| step type | requirements | statement |
0 | instantiation | 1, 2, 3, 4, 5, 6, 7, 8 | , , , , ⊢  |
| : , : , : , : , : , :  |
1 | theorem | | ⊢  |
| proveit.numbers.multiplication.association |
2 | reference | 59 | ⊢  |
3 | reference | 90 | ⊢  |
4 | instantiation | 71 | ⊢  |
| : , :  |
5 | instantiation | 12, 13, 9 | ⊢  |
| : , :  |
6 | instantiation | 12, 13, 10 | , ⊢  |
| : , :  |
7 | instantiation | 12, 13, 11 | , ⊢  |
| : , :  |
8 | instantiation | 12, 13, 14 | ⊢  |
| : , :  |
9 | instantiation | 43, 15, 16 | ⊢  |
| : , : , :  |
10 | instantiation | 43, 17, 18 | , ⊢  |
| : , : , :  |
11 | instantiation | 43, 19, 20 | , ⊢  |
| : , : , :  |
12 | theorem | | ⊢  |
| proveit.numbers.exponentiation.exp_complex_closure |
13 | instantiation | 88, 76, 21 | ⊢  |
| : , : , :  |
14 | instantiation | 43, 22, 23 | ⊢  |
| : , : , :  |
15 | instantiation | 68, 48, 24 | ⊢  |
| : , :  |
16 | instantiation | 35, 25, 26 | ⊢  |
| : , : , :  |
17 | instantiation | 68, 48, 27 | , ⊢  |
| : , :  |
18 | instantiation | 35, 28, 29 | , ⊢  |
| : , : , :  |
19 | instantiation | 68, 48, 30 | , ⊢  |
| : , :  |
20 | instantiation | 35, 31, 32 | , ⊢  |
| : , : , :  |
21 | instantiation | 88, 83, 33 | ⊢  |
| : , : , :  |
22 | instantiation | 68, 48, 34 | ⊢  |
| : , :  |
23 | instantiation | 35, 36, 37 | ⊢  |
| : , : , :  |
24 | instantiation | 68, 69, 39 | ⊢  |
| : , :  |
25 | instantiation | 57, 59, 90, 58, 38, 60, 48, 69, 39 | ⊢  |
| : , : , : , : , : , :  |
26 | instantiation | 57, 58, 90, 60, 49, 38, 63, 64, 69, 39 | ⊢  |
| : , : , : , : , : , :  |
27 | instantiation | 43, 40, 41 | , ⊢  |
| : , : , :  |
28 | instantiation | 57, 59, 46, 58, 42, 60, 48, 69, 66, 55 | , ⊢  |
| : , : , : , : , : , :  |
29 | instantiation | 57, 58, 90, 46, 60, 49, 42, 63, 64, 69, 66, 55 | , ⊢  |
| : , : , : , : , : , :  |
30 | instantiation | 43, 44, 45 | , ⊢  |
| : , : , :  |
31 | instantiation | 57, 59, 46, 58, 47, 60, 48, 69, 70, 66 | , ⊢  |
| : , : , : , : , : , :  |
32 | instantiation | 57, 58, 90, 46, 60, 49, 47, 63, 64, 69, 70, 66 | , ⊢  |
| : , : , : , : , : , :  |
33 | theorem | | ⊢  |
| proveit.numbers.number_sets.real_numbers.e_is_real_pos |
34 | instantiation | 68, 69, 51 | ⊢  |
| : , :  |
35 | axiom | | ⊢  |
| proveit.logic.equality.equals_transitivity |
36 | instantiation | 57, 59, 90, 58, 50, 60, 48, 69, 51 | ⊢  |
| : , : , : , : , : , :  |
37 | instantiation | 57, 58, 90, 60, 49, 50, 63, 64, 69, 51 | ⊢  |
| : , : , : , : , : , :  |
38 | instantiation | 71 | ⊢  |
| : , :  |
39 | instantiation | 88, 76, 52 | ⊢  |
| : , : , :  |
40 | instantiation | 68, 53, 55 | , ⊢  |
| : , :  |
41 | instantiation | 57, 58, 90, 59, 60, 54, 69, 66, 55 | , ⊢  |
| : , : , : , : , : , :  |
42 | instantiation | 62 | ⊢  |
| : , : , :  |
43 | theorem | | ⊢  |
| proveit.logic.equality.sub_right_side_into |
44 | instantiation | 68, 56, 66 | , ⊢  |
| : , :  |
45 | instantiation | 57, 58, 90, 59, 60, 61, 69, 70, 66 | , ⊢  |
| : , : , : , : , : , :  |
46 | theorem | | ⊢  |
| proveit.numbers.numerals.decimals.nat3 |
47 | instantiation | 62 | ⊢  |
| : , : , :  |
48 | instantiation | 68, 63, 64 | ⊢  |
| : , :  |
49 | instantiation | 71 | ⊢  |
| : , :  |
50 | instantiation | 71 | ⊢  |
| : , :  |
51 | instantiation | 88, 76, 65 | ⊢  |
| : , : , :  |
52 | assumption | | ⊢  |
53 | instantiation | 68, 69, 66 | ⊢  |
| : , :  |
54 | instantiation | 71 | ⊢  |
| : , :  |
55 | instantiation | 88, 76, 67 | ⊢  |
| : , : , :  |
56 | instantiation | 68, 69, 70 | ⊢  |
| : , :  |
57 | theorem | | ⊢  |
| proveit.numbers.multiplication.disassociation |
58 | axiom | | ⊢  |
| proveit.numbers.number_sets.natural_numbers.zero_in_nats |
59 | theorem | | ⊢  |
| proveit.numbers.numerals.decimals.nat1 |
60 | theorem | | ⊢  |
| proveit.core_expr_types.tuples.tuple_len_0_typical_eq |
61 | instantiation | 71 | ⊢  |
| : , :  |
62 | theorem | | ⊢  |
| proveit.numbers.numerals.decimals.tuple_len_3_typical_eq |
63 | instantiation | 88, 76, 72 | ⊢  |
| : , : , :  |
64 | instantiation | 88, 76, 73 | ⊢  |
| : , : , :  |
65 | assumption | | ⊢  |
66 | instantiation | 88, 76, 74 | ⊢  |
| : , : , :  |
67 | instantiation | 88, 80, 75 | ⊢  |
| : , : , :  |
68 | theorem | | ⊢  |
| proveit.numbers.multiplication.mult_complex_closure_bin |
69 | theorem | | ⊢  |
| proveit.numbers.number_sets.complex_numbers.i_is_complex |
70 | instantiation | 88, 76, 77 | ⊢  |
| : , : , :  |
71 | theorem | | ⊢  |
| proveit.numbers.numerals.decimals.tuple_len_2_typical_eq |
72 | instantiation | 88, 80, 78 | ⊢  |
| : , : , :  |
73 | instantiation | 88, 83, 79 | ⊢  |
| : , : , :  |
74 | instantiation | 88, 80, 81 | ⊢  |
| : , : , :  |
75 | instantiation | 88, 86, 82 | ⊢  |
| : , : , :  |
76 | theorem | | ⊢  |
| proveit.numbers.number_sets.complex_numbers.real_within_complex |
77 | instantiation | 88, 83, 84 | ⊢  |
| : , : , :  |
78 | instantiation | 88, 86, 85 | ⊢  |
| : , : , :  |
79 | theorem | | ⊢  |
| proveit.numbers.number_sets.real_numbers.pi_is_real_pos |
80 | theorem | | ⊢  |
| proveit.numbers.number_sets.real_numbers.rational_within_real |
81 | instantiation | 88, 86, 87 | ⊢  |
| : , : , :  |
82 | assumption | | ⊢  |
83 | theorem | | ⊢  |
| proveit.numbers.number_sets.real_numbers.real_pos_within_real |
84 | assumption | | ⊢  |
85 | instantiation | 88, 89, 90 | ⊢  |
| : , : , :  |
86 | theorem | | ⊢  |
| proveit.numbers.number_sets.rational_numbers.int_within_rational |
87 | assumption | | ⊢  |
88 | theorem | | ⊢  |
| proveit.logic.sets.inclusion.superset_membership_from_proper_subset |
89 | theorem | | ⊢  |
| proveit.numbers.number_sets.integers.nat_within_int |
90 | theorem | | ⊢  |
| proveit.numbers.numerals.decimals.nat2 |