| 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 |