| step type | requirements | statement |
0 | instantiation | 1, 2, 3, 4, 5 | ⊢ |
| : , : , : , : |
1 | theorem | | ⊢ |
| proveit.core_expr_types.operations.operands_substitution_via_tuple |
2 | reference | 34 | ⊢ |
3 | instantiation | 74, 6, 99, 8 | ⊢ |
| : , : , : , : |
4 | instantiation | 74, 7, 99, 8 | ⊢ |
| : , : , : , : |
5 | instantiation | 9, 10, 11 | ⊢ |
| : , : , : , : |
6 | instantiation | 12, 13, 14, 15, 16, 17, 18, 19* | ⊢ |
| : , : , : , : |
7 | instantiation | 104, 20, 21 | ⊢ |
| : , : , : |
8 | instantiation | 55, 22 | ⊢ |
| : , : |
9 | theorem | | ⊢ |
| proveit.core_expr_types.tuples.merge_front |
10 | instantiation | 23, 92, 47 | ⊢ |
| : , : |
11 | instantiation | 55, 24 | ⊢ |
| : , : |
12 | theorem | | ⊢ |
| proveit.core_expr_types.tuples.general_len |
13 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.posnat2 |
14 | instantiation | 103 | ⊢ |
| : , : |
15 | instantiation | 103 | ⊢ |
| : , : |
16 | instantiation | 103 | ⊢ |
| : , : |
17 | instantiation | 25, 134, 42 | ⊢ |
| : , : , : |
18 | instantiation | 104, 47, 26 | ⊢ |
| : , : , : |
19 | instantiation | 66, 27, 28 | ⊢ |
| : , : , : |
20 | instantiation | 29, 30 | ⊢ |
| : , : , : |
21 | instantiation | 66, 31, 32 | ⊢ |
| : , : , : |
22 | instantiation | 33, 34 | ⊢ |
| : , : |
23 | theorem | | ⊢ |
| proveit.numbers.addition.add_nat_closure_bin |
24 | instantiation | 66, 35, 36 | ⊢ |
| : , : , : |
25 | theorem | | ⊢ |
| proveit.logic.equality.sub_left_side_into |
26 | instantiation | 74, 48, 37, 38 | ⊢ |
| : , : , : , : |
27 | instantiation | 39, 139, 40, 41, 42, 56 | ⊢ |
| : , : , : , : |
28 | instantiation | 66, 43, 44 | ⊢ |
| : , : , : |
29 | theorem | | ⊢ |
| proveit.core_expr_types.tuples.range_len |
30 | instantiation | 45, 89, 46, 92, 47, 134 | ⊢ |
| : , : |
31 | instantiation | 72, 48 | ⊢ |
| : , : , : |
32 | instantiation | 74, 49, 50, 51 | ⊢ |
| : , : , : , : |
33 | theorem | | ⊢ |
| proveit.core_expr_types.tuples.range_from1_len |
34 | instantiation | 137, 52, 133 | ⊢ |
| : , : , : |
35 | instantiation | 85, 92, 139, 134, 94, 53, 97, 113 | ⊢ |
| : , : , : , : , : , : |
36 | instantiation | 91, 134, 139, 92, 54, 94, 97, 113, 111* | ⊢ |
| : , : , : , : , : , : |
37 | instantiation | 108 | ⊢ |
| : |
38 | instantiation | 55, 56 | ⊢ |
| : , : |
39 | axiom | | ⊢ |
| proveit.core_expr_types.operations.operands_substitution |
40 | instantiation | 103 | ⊢ |
| : , : |
41 | instantiation | 103 | ⊢ |
| : , : |
42 | instantiation | 57, 113, 65 | ⊢ |
| : , : , : |
43 | instantiation | 85, 134, 139, 92, 61, 94, 113, 101, 63 | ⊢ |
| : , : , : , : , : , : |
44 | instantiation | 58, 113, 101, 65 | ⊢ |
| : , : , : |
45 | theorem | | ⊢ |
| proveit.numbers.addition.add_nat_closure |
46 | instantiation | 102 | ⊢ |
| : , : , : |
47 | instantiation | 59, 60 | ⊢ |
| : |
48 | instantiation | 83, 97, 113, 84* | ⊢ |
| : , : |
49 | instantiation | 85, 134, 139, 61, 87, 101, 63, 113 | ⊢ |
| : , : , : , : , : , : |
50 | instantiation | 88, 92, 89, 94, 62, 101, 63, 113 | ⊢ |
| : , : , : , : |
51 | instantiation | 64, 113, 101, 65 | ⊢ |
| : , : , : |
52 | theorem | | ⊢ |
| proveit.numbers.number_sets.natural_numbers.nat_pos_within_nat |
53 | instantiation | 103 | ⊢ |
| : , : |
54 | instantiation | 103 | ⊢ |
| : , : |
55 | theorem | | ⊢ |
| proveit.logic.equality.equals_reversal |
56 | instantiation | 66, 67, 68 | ⊢ |
| : , : , : |
57 | theorem | | ⊢ |
| proveit.numbers.addition.subtraction.add_cancel_triple_12 |
58 | theorem | | ⊢ |
| proveit.numbers.addition.subtraction.add_cancel_triple_13 |
59 | theorem | | ⊢ |
| proveit.numbers.negation.nat_closure |
60 | instantiation | 69, 70, 71 | ⊢ |
| : |
61 | instantiation | 103 | ⊢ |
| : , : |
62 | instantiation | 102 | ⊢ |
| : , : , : |
63 | instantiation | 119, 113 | ⊢ |
| : |
64 | theorem | | ⊢ |
| proveit.numbers.addition.subtraction.add_cancel_triple_32 |
65 | instantiation | 108 | ⊢ |
| : |
66 | axiom | | ⊢ |
| proveit.logic.equality.equals_transitivity |
67 | instantiation | 72, 73 | ⊢ |
| : , : , : |
68 | instantiation | 74, 75, 76, 77 | ⊢ |
| : , : , : , : |
69 | theorem | | ⊢ |
| proveit.numbers.number_sets.integers.nonpos_int_is_int_nonpos |
70 | instantiation | 78, 121, 129 | ⊢ |
| : , : |
71 | instantiation | 79, 107, 118, 109, 80, 81*, 82* | ⊢ |
| : , : , : |
72 | axiom | | ⊢ |
| proveit.logic.equality.substitution |
73 | instantiation | 83, 97, 120, 84* | ⊢ |
| : , : |
74 | theorem | | ⊢ |
| proveit.logic.equality.four_chain_transitivity |
75 | instantiation | 85, 134, 139, 86, 87, 101, 114, 113 | ⊢ |
| : , : , : , : , : , : |
76 | instantiation | 88, 92, 89, 94, 90, 101, 114, 113 | ⊢ |
| : , : , : , : |
77 | instantiation | 91, 134, 139, 92, 93, 94, 101, 114, 113, 95* | ⊢ |
| : , : , : , : , : , : |
78 | theorem | | ⊢ |
| proveit.numbers.addition.add_int_closure_bin |
79 | theorem | | ⊢ |
| proveit.numbers.addition.weak_bound_via_left_term_bound |
80 | instantiation | 96, 133 | ⊢ |
| : |
81 | instantiation | 112, 113, 97 | ⊢ |
| : , : |
82 | instantiation | 98, 101, 99 | ⊢ |
| : , : |
83 | theorem | | ⊢ |
| proveit.numbers.negation.distribute_neg_through_binary_sum |
84 | instantiation | 100, 101 | ⊢ |
| : |
85 | theorem | | ⊢ |
| proveit.numbers.addition.disassociation |
86 | instantiation | 103 | ⊢ |
| : , : |
87 | theorem | | ⊢ |
| proveit.numbers.number_sets.complex_numbers.zero_is_complex |
88 | theorem | | ⊢ |
| proveit.numbers.addition.elim_zero_any |
89 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.nat3 |
90 | instantiation | 102 | ⊢ |
| : , : , : |
91 | theorem | | ⊢ |
| proveit.numbers.addition.association |
92 | axiom | | ⊢ |
| proveit.numbers.number_sets.natural_numbers.zero_in_nats |
93 | instantiation | 103 | ⊢ |
| : , : |
94 | theorem | | ⊢ |
| proveit.core_expr_types.tuples.tuple_len_0_typical_eq |
95 | instantiation | 104, 105, 106 | ⊢ |
| : , : , : |
96 | theorem | | ⊢ |
| proveit.numbers.number_sets.natural_numbers.natural_pos_lower_bound |
97 | instantiation | 137, 125, 107 | ⊢ |
| : , : , : |
98 | theorem | | ⊢ |
| proveit.numbers.addition.subtraction.add_cancel_basic |
99 | instantiation | 108 | ⊢ |
| : |
100 | theorem | | ⊢ |
| proveit.numbers.negation.double_negation |
101 | instantiation | 137, 125, 109 | ⊢ |
| : , : , : |
102 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.tuple_len_3_typical_eq |
103 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.tuple_len_2_typical_eq |
104 | theorem | | ⊢ |
| proveit.logic.equality.sub_right_side_into |
105 | instantiation | 110, 113, 120, 111 | ⊢ |
| : , : , : |
106 | instantiation | 112, 113, 114 | ⊢ |
| : , : |
107 | instantiation | 137, 130, 115 | ⊢ |
| : , : , : |
108 | axiom | | ⊢ |
| proveit.logic.equality.equals_reflexivity |
109 | instantiation | 116, 117, 133 | ⊢ |
| : , : , : |
110 | theorem | | ⊢ |
| proveit.numbers.addition.subtraction.subtract_from_add_reversed |
111 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.add_1_1 |
112 | theorem | | ⊢ |
| proveit.numbers.addition.commutation |
113 | instantiation | 137, 125, 118 | ⊢ |
| : , : , : |
114 | instantiation | 119, 120 | ⊢ |
| : |
115 | instantiation | 137, 135, 121 | ⊢ |
| : , : , : |
116 | theorem | | ⊢ |
| proveit.logic.sets.inclusion.unfold_subset_eq |
117 | instantiation | 122, 123 | ⊢ |
| : , : |
118 | instantiation | 137, 130, 124 | ⊢ |
| : , : , : |
119 | theorem | | ⊢ |
| proveit.numbers.negation.complex_closure |
120 | instantiation | 137, 125, 126 | ⊢ |
| : , : , : |
121 | instantiation | 127, 128 | ⊢ |
| : |
122 | theorem | | ⊢ |
| proveit.logic.sets.inclusion.relax_proper_subset |
123 | theorem | | ⊢ |
| proveit.numbers.number_sets.real_numbers.nat_pos_within_real |
124 | instantiation | 137, 135, 129 | ⊢ |
| : , : , : |
125 | theorem | | ⊢ |
| proveit.numbers.number_sets.complex_numbers.real_within_complex |
126 | instantiation | 137, 130, 131 | ⊢ |
| : , : , : |
127 | theorem | | ⊢ |
| proveit.numbers.negation.int_closure |
128 | instantiation | 137, 132, 133 | ⊢ |
| : , : , : |
129 | instantiation | 137, 138, 134 | ⊢ |
| : , : , : |
130 | theorem | | ⊢ |
| proveit.numbers.number_sets.real_numbers.rational_within_real |
131 | instantiation | 137, 135, 136 | ⊢ |
| : , : , : |
132 | theorem | | ⊢ |
| proveit.numbers.number_sets.integers.nat_pos_within_int |
133 | assumption | | ⊢ |
134 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.nat1 |
135 | theorem | | ⊢ |
| proveit.numbers.number_sets.rational_numbers.int_within_rational |
136 | instantiation | 137, 138, 139 | ⊢ |
| : , : , : |
137 | theorem | | ⊢ |
| proveit.logic.sets.inclusion.superset_membership_from_proper_subset |
138 | theorem | | ⊢ |
| proveit.numbers.number_sets.integers.nat_within_int |
139 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.nat2 |
*equality replacement requirements |