| step type | requirements | statement |
0 | instantiation | 1, 2, 3, 4, 5, 6 | , , ⊢ |
| : , : , : |
1 | theorem | | ⊢ |
| proveit.numbers.exponentiation.real_power_of_product |
2 | instantiation | 8, 18, 7 | ⊢ |
| : , : |
3 | instantiation | 8, 18, 13 | ⊢ |
| : , : |
4 | instantiation | 74, 67, 9 | ⊢ |
| : , : , : |
5 | instantiation | 10, 11, 12 | ⊢ |
| : , : , : |
6 | instantiation | 17, 18, 13, 20 | ⊢ |
| : , : |
7 | instantiation | 29, 14, 15 | ⊢ |
| : , : , : |
8 | theorem | | ⊢ |
| proveit.numbers.exponentiation.exp_complex_closure |
9 | instantiation | 74, 72, 16 | ⊢ |
| : , : , : |
10 | theorem | | ⊢ |
| proveit.logic.equality.sub_left_side_into |
11 | instantiation | 17, 18, 19, 20 | ⊢ |
| : , : |
12 | instantiation | 21, 22 | ⊢ |
| : , : , : |
13 | instantiation | 29, 23, 24 | ⊢ |
| : , : , : |
14 | instantiation | 57, 48, 25 | ⊢ |
| : , : |
15 | instantiation | 40, 26, 27 | ⊢ |
| : , : , : |
16 | assumption | | ⊢ |
17 | theorem | | ⊢ |
| proveit.numbers.exponentiation.exp_not_eq_zero |
18 | instantiation | 74, 64, 28 | ⊢ |
| : , : , : |
19 | instantiation | 29, 30, 31 | ⊢ |
| : , : , : |
20 | instantiation | 32, 33 | ⊢ |
| : |
21 | axiom | | ⊢ |
| proveit.logic.equality.substitution |
22 | instantiation | 34, 76, 47, 50, 52, 51, 58, 59, 55, 54 | ⊢ |
| : , : , : , : , : , : , : |
23 | instantiation | 57, 48, 35 | ⊢ |
| : , : |
24 | instantiation | 40, 36, 37 | ⊢ |
| : , : , : |
25 | instantiation | 57, 55, 54 | ⊢ |
| : , : |
26 | instantiation | 49, 47, 76, 50, 38, 51, 48, 55, 54 | ⊢ |
| : , : , : , : , : , : |
27 | instantiation | 49, 50, 76, 51, 52, 38, 58, 59, 55, 54 | ⊢ |
| : , : , : , : , : , : |
28 | instantiation | 74, 69, 44 | ⊢ |
| : , : , : |
29 | theorem | | ⊢ |
| proveit.logic.equality.sub_right_side_into |
30 | instantiation | 57, 48, 39 | ⊢ |
| : , : |
31 | instantiation | 40, 41, 42 | ⊢ |
| : , : , : |
32 | theorem | | ⊢ |
| proveit.numbers.number_sets.real_numbers.nonzero_if_in_real_nonzero |
33 | instantiation | 74, 43, 44 | ⊢ |
| : , : , : |
34 | theorem | | ⊢ |
| proveit.numbers.multiplication.leftward_commutation |
35 | instantiation | 57, 55, 46 | ⊢ |
| : , : |
36 | instantiation | 49, 47, 76, 50, 45, 51, 48, 55, 46 | ⊢ |
| : , : , : , : , : , : |
37 | instantiation | 49, 50, 76, 51, 52, 45, 58, 59, 55, 46 | ⊢ |
| : , : , : , : , : , : |
38 | instantiation | 60 | ⊢ |
| : , : |
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 | theorem | | ⊢ |
| proveit.numbers.number_sets.real_numbers.real_pos_within_real_nonzero |
44 | theorem | | ⊢ |
| proveit.numbers.number_sets.real_numbers.e_is_real_pos |
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 | instantiation | 74, 64, 61 | ⊢ |
| : , : , : |
55 | theorem | | ⊢ |
| proveit.numbers.number_sets.complex_numbers.i_is_complex |
56 | instantiation | 74, 69, 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, 67, 66 | ⊢ |
| : , : , : |
62 | assumption | | ⊢ |
63 | instantiation | 74, 67, 68 | ⊢ |
| : , : , : |
64 | theorem | | ⊢ |
| proveit.numbers.number_sets.complex_numbers.real_within_complex |
65 | instantiation | 74, 69, 70 | ⊢ |
| : , : , : |
66 | instantiation | 74, 72, 71 | ⊢ |
| : , : , : |
67 | theorem | | ⊢ |
| proveit.numbers.number_sets.real_numbers.rational_within_real |
68 | instantiation | 74, 72, 73 | ⊢ |
| : , : , : |
69 | theorem | | ⊢ |
| proveit.numbers.number_sets.real_numbers.real_pos_within_real |
70 | theorem | | ⊢ |
| proveit.numbers.number_sets.real_numbers.pi_is_real_pos |
71 | assumption | | ⊢ |
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 |