| step type | requirements | statement |
0 | instantiation | 1, 2, 3 | ⊢ |
| : , : , : |
1 | reference | 174 | ⊢ |
2 | instantiation | 173, 4 | ⊢ |
| : , : |
3 | instantiation | 173, 5 | ⊢ |
| : , : |
4 | instantiation | 8, 44, 10, 6, 7 | ⊢ |
| : , : , : , : |
5 | instantiation | 8, 44, 9, 10, 11 | ⊢ |
| : , : , : , : |
6 | instantiation | 163, 12, 196, 13 | ⊢ |
| : , : , : , : |
7 | instantiation | 14, 15, 16, 17* | ⊢ |
| : , : , : |
8 | theorem | | ⊢ |
| proveit.core_expr_types.operations.operands_substitution_via_tuple |
9 | instantiation | 161, 18 | ⊢ |
| : , : , : |
10 | instantiation | 161, 19 | ⊢ |
| : , : , : |
11 | instantiation | 51, 243, 29, 20, 21, 22* | ⊢ |
| : , : , : , : , : , : |
12 | instantiation | 23, 24, 25* | ⊢ |
| : , : , : , : |
13 | instantiation | 173, 26 | ⊢ |
| : , : |
14 | theorem | | ⊢ |
| proveit.core_expr_types.tuples.partition_back |
15 | instantiation | 74, 27, 28 | ⊢ |
| : |
16 | instantiation | 152, 187, 222, 60 | ⊢ |
| : , : , : |
17 | instantiation | 195, 222, 207, 181 | ⊢ |
| : , : , : |
18 | instantiation | 51, 234, 29, 30, 31, 32* | ⊢ |
| : , : , : , : , : , : |
19 | instantiation | 174, 33, 34 | ⊢ |
| : , : , : |
20 | instantiation | 173, 35 | ⊢ |
| : , : |
21 | instantiation | 173, 36 | ⊢ |
| : , : |
22 | instantiation | 198, 199, 257, 254, 202, 37, 38, 204, 207 | , ⊢ |
| : , : , : , : , : , : |
23 | theorem | | ⊢ |
| proveit.core_expr_types.tuples.extended_range_len |
24 | instantiation | 39, 40 | ⊢ |
| : , : , : |
25 | instantiation | 174, 41, 42 | ⊢ |
| : , : , : |
26 | instantiation | 43, 44 | ⊢ |
| : , : |
27 | instantiation | 242, 249, 99 | ⊢ |
| : , : |
28 | instantiation | 100, 45 | ⊢ |
| : , : |
29 | instantiation | 46, 47, 62 | ⊢ |
| : , : |
30 | instantiation | 173, 48 | ⊢ |
| : , : |
31 | instantiation | 173, 49 | ⊢ |
| : , : |
32 | instantiation | 174, 50, 158 | , ⊢ |
| : , : , : |
33 | instantiation | 51, 178, 52, 53, 54 | ⊢ |
| : , : , : , : , : , : |
34 | modus ponens | 55, 56 | ⊢ |
35 | instantiation | 174, 57, 58 | ⊢ |
| : , : , : |
36 | instantiation | 174, 59, 60 | ⊢ |
| : , : , : |
37 | instantiation | 215 | ⊢ |
| : , : |
38 | instantiation | 255, 240, 61 | , ⊢ |
| : , : , : |
39 | theorem | | ⊢ |
| proveit.core_expr_types.tuples.range_len_is_nat |
40 | instantiation | 209, 62, 63 | ⊢ |
| : , : , : |
41 | instantiation | 161, 162 | ⊢ |
| : , : , : |
42 | instantiation | 163, 64, 65, 66 | ⊢ |
| : , : , : , : |
43 | theorem | | ⊢ |
| proveit.core_expr_types.tuples.range_from1_len |
44 | instantiation | 255, 68, 251 | ⊢ |
| : , : , : |
45 | instantiation | 132, 124, 230, 218, 133, 67*, 105* | ⊢ |
| : , : , : |
46 | theorem | | ⊢ |
| proveit.numbers.addition.add_nat_closure_bin |
47 | instantiation | 255, 68, 69 | ⊢ |
| : , : , : |
48 | instantiation | 174, 70, 71 | ⊢ |
| : , : , : |
49 | instantiation | 174, 72, 73 | ⊢ |
| : , : , : |
50 | instantiation | 198, 199, 257, 254, 202, 180, 183, 203, 207 | , ⊢ |
| : , : , : , : , : , : |
51 | theorem | | ⊢ |
| proveit.core_expr_types.tuples.shift_equivalence |
52 | instantiation | 74, 75, 76 | ⊢ |
| : |
53 | instantiation | 173, 77 | ⊢ |
| : , : |
54 | instantiation | 173, 78 | ⊢ |
| : , : |
55 | instantiation | 79, 249, 245 | ⊢ |
| : , : , : , : , : |
56 | generalization | 80 | ⊢ |
57 | instantiation | 161, 83 | ⊢ |
| : , : , : |
58 | instantiation | 174, 81, 82 | ⊢ |
| : , : , : |
59 | instantiation | 161, 83 | ⊢ |
| : , : , : |
60 | instantiation | 97, 222 | ⊢ |
| : |
61 | instantiation | 255, 246, 84 | , ⊢ |
| : , : , : |
62 | instantiation | 85, 86 | ⊢ |
| : |
63 | instantiation | 163, 121, 87, 88 | ⊢ |
| : , : , : , : |
64 | instantiation | 198, 254, 257, 186, 187, 207, 223, 232 | ⊢ |
| : , : , : , : , : , : |
65 | instantiation | 188, 199, 189, 202, 89, 207, 223, 232 | ⊢ |
| : , : , : , : |
66 | instantiation | 182, 232, 207, 148 | ⊢ |
| : , : , : |
67 | instantiation | 163, 90, 91, 92 | ⊢ |
| : , : , : , : |
68 | theorem | | ⊢ |
| proveit.numbers.number_sets.natural_numbers.nat_pos_within_nat |
69 | instantiation | 93, 254, 199, 202, 94 | ⊢ |
| : , : , : , : , : |
70 | instantiation | 161, 185 | ⊢ |
| : , : , : |
71 | instantiation | 174, 95, 96 | ⊢ |
| : , : , : |
72 | instantiation | 161, 185 | ⊢ |
| : , : , : |
73 | instantiation | 97, 207 | ⊢ |
| : |
74 | theorem | | ⊢ |
| proveit.numbers.number_sets.integers.nonneg_int_is_natural |
75 | instantiation | 242, 98, 99 | ⊢ |
| : , : |
76 | instantiation | 100, 101 | ⊢ |
| : , : |
77 | instantiation | 174, 102, 103 | ⊢ |
| : , : , : |
78 | instantiation | 152, 207, 104, 222, 105 | ⊢ |
| : , : , : |
79 | theorem | | ⊢ |
| proveit.core_expr_types.tuples.range_fn_transformation |
80 | instantiation | 174, 106, 107 | , ⊢ |
| : , : , : |
81 | instantiation | 198, 199, 257, 254, 202, 154, 203, 222 | ⊢ |
| : , : , : , : , : , : |
82 | instantiation | 191, 254, 257, 199, 168, 202, 203, 222, 220* | ⊢ |
| : , : , : , : , : , : |
83 | instantiation | 206, 222 | ⊢ |
| : |
84 | instantiation | 255, 252, 108 | , ⊢ |
| : , : , : |
85 | theorem | | ⊢ |
| proveit.numbers.negation.nat_closure |
86 | instantiation | 109, 178, 110 | ⊢ |
| : |
87 | instantiation | 213 | ⊢ |
| : |
88 | instantiation | 173, 111 | ⊢ |
| : , : |
89 | instantiation | 208 | ⊢ |
| : , : , : |
90 | instantiation | 174, 112, 113 | ⊢ |
| : , : , : |
91 | instantiation | 152, 169, 207, 232, 114 | ⊢ |
| : , : , : |
92 | instantiation | 213 | ⊢ |
| : |
93 | theorem | | ⊢ |
| proveit.numbers.addition.add_nat_pos_from_nonneg |
94 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.less_0_1 |
95 | instantiation | 198, 199, 257, 254, 202, 154, 203, 222, 207 | ⊢ |
| : , : , : , : , : , : |
96 | instantiation | 115, 207, 222, 196 | ⊢ |
| : , : , : |
97 | theorem | | ⊢ |
| proveit.numbers.addition.elim_zero_left |
98 | instantiation | 255, 250, 116 | ⊢ |
| : , : , : |
99 | instantiation | 248, 224 | ⊢ |
| : |
100 | theorem | | ⊢ |
| proveit.numbers.addition.subtraction.nonneg_difference |
101 | instantiation | 132, 194, 117, 218, 118, 119*, 120* | ⊢ |
| : , : , : |
102 | instantiation | 161, 121 | ⊢ |
| : , : , : |
103 | instantiation | 174, 122, 123 | ⊢ |
| : , : , : |
104 | instantiation | 255, 240, 124 | ⊢ |
| : , : , : |
105 | instantiation | 174, 125, 126 | ⊢ |
| : , : , : |
106 | instantiation | 161, 127 | , ⊢ |
| : , : , : |
107 | instantiation | 174, 128, 129 | , ⊢ |
| : , : , : |
108 | instantiation | 255, 130, 131 | , ⊢ |
| : , : , : |
109 | theorem | | ⊢ |
| proveit.numbers.number_sets.integers.nonpos_int_is_int_nonpos |
110 | instantiation | 132, 216, 230, 218, 133, 134*, 135* | ⊢ |
| : , : , : |
111 | instantiation | 174, 136, 137 | ⊢ |
| : , : , : |
112 | instantiation | 198, 254, 257, 199, 154, 202, 222, 203 | ⊢ |
| : , : , : , : , : , : |
113 | instantiation | 174, 138, 139 | ⊢ |
| : , : , : |
114 | instantiation | 209, 147, 140 | ⊢ |
| : , : , : |
115 | theorem | | ⊢ |
| proveit.numbers.addition.subtraction.add_cancel_triple_31 |
116 | instantiation | 141, 142 | ⊢ |
| : , : |
117 | theorem | | ⊢ |
| proveit.numbers.number_sets.real_numbers.zero_is_real |
118 | instantiation | 143, 144 | ⊢ |
| : , : |
119 | instantiation | 174, 145, 146 | ⊢ |
| : , : , : |
120 | instantiation | 163, 147, 148, 149 | ⊢ |
| : , : , : , : |
121 | instantiation | 184, 203, 222, 185* | ⊢ |
| : , : |
122 | instantiation | 174, 150, 151 | ⊢ |
| : , : , : |
123 | instantiation | 152, 222, 232, 220 | ⊢ |
| : , : , : |
124 | instantiation | 255, 246, 153 | ⊢ |
| : , : , : |
125 | instantiation | 198, 254, 257, 199, 154, 202, 207, 203, 222 | ⊢ |
| : , : , : , : , : , : |
126 | instantiation | 195, 207, 222, 196 | ⊢ |
| : , : , : |
127 | instantiation | 198, 254, 257, 199, 154, 202, 183, 203, 222 | , ⊢ |
| : , : , : , : , : , : |
128 | instantiation | 198, 199, 189, 257, 202, 155, 156, 183, 203, 222, 204, 207 | , ⊢ |
| : , : , : , : , : , : |
129 | instantiation | 174, 157, 158 | , ⊢ |
| : , : , : |
130 | instantiation | 244, 224, 249 | ⊢ |
| : , : |
131 | assumption | | ⊢ |
132 | theorem | | ⊢ |
| proveit.numbers.addition.weak_bound_via_left_term_bound |
133 | instantiation | 159, 251 | ⊢ |
| : |
134 | instantiation | 221, 222, 203 | ⊢ |
| : , : |
135 | instantiation | 160, 207, 196 | ⊢ |
| : , : |
136 | instantiation | 161, 162 | ⊢ |
| : , : , : |
137 | instantiation | 163, 164, 165, 166 | ⊢ |
| : , : , : , : |
138 | instantiation | 167, 254, 199, 202, 222, 203 | ⊢ |
| : , : , : , : , : , : , : |
139 | instantiation | 191, 199, 257, 254, 202, 168, 222, 203, 220* | ⊢ |
| : , : , : , : , : , : |
140 | instantiation | 221, 207, 169 | ⊢ |
| : , : |
141 | theorem | | ⊢ |
| proveit.numbers.addition.add_nat_pos_closure_bin |
142 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.posnat1 |
143 | theorem | | ⊢ |
| proveit.numbers.ordering.relax_less |
144 | instantiation | 170, 251 | ⊢ |
| : |
145 | instantiation | 198, 254, 257, 199, 200, 202, 187, 203, 232 | ⊢ |
| : , : , : , : , : , : |
146 | instantiation | 188, 199, 257, 202, 200, 203, 232 | ⊢ |
| : , : , : , : |
147 | instantiation | 174, 171, 172 | ⊢ |
| : , : , : |
148 | instantiation | 213 | ⊢ |
| : |
149 | instantiation | 173, 220 | ⊢ |
| : , : |
150 | instantiation | 174, 175, 176 | ⊢ |
| : , : , : |
151 | instantiation | 177, 199, 254, 202, 207, 232, 204 | ⊢ |
| : , : , : , : , : , : , : , : |
152 | theorem | | ⊢ |
| proveit.numbers.addition.subtraction.subtract_from_add |
153 | instantiation | 255, 252, 178 | ⊢ |
| : , : , : |
154 | instantiation | 215 | ⊢ |
| : , : |
155 | instantiation | 208 | ⊢ |
| : , : , : |
156 | instantiation | 215 | ⊢ |
| : , : |
157 | instantiation | 179, 257, 199, 254, 180, 202, 183, 203, 222, 207, 181 | , ⊢ |
| : , : , : , : , : , : , : , : |
158 | instantiation | 182, 207, 183, 196 | , ⊢ |
| : , : , : |
159 | theorem | | ⊢ |
| proveit.numbers.number_sets.natural_numbers.natural_pos_lower_bound |
160 | theorem | | ⊢ |
| proveit.numbers.addition.subtraction.add_cancel_basic |
161 | axiom | | ⊢ |
| proveit.logic.equality.substitution |
162 | instantiation | 184, 203, 232, 185* | ⊢ |
| : , : |
163 | theorem | | ⊢ |
| proveit.logic.equality.four_chain_transitivity |
164 | instantiation | 198, 254, 257, 186, 187, 207, 223, 222 | ⊢ |
| : , : , : , : , : , : |
165 | instantiation | 188, 199, 189, 202, 190, 207, 223, 222 | ⊢ |
| : , : , : , : |
166 | instantiation | 191, 254, 257, 199, 192, 202, 207, 223, 222, 193* | ⊢ |
| : , : , : , : , : , : |
167 | theorem | | ⊢ |
| proveit.numbers.addition.leftward_commutation |
168 | instantiation | 215 | ⊢ |
| : , : |
169 | instantiation | 255, 240, 194 | ⊢ |
| : , : , : |
170 | theorem | | ⊢ |
| proveit.numbers.number_sets.natural_numbers.natural_pos_is_pos |
171 | instantiation | 198, 254, 257, 199, 200, 202, 207, 203, 232 | ⊢ |
| : , : , : , : , : , : |
172 | instantiation | 195, 207, 232, 196 | ⊢ |
| : , : , : |
173 | theorem | | ⊢ |
| proveit.logic.equality.equals_reversal |
174 | axiom | | ⊢ |
| proveit.logic.equality.equals_transitivity |
175 | instantiation | 198, 199, 257, 254, 202, 200, 203, 232, 197 | ⊢ |
| : , : , : , : , : , : |
176 | instantiation | 198, 257, 199, 200, 201, 202, 203, 232, 207, 204 | ⊢ |
| : , : , : , : , : , : |
177 | theorem | | ⊢ |
| proveit.numbers.addition.subtraction.add_cancel_general_rev |
178 | instantiation | 242, 234, 249 | ⊢ |
| : , : |
179 | theorem | | ⊢ |
| proveit.numbers.addition.subtraction.add_cancel_general |
180 | instantiation | 215 | ⊢ |
| : , : |
181 | instantiation | 213 | ⊢ |
| : |
182 | theorem | | ⊢ |
| proveit.numbers.addition.subtraction.add_cancel_triple_32 |
183 | instantiation | 255, 240, 205 | , ⊢ |
| : , : , : |
184 | theorem | | ⊢ |
| proveit.numbers.negation.distribute_neg_through_binary_sum |
185 | instantiation | 206, 207 | ⊢ |
| : |
186 | instantiation | 215 | ⊢ |
| : , : |
187 | theorem | | ⊢ |
| proveit.numbers.number_sets.complex_numbers.zero_is_complex |
188 | theorem | | ⊢ |
| proveit.numbers.addition.elim_zero_any |
189 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.nat3 |
190 | instantiation | 208 | ⊢ |
| : , : , : |
191 | theorem | | ⊢ |
| proveit.numbers.addition.association |
192 | instantiation | 215 | ⊢ |
| : , : |
193 | instantiation | 209, 210, 211 | ⊢ |
| : , : , : |
194 | instantiation | 255, 246, 212 | ⊢ |
| : , : , : |
195 | theorem | | ⊢ |
| proveit.numbers.addition.subtraction.add_cancel_triple_12 |
196 | instantiation | 213 | ⊢ |
| : |
197 | instantiation | 255, 240, 214 | ⊢ |
| : , : , : |
198 | theorem | | ⊢ |
| proveit.numbers.addition.disassociation |
199 | axiom | | ⊢ |
| proveit.numbers.number_sets.natural_numbers.zero_in_nats |
200 | instantiation | 215 | ⊢ |
| : , : |
201 | instantiation | 215 | ⊢ |
| : , : |
202 | theorem | | ⊢ |
| proveit.core_expr_types.tuples.tuple_len_0_typical_eq |
203 | instantiation | 255, 240, 216 | ⊢ |
| : , : , : |
204 | instantiation | 231, 222 | ⊢ |
| : |
205 | instantiation | 255, 246, 217 | , ⊢ |
| : , : , : |
206 | theorem | | ⊢ |
| proveit.numbers.negation.double_negation |
207 | instantiation | 255, 240, 218 | ⊢ |
| : , : , : |
208 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.tuple_len_3_typical_eq |
209 | theorem | | ⊢ |
| proveit.logic.equality.sub_right_side_into |
210 | instantiation | 219, 222, 232, 220 | ⊢ |
| : , : , : |
211 | instantiation | 221, 222, 223 | ⊢ |
| : , : |
212 | instantiation | 255, 252, 224 | ⊢ |
| : , : , : |
213 | axiom | | ⊢ |
| proveit.logic.equality.equals_reflexivity |
214 | instantiation | 255, 246, 225 | ⊢ |
| : , : , : |
215 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.tuple_len_2_typical_eq |
216 | instantiation | 255, 246, 226 | ⊢ |
| : , : , : |
217 | instantiation | 255, 252, 227 | , ⊢ |
| : , : , : |
218 | instantiation | 228, 229, 251 | ⊢ |
| : , : , : |
219 | theorem | | ⊢ |
| proveit.numbers.addition.subtraction.subtract_from_add_reversed |
220 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.add_1_1 |
221 | theorem | | ⊢ |
| proveit.numbers.addition.commutation |
222 | instantiation | 255, 240, 230 | ⊢ |
| : , : , : |
223 | instantiation | 231, 232 | ⊢ |
| : |
224 | instantiation | 242, 234, 253 | ⊢ |
| : , : |
225 | instantiation | 255, 252, 233 | ⊢ |
| : , : , : |
226 | instantiation | 255, 252, 234 | ⊢ |
| : , : , : |
227 | instantiation | 255, 235, 236 | , ⊢ |
| : , : , : |
228 | theorem | | ⊢ |
| proveit.logic.sets.inclusion.unfold_subset_eq |
229 | instantiation | 237, 238 | ⊢ |
| : , : |
230 | instantiation | 255, 246, 239 | ⊢ |
| : , : , : |
231 | theorem | | ⊢ |
| proveit.numbers.negation.complex_closure |
232 | instantiation | 255, 240, 241 | ⊢ |
| : , : , : |
233 | instantiation | 242, 245, 243 | ⊢ |
| : , : |
234 | instantiation | 248, 245 | ⊢ |
| : |
235 | instantiation | 244, 249, 245 | ⊢ |
| : , : |
236 | assumption | | ⊢ |
237 | theorem | | ⊢ |
| proveit.logic.sets.inclusion.relax_proper_subset |
238 | theorem | | ⊢ |
| proveit.numbers.number_sets.real_numbers.nat_pos_within_real |
239 | instantiation | 255, 252, 249 | ⊢ |
| : , : , : |
240 | theorem | | ⊢ |
| proveit.numbers.number_sets.complex_numbers.real_within_complex |
241 | instantiation | 255, 246, 247 | ⊢ |
| : , : , : |
242 | theorem | | ⊢ |
| proveit.numbers.addition.add_int_closure_bin |
243 | instantiation | 248, 249 | ⊢ |
| : |
244 | theorem | | ⊢ |
| proveit.numbers.number_sets.integers.int_interval_within_int |
245 | instantiation | 255, 250, 251 | ⊢ |
| : , : , : |
246 | theorem | | ⊢ |
| proveit.numbers.number_sets.real_numbers.rational_within_real |
247 | instantiation | 255, 252, 253 | ⊢ |
| : , : , : |
248 | theorem | | ⊢ |
| proveit.numbers.negation.int_closure |
249 | instantiation | 255, 256, 254 | ⊢ |
| : , : , : |
250 | theorem | | ⊢ |
| proveit.numbers.number_sets.integers.nat_pos_within_int |
251 | assumption | | ⊢ |
252 | theorem | | ⊢ |
| proveit.numbers.number_sets.rational_numbers.int_within_rational |
253 | instantiation | 255, 256, 257 | ⊢ |
| : , : , : |
254 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.nat1 |
255 | theorem | | ⊢ |
| proveit.logic.sets.inclusion.superset_membership_from_proper_subset |
256 | theorem | | ⊢ |
| proveit.numbers.number_sets.integers.nat_within_int |
257 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.nat2 |
*equality replacement requirements |