proper_subset |
266 | conjecture | | ⊢ |
| proveit.numbers.number_sets.real_numbers.nat_pos_within_real |
267 | axiom | | ⊢ |
| proveit.numbers.rounding.ceil_is_an_int |
268 | instantiation | 274, 299, 275, 276 | ⊢ |
| : , : |
269 | instantiation | 317, 277, 278 | ⊢ |
| : , : , : |
270 | conjecture | | ⊢ |
| proveit.numbers.numerals.decimals.tuple_len_2_typical_eq |
271 | conjecture | | ⊢ |
| proveit.numbers.multiplication.elim_one_right |
272 | instantiation | 317, 279, 311 | ⊢ |
| : , : , : |
273 | instantiation | 317, 315, 280 | ⊢ |
| : , : , : |
274 | conjecture | | ⊢ |
| proveit.numbers.logarithms.log_real_pos_real_closure |
275 | instantiation | 281, 299, 282 | ⊢ |
| : , : |
276 | instantiation | 283, 284 | ⊢ |
| : , : |
277 | conjecture | | ⊢ |
| proveit.numbers.number_sets.rational_numbers.rational_pos_within_rational |
278 | instantiation | 285, 292, 302 | ⊢ |
| : , : |
279 | conjecture | | ⊢ |
| proveit.numbers.number_sets.complex_numbers.real_within_complex |
280 | instantiation | 317, 318, 290 | ⊢ |
| : , : , : |
281 | conjecture | | ⊢ |
| proveit.numbers.addition.add_real_pos_closure_bin |
282 | instantiation | 286, 287, 297, 288 | ⊢ |
| : , : |
283 | theorem | | ⊢ |
| proveit.logic.equality.not_equals_symmetry |
284 | instantiation | 289, 319, 290, 291 | ⊢ |
| : , : |
285 | conjecture | | ⊢ |
| proveit.numbers.division.div_rational_pos_closure |
286 | conjecture | | ⊢ |
| proveit.numbers.division.div_real_pos_closure |
287 | instantiation | 317, 301, 292 | ⊢ |
| : , : , : |
288 | instantiation | 293, 294 | ⊢ |
| : |
289 | conjecture | | ⊢ |
| proveit.numbers.ordering.less_is_not_eq_nat |
290 | conjecture | | ⊢ |
| proveit.numbers.numerals.decimals.nat2 |
291 | conjecture | | ⊢ |
| proveit.numbers.numerals.decimals.less_1_2 |
292 | instantiation | 317, 306, 295 | ⊢ |
| : , : , : |
293 | conjecture | | ⊢ |
| proveit.numbers.number_sets.real_numbers.nonzero_if_in_real_nonzero |
294 | instantiation | 317, 296, 297 | ⊢ |
| : , : , : |
295 | conjecture | | ⊢ |
| proveit.numbers.numerals.decimals.posnat1 |
296 | conjecture | | ⊢ |
| proveit.numbers.number_sets.real_numbers.real_pos_within_real_nonzero |
297 | instantiation | 298, 299, 300 | ⊢ |
| : , : |
298 | conjecture | | ⊢ |
| proveit.numbers.multiplication.mult_real_pos_closure_bin |
299 | instantiation | 317, 301, 302 | ⊢ |
| : , : , : |
300 | instantiation | 303, 304, 305 | ⊢ |
| : |
301 | conjecture | | ⊢ |
| proveit.numbers.number_sets.real_numbers.rational_pos_within_real_pos |
302 | instantiation | 317, 306, 307 | ⊢ |
| : , : , : |
303 | conjecture | | ⊢ |
| proveit.numbers.number_sets.real_numbers.pos_real_is_real_pos |
304 | instantiation | 308, 310, 311, 312 | ⊢ |
| : , : , : |
305 | instantiation | 309, 310, 311, 312 | ⊢ |
| : , : , : |
306 | conjecture | | ⊢ |
| proveit.numbers.number_sets.rational_numbers.nat_pos_within_rational_pos |
307 | conjecture | | ⊢ |
| proveit.numbers.numerals.decimals.posnat2 |
308 | conjecture | | ⊢ |
| proveit.numbers.number_sets.real_numbers.all_in_interval_oc__is__real |
309 | conjecture | | ⊢ |
| proveit.numbers.number_sets.real_numbers.interval_oc_lower_bound |
310 | conjecture | | ⊢ |
| proveit.numbers.number_sets.real_numbers.zero_is_real |
311 | instantiation | 317, 313, 314 | ⊢ |
| : , : , : |
312 | axiom | | ⊢ |
| proveit.physics.quantum.QPE._eps_in_interval |
313 | conjecture | | ⊢ |
| proveit.numbers.number_sets.real_numbers.rational_within_real |
314 | instantiation | 317, 315, 316 | ⊢ |
| : , : , : |
315 | conjecture | | ⊢ |
| proveit.numbers.number_sets.rational_numbers.int_within_rational |
316 | instantiation | 317, 318, 319 | ⊢ |
| : , : , : |
317 | theorem | | ⊢ |
| proveit.logic.sets.inclusion.superset_membership_from_proper_subset |
318 | conjecture | | ⊢ |
| proveit.numbers.number_sets.integers.nat_within_int |
319 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.nat1 |
*equality replacement requirements |