| step type | requirements | statement |
0 | instantiation | 1, 2, 3 | ⊢  |
| : , : , :  |
1 | reference | 10 | ⊢  |
2 | instantiation | 4, 5, 6, 7 | ⊢  |
| : , : , : , :  |
3 | instantiation | 10, 8, 9 | ⊢  |
| : , : , :  |
4 | theorem | | ⊢  |
| proveit.logic.equality.four_chain_transitivity |
5 | instantiation | 10, 11, 12 | ⊢  |
| : , : , :  |
6 | instantiation | 16, 20, 70, 79, 22, 13, 14, 46, 28, 29, 48, 30, 31, 15* | ⊢  |
| : , : , : , : , : , :  |
7 | instantiation | 16, 83, 70, 17, 18, 23, 29, 48, 30, 31, 19* | ⊢  |
| : , : , : , : , : , :  |
8 | instantiation | 26, 20, 70, 83, 22, 21, 23, 24, 30, 31 | ⊢  |
| : , : , : , : , : , : , :  |
9 | instantiation | 26, 83, 70, 20, 21, 22, 30, 23, 24, 31 | ⊢  |
| : , : , : , : , : , : , :  |
10 | axiom | | ⊢  |
| proveit.logic.equality.equals_transitivity |
11 | instantiation | 26, 83, 80, 25, 46, 29, 28, 30, 48, 31 | ⊢  |
| : , : , : , : , : , : , :  |
12 | instantiation | 26, 80, 83, 27, 46, 28, 29, 30, 48, 31 | ⊢  |
| : , : , : , : , : , : , :  |
13 | instantiation | 37 | ⊢  |
| : , :  |
14 | instantiation | 32 | ⊢  |
| : , : , : , :  |
15 | instantiation | 34, 46, 35, 67, 33* | ⊢  |
| : , : , :  |
16 | theorem | | ⊢  |
| proveit.numbers.multiplication.association |
17 | instantiation | 37 | ⊢  |
| : , :  |
18 | instantiation | 37 | ⊢  |
| : , :  |
19 | instantiation | 34, 48, 67, 35, 36* | ⊢  |
| : , : , :  |
20 | axiom | | ⊢  |
| proveit.numbers.number_sets.natural_numbers.zero_in_nats |
21 | instantiation | 37 | ⊢  |
| : , :  |
22 | theorem | | ⊢  |
| proveit.core_expr_types.tuples.tuple_len_0_typical_eq |
23 | instantiation | 41, 46, 38 | ⊢  |
| : , :  |
24 | instantiation | 41, 48, 39 | ⊢  |
| : , :  |
25 | instantiation | 40 | ⊢  |
| : , : , :  |
26 | theorem | | ⊢  |
| proveit.numbers.multiplication.leftward_commutation |
27 | instantiation | 40 | ⊢  |
| : , : , :  |
28 | instantiation | 41, 46, 50 | ⊢  |
| : , :  |
29 | instantiation | 41, 48, 50 | ⊢  |
| : , :  |
30 | instantiation | 81, 59, 42 | ⊢  |
| : , : , :  |
31 | instantiation | 43, 51, 44, 45 | ⊢  |
| : , :  |
32 | theorem | | ⊢  |
| proveit.numbers.numerals.decimals.tuple_len_4_typical_eq |
33 | instantiation | 47, 46 | ⊢  |
| :  |
34 | theorem | | ⊢  |
| proveit.numbers.exponentiation.product_of_posnat_powers |
35 | theorem | | ⊢  |
| proveit.numbers.numerals.decimals.posnat1 |
36 | instantiation | 47, 48 | ⊢  |
| :  |
37 | theorem | | ⊢  |
| proveit.numbers.numerals.decimals.tuple_len_2_typical_eq |
38 | instantiation | 49, 51, 50 | ⊢  |
| : , :  |
39 | instantiation | 49, 50, 51 | ⊢  |
| : , :  |
40 | theorem | | ⊢  |
| proveit.numbers.numerals.decimals.tuple_len_3_typical_eq |
41 | theorem | | ⊢  |
| proveit.numbers.exponentiation.exp_complex_closure |
42 | instantiation | 81, 68, 52 | ⊢  |
| : , : , :  |
43 | theorem | | ⊢  |
| proveit.numbers.division.div_complex_closure |
44 | instantiation | 81, 59, 53 | ⊢  |
| : , : , :  |
45 | instantiation | 54, 55 | ⊢  |
| :  |
46 | instantiation | 81, 59, 56 | ⊢  |
| : , : , :  |
47 | theorem | | ⊢  |
| proveit.numbers.exponentiation.complex_x_to_first_power_is_x |
48 | instantiation | 81, 59, 57 | ⊢  |
| : , : , :  |
49 | theorem | | ⊢  |
| proveit.numbers.addition.add_complex_closure_bin |
50 | instantiation | 81, 59, 58 | ⊢  |
| : , : , :  |
51 | instantiation | 81, 59, 60 | ⊢  |
| : , : , :  |
52 | instantiation | 81, 76, 61 | ⊢  |
| : , : , :  |
53 | instantiation | 81, 68, 62 | ⊢  |
| : , : , :  |
54 | theorem | | ⊢  |
| proveit.numbers.number_sets.natural_numbers.nonzero_if_is_nat_pos |
55 | theorem | | ⊢  |
| proveit.numbers.numerals.decimals.posnat5 |
56 | instantiation | 81, 68, 63 | ⊢  |
| : , : , :  |
57 | instantiation | 81, 68, 64 | ⊢  |
| : , : , :  |
58 | instantiation | 65, 66, 67 | ⊢  |
| : , : , :  |
59 | theorem | | ⊢  |
| proveit.numbers.number_sets.complex_numbers.real_within_complex |
60 | instantiation | 81, 68, 69 | ⊢  |
| : , : , :  |
61 | instantiation | 81, 82, 70 | ⊢  |
| : , : , :  |
62 | instantiation | 81, 76, 71 | ⊢  |
| : , : , :  |
63 | instantiation | 81, 76, 72 | ⊢  |
| : , : , :  |
64 | instantiation | 81, 76, 73 | ⊢  |
| : , : , :  |
65 | theorem | | ⊢  |
| proveit.logic.sets.inclusion.unfold_subset_eq |
66 | instantiation | 74, 75 | ⊢  |
| : , :  |
67 | assumption | | ⊢  |
68 | theorem | | ⊢  |
| proveit.numbers.number_sets.real_numbers.rational_within_real |
69 | instantiation | 81, 76, 77 | ⊢  |
| : , : , :  |
70 | theorem | | ⊢  |
| proveit.numbers.numerals.decimals.nat2 |
71 | instantiation | 81, 82, 78 | ⊢  |
| : , : , :  |
72 | instantiation | 81, 82, 79 | ⊢  |
| : , : , :  |
73 | instantiation | 81, 82, 80 | ⊢  |
| : , : , :  |
74 | theorem | | ⊢  |
| proveit.logic.sets.inclusion.relax_proper_subset |
75 | theorem | | ⊢  |
| proveit.numbers.number_sets.real_numbers.nat_pos_within_real |
76 | theorem | | ⊢  |
| proveit.numbers.number_sets.rational_numbers.int_within_rational |
77 | instantiation | 81, 82, 83 | ⊢  |
| : , : , :  |
78 | theorem | | ⊢  |
| proveit.numbers.numerals.decimals.nat5 |
79 | theorem | | ⊢  |
| proveit.numbers.numerals.decimals.nat4 |
80 | theorem | | ⊢  |
| proveit.numbers.numerals.decimals.nat3 |
81 | theorem | | ⊢  |
| proveit.logic.sets.inclusion.superset_membership_from_proper_subset |
82 | theorem | | ⊢  |
| proveit.numbers.number_sets.integers.nat_within_int |
83 | theorem | | ⊢  |
| proveit.numbers.numerals.decimals.nat1 |
*equality replacement requirements |