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