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