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