| step type | requirements | statement |
0 | instantiation | 1, 2, 3, 4, 5, 6, 7, 8 | , , , , ⊢  |
| : , : , : , : , : , :  |
1 | theorem | | ⊢  |
| proveit.numbers.multiplication.association |
2 | reference | 53 | ⊢  |
3 | reference | 84 | ⊢  |
4 | instantiation | 65 | ⊢  |
| : , :  |
5 | instantiation | 82, 70, 9 | , ⊢  |
| : , : , :  |
6 | instantiation | 12, 13, 10 | , ⊢  |
| : , :  |
7 | instantiation | 12, 13, 11 | , ⊢  |
| : , :  |
8 | instantiation | 12, 13, 14 | ⊢  |
| : , :  |
9 | instantiation | 15, 16, 59 | , ⊢  |
| : , :  |
10 | instantiation | 38, 17, 18 | , ⊢  |
| : , : , :  |
11 | instantiation | 38, 19, 20 | , ⊢  |
| : , : , :  |
12 | theorem | | ⊢  |
| proveit.numbers.exponentiation.exp_complex_closure |
13 | instantiation | 82, 70, 21 | ⊢  |
| : , : , :  |
14 | instantiation | 38, 22, 23 | ⊢  |
| : , : , :  |
15 | theorem | | ⊢  |
| proveit.numbers.addition.add_real_closure_bin |
16 | assumption | | ⊢  |
17 | instantiation | 62, 43, 24 | , ⊢  |
| : , :  |
18 | instantiation | 32, 25, 26 | , ⊢  |
| : , : , :  |
19 | instantiation | 62, 43, 27 | , ⊢  |
| : , :  |
20 | instantiation | 32, 28, 29 | , ⊢  |
| : , : , :  |
21 | instantiation | 82, 77, 30 | ⊢  |
| : , : , :  |
22 | instantiation | 62, 43, 31 | ⊢  |
| : , :  |
23 | instantiation | 32, 33, 34 | ⊢  |
| : , : , :  |
24 | instantiation | 38, 35, 36 | , ⊢  |
| : , : , :  |
25 | instantiation | 51, 53, 41, 52, 37, 54, 43, 63, 60, 49 | , ⊢  |
| : , : , : , : , : , :  |
26 | instantiation | 51, 52, 84, 41, 54, 44, 37, 57, 58, 63, 60, 49 | , ⊢  |
| : , : , : , : , : , :  |
27 | instantiation | 38, 39, 40 | , ⊢  |
| : , : , :  |
28 | instantiation | 51, 53, 41, 52, 42, 54, 43, 63, 64, 60 | , ⊢  |
| : , : , : , : , : , :  |
29 | instantiation | 51, 52, 84, 41, 54, 44, 42, 57, 58, 63, 64, 60 | , ⊢  |
| : , : , : , : , : , :  |
30 | theorem | | ⊢  |
| proveit.numbers.number_sets.real_numbers.e_is_real_pos |
31 | instantiation | 62, 63, 46 | ⊢  |
| : , :  |
32 | axiom | | ⊢  |
| proveit.logic.equality.equals_transitivity |
33 | instantiation | 51, 53, 84, 52, 45, 54, 43, 63, 46 | ⊢  |
| : , : , : , : , : , :  |
34 | instantiation | 51, 52, 84, 54, 44, 45, 57, 58, 63, 46 | ⊢  |
| : , : , : , : , : , :  |
35 | instantiation | 62, 47, 49 | , ⊢  |
| : , :  |
36 | instantiation | 51, 52, 84, 53, 54, 48, 63, 60, 49 | , ⊢  |
| : , : , : , : , : , :  |
37 | instantiation | 56 | ⊢  |
| : , : , :  |
38 | theorem | | ⊢  |
| proveit.logic.equality.sub_right_side_into |
39 | instantiation | 62, 50, 60 | , ⊢  |
| : , :  |
40 | instantiation | 51, 52, 84, 53, 54, 55, 63, 64, 60 | , ⊢  |
| : , : , : , : , : , :  |
41 | theorem | | ⊢  |
| proveit.numbers.numerals.decimals.nat3 |
42 | instantiation | 56 | ⊢  |
| : , : , :  |
43 | instantiation | 62, 57, 58 | ⊢  |
| : , :  |
44 | instantiation | 65 | ⊢  |
| : , :  |
45 | instantiation | 65 | ⊢  |
| : , :  |
46 | instantiation | 82, 70, 59 | ⊢  |
| : , : , :  |
47 | instantiation | 62, 63, 60 | ⊢  |
| : , :  |
48 | instantiation | 65 | ⊢  |
| : , :  |
49 | instantiation | 82, 70, 61 | ⊢  |
| : , : , :  |
50 | instantiation | 62, 63, 64 | ⊢  |
| : , :  |
51 | theorem | | ⊢  |
| proveit.numbers.multiplication.disassociation |
52 | axiom | | ⊢  |
| proveit.numbers.number_sets.natural_numbers.zero_in_nats |
53 | theorem | | ⊢  |
| proveit.numbers.numerals.decimals.nat1 |
54 | theorem | | ⊢  |
| proveit.core_expr_types.tuples.tuple_len_0_typical_eq |
55 | instantiation | 65 | ⊢  |
| : , :  |
56 | theorem | | ⊢  |
| proveit.numbers.numerals.decimals.tuple_len_3_typical_eq |
57 | instantiation | 82, 70, 66 | ⊢  |
| : , : , :  |
58 | instantiation | 82, 70, 67 | ⊢  |
| : , : , :  |
59 | assumption | | ⊢  |
60 | instantiation | 82, 70, 68 | ⊢  |
| : , : , :  |
61 | instantiation | 82, 74, 69 | ⊢  |
| : , : , :  |
62 | theorem | | ⊢  |
| proveit.numbers.multiplication.mult_complex_closure_bin |
63 | theorem | | ⊢  |
| proveit.numbers.number_sets.complex_numbers.i_is_complex |
64 | instantiation | 82, 70, 71 | ⊢  |
| : , : , :  |
65 | theorem | | ⊢  |
| proveit.numbers.numerals.decimals.tuple_len_2_typical_eq |
66 | instantiation | 82, 74, 72 | ⊢  |
| : , : , :  |
67 | instantiation | 82, 77, 73 | ⊢  |
| : , : , :  |
68 | instantiation | 82, 74, 75 | ⊢  |
| : , : , :  |
69 | instantiation | 82, 80, 76 | ⊢  |
| : , : , :  |
70 | theorem | | ⊢  |
| proveit.numbers.number_sets.complex_numbers.real_within_complex |
71 | instantiation | 82, 77, 78 | ⊢  |
| : , : , :  |
72 | instantiation | 82, 80, 79 | ⊢  |
| : , : , :  |
73 | theorem | | ⊢  |
| proveit.numbers.number_sets.real_numbers.pi_is_real_pos |
74 | theorem | | ⊢  |
| proveit.numbers.number_sets.real_numbers.rational_within_real |
75 | instantiation | 82, 80, 81 | ⊢  |
| : , : , :  |
76 | assumption | | ⊢  |
77 | theorem | | ⊢  |
| proveit.numbers.number_sets.real_numbers.real_pos_within_real |
78 | assumption | | ⊢  |
79 | instantiation | 82, 83, 84 | ⊢  |
| : , : , :  |
80 | theorem | | ⊢  |
| proveit.numbers.number_sets.rational_numbers.int_within_rational |
81 | assumption | | ⊢  |
82 | theorem | | ⊢  |
| proveit.logic.sets.inclusion.superset_membership_from_proper_subset |
83 | theorem | | ⊢  |
| proveit.numbers.number_sets.integers.nat_within_int |
84 | theorem | | ⊢  |
| proveit.numbers.numerals.decimals.nat2 |