| step type | requirements | statement |
0 | instantiation | 1, 2, 3 | ⊢ |
| : , : , : |
1 | reference | 12 | ⊢ |
2 | instantiation | 4, 34, 5, 6, 7, 8 | ⊢ |
| : , : , : , : |
3 | instantiation | 12, 9, 10 | ⊢ |
| : , : , : |
4 | axiom | | ⊢ |
| proveit.core_expr_types.operations.operands_substitution |
5 | instantiation | 44 | ⊢ |
| : , : , : |
6 | instantiation | 44 | ⊢ |
| : , : , : |
7 | instantiation | 11, 46, 39 | ⊢ |
| : , : , : |
8 | instantiation | 12, 13, 14 | ⊢ |
| : , : , : |
9 | instantiation | 15, 67, 33, 35, 46, 42 | ⊢ |
| : , : , : , : , : , : , : |
10 | instantiation | 16, 33, 29, 67, 35, 17, 46, 42, 18* | ⊢ |
| : , : , : , : , : , : |
11 | theorem | | ⊢ |
| proveit.numbers.addition.subtraction.add_cancel_triple_12 |
12 | axiom | | ⊢ |
| proveit.logic.equality.equals_transitivity |
13 | instantiation | 19, 20 | ⊢ |
| : , : , : |
14 | instantiation | 21, 22, 23, 24 | ⊢ |
| : , : , : , : |
15 | theorem | | ⊢ |
| proveit.numbers.addition.leftward_commutation |
16 | theorem | | ⊢ |
| proveit.numbers.addition.association |
17 | instantiation | 43 | ⊢ |
| : , : |
18 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.add_1_1 |
19 | axiom | | ⊢ |
| proveit.logic.equality.substitution |
20 | instantiation | 25, 26, 46, 27* | ⊢ |
| : , : |
21 | theorem | | ⊢ |
| proveit.logic.equality.four_chain_transitivity |
22 | instantiation | 28, 67, 29, 30, 31, 42, 37, 46 | ⊢ |
| : , : , : , : , : , : |
23 | instantiation | 32, 33, 34, 35, 36, 42, 37, 46 | ⊢ |
| : , : , : , : |
24 | instantiation | 38, 46, 42, 39 | ⊢ |
| : , : , : |
25 | theorem | | ⊢ |
| proveit.numbers.negation.distribute_neg_through_binary_sum |
26 | instantiation | 65, 50, 40 | ⊢ |
| : , : , : |
27 | instantiation | 41, 42 | ⊢ |
| : |
28 | theorem | | ⊢ |
| proveit.numbers.addition.disassociation |
29 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.nat2 |
30 | instantiation | 43 | ⊢ |
| : , : |
31 | theorem | | ⊢ |
| proveit.numbers.number_sets.complex_numbers.zero_is_complex |
32 | theorem | | ⊢ |
| proveit.numbers.addition.elim_zero_any |
33 | axiom | | ⊢ |
| proveit.numbers.number_sets.natural_numbers.zero_in_nats |
34 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.nat3 |
35 | theorem | | ⊢ |
| proveit.core_expr_types.tuples.tuple_len_0_typical_eq |
36 | instantiation | 44 | ⊢ |
| : , : , : |
37 | instantiation | 45, 46 | ⊢ |
| : |
38 | theorem | | ⊢ |
| proveit.numbers.addition.subtraction.add_cancel_triple_32 |
39 | instantiation | 47 | ⊢ |
| : |
40 | instantiation | 65, 55, 48 | ⊢ |
| : , : , : |
41 | theorem | | ⊢ |
| proveit.numbers.negation.double_negation |
42 | instantiation | 65, 50, 49 | ⊢ |
| : , : , : |
43 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.tuple_len_2_typical_eq |
44 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.tuple_len_3_typical_eq |
45 | theorem | | ⊢ |
| proveit.numbers.negation.complex_closure |
46 | instantiation | 65, 50, 51 | ⊢ |
| : , : , : |
47 | axiom | | ⊢ |
| proveit.logic.equality.equals_reflexivity |
48 | instantiation | 65, 61, 52 | ⊢ |
| : , : , : |
49 | instantiation | 53, 54, 64 | ⊢ |
| : , : , : |
50 | theorem | | ⊢ |
| proveit.numbers.number_sets.complex_numbers.real_within_complex |
51 | instantiation | 65, 55, 56 | ⊢ |
| : , : , : |
52 | instantiation | 57, 58 | ⊢ |
| : |
53 | theorem | | ⊢ |
| proveit.logic.sets.inclusion.unfold_subset_eq |
54 | instantiation | 59, 60 | ⊢ |
| : , : |
55 | theorem | | ⊢ |
| proveit.numbers.number_sets.real_numbers.rational_within_real |
56 | instantiation | 65, 61, 62 | ⊢ |
| : , : , : |
57 | theorem | | ⊢ |
| proveit.numbers.negation.int_closure |
58 | instantiation | 65, 63, 64 | ⊢ |
| : , : , : |
59 | theorem | | ⊢ |
| proveit.logic.sets.inclusion.relax_proper_subset |
60 | theorem | | ⊢ |
| proveit.numbers.number_sets.real_numbers.nat_pos_within_real |
61 | theorem | | ⊢ |
| proveit.numbers.number_sets.rational_numbers.int_within_rational |
62 | instantiation | 65, 66, 67 | ⊢ |
| : , : , : |
63 | theorem | | ⊢ |
| proveit.numbers.number_sets.integers.nat_pos_within_int |
64 | assumption | | ⊢ |
65 | theorem | | ⊢ |
| proveit.logic.sets.inclusion.superset_membership_from_proper_subset |
66 | theorem | | ⊢ |
| proveit.numbers.number_sets.integers.nat_within_int |
67 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.nat1 |
*equality replacement requirements |