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