| step type | requirements | statement |
0 | instantiation | 1, 2, 3, 4, 5, 6, 7 | , , , , ⊢ |
| : , : , : |
1 | theorem | | ⊢ |
| proveit.numbers.exponentiation.products_of_complex_powers |
2 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.posnat3 |
3 | instantiation | 8 | ⊢ |
| : , : , : |
4 | theorem | | ⊢ |
| proveit.numbers.number_sets.real_numbers.e_is_real_pos |
5 | instantiation | 29, 9, 10 | ⊢ |
| : , : , : |
6 | instantiation | 57, 11, 12 | , , ⊢ |
| : , : |
7 | instantiation | 29, 13, 14 | ⊢ |
| : , : , : |
8 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.tuple_len_3_typical_eq |
9 | instantiation | 57, 48, 15 | ⊢ |
| : , : |
10 | instantiation | 40, 16, 17 | ⊢ |
| : , : , : |
11 | instantiation | 18, 19, 20 | , ⊢ |
| : , : |
12 | instantiation | 74, 64, 21 | ⊢ |
| : , : , : |
13 | instantiation | 57, 48, 22 | ⊢ |
| : , : |
14 | instantiation | 40, 23, 24 | ⊢ |
| : , : , : |
15 | instantiation | 57, 54, 26 | ⊢ |
| : , : |
16 | instantiation | 49, 47, 76, 50, 25, 51, 48, 54, 26 | ⊢ |
| : , : , : , : , : , : |
17 | instantiation | 49, 50, 76, 51, 52, 25, 58, 59, 54, 26 | ⊢ |
| : , : , : , : , : , : |
18 | theorem | | ⊢ |
| proveit.numbers.addition.add_complex_closure_bin |
19 | instantiation | 29, 27, 28 | ⊢ |
| : , : , : |
20 | instantiation | 29, 30, 31 | ⊢ |
| : , : , : |
21 | instantiation | 74, 68, 32 | ⊢ |
| : , : , : |
22 | instantiation | 57, 54, 34 | ⊢ |
| : , : |
23 | instantiation | 49, 47, 76, 50, 33, 51, 48, 54, 34 | ⊢ |
| : , : , : , : , : , : |
24 | instantiation | 49, 50, 76, 51, 52, 33, 58, 59, 54, 34 | ⊢ |
| : , : , : , : , : , : |
25 | instantiation | 60 | ⊢ |
| : , : |
26 | instantiation | 74, 64, 35 | ⊢ |
| : , : , : |
27 | instantiation | 57, 48, 36 | ⊢ |
| : , : |
28 | instantiation | 40, 37, 38 | ⊢ |
| : , : , : |
29 | theorem | | ⊢ |
| proveit.logic.equality.sub_right_side_into |
30 | instantiation | 57, 48, 39 | ⊢ |
| : , : |
31 | instantiation | 40, 41, 42 | ⊢ |
| : , : , : |
32 | instantiation | 74, 72, 43 | ⊢ |
| : , : , : |
33 | instantiation | 60 | ⊢ |
| : , : |
34 | instantiation | 74, 64, 44 | ⊢ |
| : , : , : |
35 | assumption | | ⊢ |
36 | instantiation | 57, 54, 46 | ⊢ |
| : , : |
37 | instantiation | 49, 47, 76, 50, 45, 51, 48, 54, 46 | ⊢ |
| : , : , : , : , : , : |
38 | instantiation | 49, 50, 76, 51, 52, 45, 58, 59, 54, 46 | ⊢ |
| : , : , : , : , : , : |
39 | instantiation | 57, 54, 55 | ⊢ |
| : , : |
40 | axiom | | ⊢ |
| proveit.logic.equality.equals_transitivity |
41 | instantiation | 49, 47, 76, 50, 53, 51, 48, 54, 55 | ⊢ |
| : , : , : , : , : , : |
42 | instantiation | 49, 50, 76, 51, 52, 53, 58, 59, 54, 55 | ⊢ |
| : , : , : , : , : , : |
43 | assumption | | ⊢ |
44 | assumption | | ⊢ |
45 | instantiation | 60 | ⊢ |
| : , : |
46 | instantiation | 74, 64, 56 | ⊢ |
| : , : , : |
47 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.nat1 |
48 | instantiation | 57, 58, 59 | ⊢ |
| : , : |
49 | theorem | | ⊢ |
| proveit.numbers.multiplication.disassociation |
50 | axiom | | ⊢ |
| proveit.numbers.number_sets.natural_numbers.zero_in_nats |
51 | theorem | | ⊢ |
| proveit.core_expr_types.tuples.tuple_len_0_typical_eq |
52 | instantiation | 60 | ⊢ |
| : , : |
53 | instantiation | 60 | ⊢ |
| : , : |
54 | theorem | | ⊢ |
| proveit.numbers.number_sets.complex_numbers.i_is_complex |
55 | instantiation | 74, 64, 61 | ⊢ |
| : , : , : |
56 | instantiation | 74, 68, 62 | ⊢ |
| : , : , : |
57 | theorem | | ⊢ |
| proveit.numbers.multiplication.mult_complex_closure_bin |
58 | instantiation | 74, 64, 63 | ⊢ |
| : , : , : |
59 | instantiation | 74, 64, 65 | ⊢ |
| : , : , : |
60 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.tuple_len_2_typical_eq |
61 | instantiation | 74, 70, 66 | ⊢ |
| : , : , : |
62 | instantiation | 74, 72, 67 | ⊢ |
| : , : , : |
63 | instantiation | 74, 68, 69 | ⊢ |
| : , : , : |
64 | theorem | | ⊢ |
| proveit.numbers.number_sets.complex_numbers.real_within_complex |
65 | instantiation | 74, 70, 71 | ⊢ |
| : , : , : |
66 | assumption | | ⊢ |
67 | assumption | | ⊢ |
68 | theorem | | ⊢ |
| proveit.numbers.number_sets.real_numbers.rational_within_real |
69 | instantiation | 74, 72, 73 | ⊢ |
| : , : , : |
70 | theorem | | ⊢ |
| proveit.numbers.number_sets.real_numbers.real_pos_within_real |
71 | theorem | | ⊢ |
| proveit.numbers.number_sets.real_numbers.pi_is_real_pos |
72 | theorem | | ⊢ |
| proveit.numbers.number_sets.rational_numbers.int_within_rational |
73 | instantiation | 74, 75, 76 | ⊢ |
| : , : , : |
74 | theorem | | ⊢ |
| proveit.logic.sets.inclusion.superset_membership_from_proper_subset |
75 | theorem | | ⊢ |
| proveit.numbers.number_sets.integers.nat_within_int |
76 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.nat2 |