| step type | requirements | statement |
0 | instantiation | 1, 2, 3, 4, 5 | ⊢ |
| : , : , : , : |
1 | theorem | | ⊢ |
| proveit.core_expr_types.operations.operands_substitution_via_tuple |
2 | reference | 27 | ⊢ |
3 | instantiation | 6, 27 | ⊢ |
| : , : |
4 | instantiation | 7, 8, 9, 10 | ⊢ |
| : , : , : , : |
5 | instantiation | 11, 23, 68 | ⊢ |
| : , : , : |
6 | theorem | | ⊢ |
| proveit.core_expr_types.tuples.range_from1_len_typical_eq |
7 | theorem | | ⊢ |
| proveit.logic.equality.four_chain_transitivity |
8 | instantiation | 12, 13, 14, 15, 16, 17, 18, 19* | ⊢ |
| : , : , : , : |
9 | instantiation | 66 | ⊢ |
| : |
10 | instantiation | 20, 21 | ⊢ |
| : , : |
11 | theorem | | ⊢ |
| proveit.core_expr_types.tuples.partition_front |
12 | theorem | | ⊢ |
| proveit.core_expr_types.tuples.general_len |
13 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.posnat2 |
14 | instantiation | 63 | ⊢ |
| : , : |
15 | instantiation | 63 | ⊢ |
| : , : |
16 | instantiation | 63 | ⊢ |
| : , : |
17 | instantiation | 22, 94, 34 | ⊢ |
| : , : , : |
18 | instantiation | 22, 23, 35 | ⊢ |
| : , : , : |
19 | instantiation | 36, 24, 25 | ⊢ |
| : , : , : |
20 | theorem | | ⊢ |
| proveit.logic.equality.equals_reversal |
21 | instantiation | 26, 27 | ⊢ |
| : , : |
22 | theorem | | ⊢ |
| proveit.logic.equality.sub_left_side_into |
23 | instantiation | 28, 29, 30 | ⊢ |
| : |
24 | instantiation | 31, 99, 32, 33, 34, 35 | ⊢ |
| : , : , : , : |
25 | instantiation | 36, 37, 38 | ⊢ |
| : , : , : |
26 | theorem | | ⊢ |
| proveit.core_expr_types.tuples.range_from1_len |
27 | instantiation | 97, 39, 76 | ⊢ |
| : , : , : |
28 | theorem | | ⊢ |
| proveit.numbers.number_sets.integers.nonneg_int_is_natural |
29 | instantiation | 40, 41, 42 | ⊢ |
| : , : |
30 | instantiation | 43, 44 | ⊢ |
| : , : |
31 | axiom | | ⊢ |
| proveit.core_expr_types.operations.operands_substitution |
32 | instantiation | 63 | ⊢ |
| : , : |
33 | instantiation | 63 | ⊢ |
| : , : |
34 | instantiation | 45, 70, 56 | ⊢ |
| : , : , : |
35 | instantiation | 46, 94, 99, 50, 47, 52, 55, 71, 70, 48* | ⊢ |
| : , : , : , : , : , : |
36 | axiom | | ⊢ |
| proveit.logic.equality.equals_transitivity |
37 | instantiation | 49, 94, 99, 50, 51, 52, 70, 55, 53 | ⊢ |
| : , : , : , : , : , : |
38 | instantiation | 54, 70, 55, 56 | ⊢ |
| : , : , : |
39 | theorem | | ⊢ |
| proveit.numbers.number_sets.natural_numbers.nat_pos_within_nat |
40 | theorem | | ⊢ |
| proveit.numbers.addition.add_int_closure_bin |
41 | instantiation | 97, 57, 76 | ⊢ |
| : , : , : |
42 | instantiation | 97, 58, 88 | ⊢ |
| : , : , : |
43 | theorem | | ⊢ |
| proveit.numbers.addition.subtraction.nonneg_difference |
44 | instantiation | 59, 76 | ⊢ |
| : |
45 | theorem | | ⊢ |
| proveit.numbers.addition.subtraction.add_cancel_triple_12 |
46 | theorem | | ⊢ |
| proveit.numbers.addition.association |
47 | instantiation | 63 | ⊢ |
| : , : |
48 | instantiation | 60, 61, 62 | ⊢ |
| : , : , : |
49 | theorem | | ⊢ |
| proveit.numbers.addition.disassociation |
50 | axiom | | ⊢ |
| proveit.numbers.number_sets.natural_numbers.zero_in_nats |
51 | instantiation | 63 | ⊢ |
| : , : |
52 | theorem | | ⊢ |
| proveit.core_expr_types.tuples.tuple_len_0_typical_eq |
53 | instantiation | 97, 85, 64 | ⊢ |
| : , : , : |
54 | theorem | | ⊢ |
| proveit.numbers.addition.subtraction.add_cancel_triple_13 |
55 | instantiation | 97, 85, 65 | ⊢ |
| : , : , : |
56 | instantiation | 66 | ⊢ |
| : |
57 | theorem | | ⊢ |
| proveit.numbers.number_sets.integers.nat_pos_within_int |
58 | theorem | | ⊢ |
| proveit.numbers.number_sets.integers.neg_int_within_int |
59 | theorem | | ⊢ |
| proveit.numbers.number_sets.natural_numbers.natural_pos_lower_bound |
60 | theorem | | ⊢ |
| proveit.logic.equality.sub_right_side_into |
61 | instantiation | 67, 70, 79, 68 | ⊢ |
| : , : , : |
62 | instantiation | 69, 70, 71 | ⊢ |
| : , : |
63 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.tuple_len_2_typical_eq |
64 | instantiation | 97, 72, 73 | ⊢ |
| : , : , : |
65 | instantiation | 74, 75, 76 | ⊢ |
| : , : , : |
66 | axiom | | ⊢ |
| proveit.logic.equality.equals_reflexivity |
67 | theorem | | ⊢ |
| proveit.numbers.addition.subtraction.subtract_from_add_reversed |
68 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.add_1_1 |
69 | theorem | | ⊢ |
| proveit.numbers.addition.commutation |
70 | instantiation | 97, 85, 77 | ⊢ |
| : , : , : |
71 | instantiation | 78, 79 | ⊢ |
| : |
72 | theorem | | ⊢ |
| proveit.numbers.number_sets.real_numbers.real_neg_within_real |
73 | instantiation | 97, 80, 81 | ⊢ |
| : , : , : |
74 | theorem | | ⊢ |
| proveit.logic.sets.inclusion.unfold_subset_eq |
75 | instantiation | 82, 83 | ⊢ |
| : , : |
76 | assumption | | ⊢ |
77 | instantiation | 97, 90, 84 | ⊢ |
| : , : , : |
78 | theorem | | ⊢ |
| proveit.numbers.negation.complex_closure |
79 | instantiation | 97, 85, 86 | ⊢ |
| : , : , : |
80 | theorem | | ⊢ |
| proveit.numbers.number_sets.real_numbers.rational_neg_within_real_neg |
81 | instantiation | 97, 87, 88 | ⊢ |
| : , : , : |
82 | theorem | | ⊢ |
| proveit.logic.sets.inclusion.relax_proper_subset |
83 | theorem | | ⊢ |
| proveit.numbers.number_sets.real_numbers.nat_pos_within_real |
84 | instantiation | 97, 95, 89 | ⊢ |
| : , : , : |
85 | theorem | | ⊢ |
| proveit.numbers.number_sets.complex_numbers.real_within_complex |
86 | instantiation | 97, 90, 91 | ⊢ |
| : , : , : |
87 | theorem | | ⊢ |
| proveit.numbers.number_sets.rational_numbers.neg_int_within_rational_neg |
88 | instantiation | 92, 93 | ⊢ |
| : |
89 | instantiation | 97, 98, 94 | ⊢ |
| : , : , : |
90 | theorem | | ⊢ |
| proveit.numbers.number_sets.real_numbers.rational_within_real |
91 | instantiation | 97, 95, 96 | ⊢ |
| : , : , : |
92 | theorem | | ⊢ |
| proveit.numbers.negation.int_neg_closure |
93 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.posnat1 |
94 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.nat1 |
95 | theorem | | ⊢ |
| proveit.numbers.number_sets.rational_numbers.int_within_rational |
96 | instantiation | 97, 98, 99 | ⊢ |
| : , : , : |
97 | theorem | | ⊢ |
| proveit.logic.sets.inclusion.superset_membership_from_proper_subset |
98 | theorem | | ⊢ |
| proveit.numbers.number_sets.integers.nat_within_int |
99 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.nat2 |
*equality replacement requirements |