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