| step type | requirements | statement |
0 | instantiation | 1, 2, 3, 4 | , ⊢ |
| : , : , : , : |
1 | reference | 10 | ⊢ |
2 | instantiation | 22, 5, 6 | , ⊢ |
| : , : , : |
3 | instantiation | 51 | ⊢ |
| : |
4 | instantiation | 7, 8 | ⊢ |
| : , : |
5 | instantiation | 27, 9 | , ⊢ |
| : , : , : |
6 | instantiation | 10, 11, 12, 13 | , ⊢ |
| : , : , : , : |
7 | theorem | | ⊢ |
| proveit.logic.equality.equals_reversal |
8 | instantiation | 22, 14, 15 | ⊢ |
| : , : , : |
9 | instantiation | 22, 16, 17 | , ⊢ |
| : , : , : |
10 | theorem | | ⊢ |
| proveit.logic.equality.four_chain_transitivity |
11 | instantiation | 29, 35, 19, 75, 37, 20, 41, 38, 45, 18 | , ⊢ |
| : , : , : , : , : , : |
12 | instantiation | 29, 19, 34, 35, 20, 21, 37, 41, 38, 45, 49, 26 | , ⊢ |
| : , : , : , : , : , : |
13 | instantiation | 22, 23, 24 | , ⊢ |
| : , : , : |
14 | instantiation | 29, 35, 34, 75, 37, 25, 41, 26, 45 | ⊢ |
| : , : , : , : , : , : |
15 | instantiation | 40, 45, 41, 39 | ⊢ |
| : , : , : |
16 | instantiation | 27, 28 | ⊢ |
| : , : , : |
17 | instantiation | 29, 75, 34, 35, 30, 37, 41, 38, 45 | , ⊢ |
| : , : , : , : , : , : |
18 | instantiation | 73, 56, 31 | ⊢ |
| : , : , : |
19 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.nat3 |
20 | instantiation | 32 | ⊢ |
| : , : , : |
21 | instantiation | 47 | ⊢ |
| : , : |
22 | axiom | | ⊢ |
| proveit.logic.equality.equals_transitivity |
23 | instantiation | 33, 34, 75, 35, 36, 37, 41, 38, 45, 49, 39 | , ⊢ |
| : , : , : , : , : , : , : , : |
24 | instantiation | 40, 49, 41, 42 | , ⊢ |
| : , : , : |
25 | instantiation | 47 | ⊢ |
| : , : |
26 | instantiation | 73, 56, 43 | ⊢ |
| : , : , : |
27 | axiom | | ⊢ |
| proveit.logic.equality.substitution |
28 | instantiation | 44, 49, 45 | ⊢ |
| : , : |
29 | theorem | | ⊢ |
| proveit.numbers.addition.disassociation |
30 | instantiation | 47 | ⊢ |
| : , : |
31 | instantiation | 73, 64, 46 | ⊢ |
| : , : , : |
32 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.tuple_len_3_typical_eq |
33 | theorem | | ⊢ |
| proveit.numbers.addition.subtraction.add_cancel_general |
34 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.nat2 |
35 | axiom | | ⊢ |
| proveit.numbers.number_sets.natural_numbers.zero_in_nats |
36 | instantiation | 47 | ⊢ |
| : , : |
37 | theorem | | ⊢ |
| proveit.core_expr_types.tuples.tuple_len_0_typical_eq |
38 | instantiation | 48, 49 | ⊢ |
| : |
39 | instantiation | 51 | ⊢ |
| : |
40 | theorem | | ⊢ |
| proveit.numbers.addition.subtraction.add_cancel_triple_32 |
41 | instantiation | 73, 56, 50 | ⊢ |
| : , : , : |
42 | instantiation | 51 | ⊢ |
| : |
43 | instantiation | 73, 52, 53 | ⊢ |
| : , : , : |
44 | theorem | | ⊢ |
| proveit.numbers.negation.distribute_neg_through_subtract |
45 | instantiation | 73, 56, 54 | ⊢ |
| : , : , : |
46 | instantiation | 73, 71, 55 | ⊢ |
| : , : , : |
47 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.tuple_len_2_typical_eq |
48 | theorem | | ⊢ |
| proveit.numbers.negation.complex_closure |
49 | instantiation | 73, 56, 57 | ⊢ |
| : , : , : |
50 | instantiation | 73, 64, 58 | ⊢ |
| : , : , : |
51 | axiom | | ⊢ |
| proveit.logic.equality.equals_reflexivity |
52 | theorem | | ⊢ |
| proveit.numbers.number_sets.real_numbers.real_neg_within_real |
53 | instantiation | 73, 59, 60 | ⊢ |
| : , : , : |
54 | instantiation | 73, 64, 61 | ⊢ |
| : , : , : |
55 | instantiation | 62, 72, 63 | ⊢ |
| : , : |
56 | theorem | | ⊢ |
| proveit.numbers.number_sets.complex_numbers.real_within_complex |
57 | instantiation | 73, 64, 65 | ⊢ |
| : , : , : |
58 | instantiation | 73, 71, 66 | ⊢ |
| : , : , : |
59 | theorem | | ⊢ |
| proveit.numbers.number_sets.real_numbers.rational_neg_within_real_neg |
60 | instantiation | 73, 67, 70 | ⊢ |
| : , : , : |
61 | instantiation | 73, 71, 68 | ⊢ |
| : , : , : |
62 | theorem | | ⊢ |
| proveit.numbers.addition.add_int_closure_bin |
63 | instantiation | 73, 69, 70 | ⊢ |
| : , : , : |
64 | theorem | | ⊢ |
| proveit.numbers.number_sets.real_numbers.rational_within_real |
65 | instantiation | 73, 71, 72 | ⊢ |
| : , : , : |
66 | assumption | | ⊢ |
67 | theorem | | ⊢ |
| proveit.numbers.number_sets.rational_numbers.neg_int_within_rational_neg |
68 | instantiation | 73, 74, 75 | ⊢ |
| : , : , : |
69 | theorem | | ⊢ |
| proveit.numbers.number_sets.integers.neg_int_within_int |
70 | instantiation | 76, 77 | ⊢ |
| : |
71 | theorem | | ⊢ |
| proveit.numbers.number_sets.rational_numbers.int_within_rational |
72 | assumption | | ⊢ |
73 | theorem | | ⊢ |
| proveit.logic.sets.inclusion.superset_membership_from_proper_subset |
74 | theorem | | ⊢ |
| proveit.numbers.number_sets.integers.nat_within_int |
75 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.nat1 |
76 | theorem | | ⊢ |
| proveit.numbers.negation.int_neg_closure |
77 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.posnat1 |