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