| step type | requirements | statement |
0 | instantiation | 1, 2, 3, 4 | , , , ⊢  |
| : , : , :  |
1 | theorem | | ⊢  |
| proveit.numbers.exponentiation.product_of_complex_powers |
2 | theorem | | ⊢  |
| proveit.numbers.number_sets.real_numbers.e_is_real_pos |
3 | instantiation | 45, 5, 6 | , , ⊢  |
| : , :  |
4 | instantiation | 18, 7, 8 | ⊢  |
| : , : , :  |
5 | instantiation | 9, 10, 11 | , ⊢  |
| : , :  |
6 | instantiation | 62, 52, 12 | ⊢  |
| : , : , :  |
7 | instantiation | 45, 36, 13 | ⊢  |
| : , :  |
8 | instantiation | 28, 14, 15 | ⊢  |
| : , : , :  |
9 | theorem | | ⊢  |
| proveit.numbers.addition.add_complex_closure_bin |
10 | instantiation | 18, 16, 17 | ⊢  |
| : , : , :  |
11 | instantiation | 18, 19, 20 | ⊢  |
| : , : , :  |
12 | instantiation | 62, 56, 21 | ⊢  |
| : , : , :  |
13 | instantiation | 45, 42, 23 | ⊢  |
| : , :  |
14 | instantiation | 37, 35, 64, 38, 22, 39, 36, 42, 23 | ⊢  |
| : , : , : , : , : , :  |
15 | instantiation | 37, 38, 64, 39, 40, 22, 46, 47, 42, 23 | ⊢  |
| : , : , : , : , : , :  |
16 | instantiation | 45, 36, 24 | ⊢  |
| : , :  |
17 | instantiation | 28, 25, 26 | ⊢  |
| : , : , :  |
18 | theorem | | ⊢  |
| proveit.logic.equality.sub_right_side_into |
19 | instantiation | 45, 36, 27 | ⊢  |
| : , :  |
20 | instantiation | 28, 29, 30 | ⊢  |
| : , : , :  |
21 | instantiation | 62, 60, 31 | ⊢  |
| : , : , :  |
22 | instantiation | 48 | ⊢  |
| : , :  |
23 | instantiation | 62, 52, 32 | ⊢  |
| : , : , :  |
24 | instantiation | 45, 42, 34 | ⊢  |
| : , :  |
25 | instantiation | 37, 35, 64, 38, 33, 39, 36, 42, 34 | ⊢  |
| : , : , : , : , : , :  |
26 | instantiation | 37, 38, 64, 39, 40, 33, 46, 47, 42, 34 | ⊢  |
| : , : , : , : , : , :  |
27 | instantiation | 45, 42, 43 | ⊢  |
| : , :  |
28 | axiom | | ⊢  |
| proveit.logic.equality.equals_transitivity |
29 | instantiation | 37, 35, 64, 38, 41, 39, 36, 42, 43 | ⊢  |
| : , : , : , : , : , :  |
30 | instantiation | 37, 38, 64, 39, 40, 41, 46, 47, 42, 43 | ⊢  |
| : , : , : , : , : , :  |
31 | assumption | | ⊢  |
32 | assumption | | ⊢  |
33 | instantiation | 48 | ⊢  |
| : , :  |
34 | instantiation | 62, 52, 44 | ⊢  |
| : , : , :  |
35 | theorem | | ⊢  |
| proveit.numbers.numerals.decimals.nat1 |
36 | instantiation | 45, 46, 47 | ⊢  |
| : , :  |
37 | theorem | | ⊢  |
| proveit.numbers.multiplication.disassociation |
38 | axiom | | ⊢  |
| proveit.numbers.number_sets.natural_numbers.zero_in_nats |
39 | theorem | | ⊢  |
| proveit.core_expr_types.tuples.tuple_len_0_typical_eq |
40 | instantiation | 48 | ⊢  |
| : , :  |
41 | instantiation | 48 | ⊢  |
| : , :  |
42 | theorem | | ⊢  |
| proveit.numbers.number_sets.complex_numbers.i_is_complex |
43 | instantiation | 62, 52, 49 | ⊢  |
| : , : , :  |
44 | instantiation | 62, 56, 50 | ⊢  |
| : , : , :  |
45 | theorem | | ⊢  |
| proveit.numbers.multiplication.mult_complex_closure_bin |
46 | instantiation | 62, 52, 51 | ⊢  |
| : , : , :  |
47 | instantiation | 62, 52, 53 | ⊢  |
| : , : , :  |
48 | theorem | | ⊢  |
| proveit.numbers.numerals.decimals.tuple_len_2_typical_eq |
49 | instantiation | 62, 58, 54 | ⊢  |
| : , : , :  |
50 | instantiation | 62, 60, 55 | ⊢  |
| : , : , :  |
51 | instantiation | 62, 56, 57 | ⊢  |
| : , : , :  |
52 | theorem | | ⊢  |
| proveit.numbers.number_sets.complex_numbers.real_within_complex |
53 | instantiation | 62, 58, 59 | ⊢  |
| : , : , :  |
54 | assumption | | ⊢  |
55 | assumption | | ⊢  |
56 | theorem | | ⊢  |
| proveit.numbers.number_sets.real_numbers.rational_within_real |
57 | instantiation | 62, 60, 61 | ⊢  |
| : , : , :  |
58 | theorem | | ⊢  |
| proveit.numbers.number_sets.real_numbers.real_pos_within_real |
59 | theorem | | ⊢  |
| proveit.numbers.number_sets.real_numbers.pi_is_real_pos |
60 | theorem | | ⊢  |
| proveit.numbers.number_sets.rational_numbers.int_within_rational |
61 | instantiation | 62, 63, 64 | ⊢  |
| : , : , :  |
62 | theorem | | ⊢  |
| proveit.logic.sets.inclusion.superset_membership_from_proper_subset |
63 | theorem | | ⊢  |
| proveit.numbers.number_sets.integers.nat_within_int |
64 | theorem | | ⊢  |
| proveit.numbers.numerals.decimals.nat2 |