| | step type | requirements | statement |
| 0 | instantiation | 1, 2, 3, 4, 5, 6, 7, 8, 9, 10* | , , , , ⊢  |
| | : , : , : , : , : , :  |
| 1 | theorem | | ⊢  |
| | proveit.numbers.multiplication.association |
| 2 | reference | 51 | ⊢  |
| 3 | reference | 80 | ⊢  |
| 4 | reference | 54 | ⊢  |
| 5 | instantiation | 64 | ⊢  |
| | : , :  |
| 6 | reference | 55 | ⊢  |
| 7 | instantiation | 78, 68, 11 | , ⊢  |
| | : , : , :  |
| 8 | instantiation | 12, 13, 15 | , , ⊢  |
| | : , :  |
| 9 | instantiation | 12, 13, 16 | ⊢  |
| | : , :  |
| 10 | instantiation | 14, 24, 15, 16 | , , , ⊢  |
| | : , : , :  |
| 11 | instantiation | 17, 18, 48 | , ⊢  |
| | : , :  |
| 12 | theorem | | ⊢  |
| | proveit.numbers.exponentiation.exp_complex_closure |
| 13 | instantiation | 78, 68, 19 | ⊢  |
| | : , : , :  |
| 14 | theorem | | ⊢  |
| | proveit.numbers.exponentiation.product_of_complex_powers |
| 15 | instantiation | 61, 20, 21 | , , ⊢  |
| | : , :  |
| 16 | instantiation | 34, 22, 23 | ⊢  |
| | : , : , :  |
| 17 | theorem | | ⊢  |
| | proveit.numbers.addition.add_real_closure_bin |
| 18 | assumption | | ⊢  |
| 19 | instantiation | 78, 74, 24 | ⊢  |
| | : , : , :  |
| 20 | instantiation | 25, 26, 27 | , ⊢  |
| | : , :  |
| 21 | instantiation | 78, 68, 28 | ⊢  |
| | : , : , :  |
| 22 | instantiation | 61, 52, 29 | ⊢  |
| | : , :  |
| 23 | instantiation | 44, 30, 31 | ⊢  |
| | : , : , :  |
| 24 | theorem | | ⊢  |
| | proveit.numbers.number_sets.real_numbers.e_is_real_pos |
| 25 | theorem | | ⊢  |
| | proveit.numbers.addition.add_complex_closure_bin |
| 26 | instantiation | 34, 32, 33 | ⊢  |
| | : , : , :  |
| 27 | instantiation | 34, 35, 36 | ⊢  |
| | : , : , :  |
| 28 | instantiation | 78, 72, 37 | ⊢  |
| | : , : , :  |
| 29 | instantiation | 61, 58, 39 | ⊢  |
| | : , :  |
| 30 | instantiation | 53, 51, 80, 54, 38, 55, 52, 58, 39 | ⊢  |
| | : , : , : , : , : , :  |
| 31 | instantiation | 53, 54, 80, 55, 56, 38, 62, 63, 58, 39 | ⊢  |
| | : , : , : , : , : , :  |
| 32 | instantiation | 61, 52, 40 | ⊢  |
| | : , :  |
| 33 | instantiation | 44, 41, 42 | ⊢  |
| | : , : , :  |
| 34 | theorem | | ⊢  |
| | proveit.logic.equality.sub_right_side_into |
| 35 | instantiation | 61, 52, 43 | ⊢  |
| | : , :  |
| 36 | instantiation | 44, 45, 46 | ⊢  |
| | : , : , :  |
| 37 | instantiation | 78, 76, 47 | ⊢  |
| | : , : , :  |
| 38 | instantiation | 64 | ⊢  |
| | : , :  |
| 39 | instantiation | 78, 68, 48 | ⊢  |
| | : , : , :  |
| 40 | instantiation | 61, 58, 50 | ⊢  |
| | : , :  |
| 41 | instantiation | 53, 51, 80, 54, 49, 55, 52, 58, 50 | ⊢  |
| | : , : , : , : , : , :  |
| 42 | instantiation | 53, 54, 80, 55, 56, 49, 62, 63, 58, 50 | ⊢  |
| | : , : , : , : , : , :  |
| 43 | instantiation | 61, 58, 59 | ⊢  |
| | : , :  |
| 44 | axiom | | ⊢  |
| | proveit.logic.equality.equals_transitivity |
| 45 | instantiation | 53, 51, 80, 54, 57, 55, 52, 58, 59 | ⊢  |
| | : , : , : , : , : , :  |
| 46 | instantiation | 53, 54, 80, 55, 56, 57, 62, 63, 58, 59 | ⊢  |
| | : , : , : , : , : , :  |
| 47 | assumption | | ⊢  |
| 48 | assumption | | ⊢  |
| 49 | instantiation | 64 | ⊢  |
| | : , :  |
| 50 | instantiation | 78, 68, 60 | ⊢  |
| | : , : , :  |
| 51 | theorem | | ⊢  |
| | proveit.numbers.numerals.decimals.nat1 |
| 52 | instantiation | 61, 62, 63 | ⊢  |
| | : , :  |
| 53 | theorem | | ⊢  |
| | proveit.numbers.multiplication.disassociation |
| 54 | axiom | | ⊢  |
| | proveit.numbers.number_sets.natural_numbers.zero_in_nats |
| 55 | theorem | | ⊢  |
| | proveit.core_expr_types.tuples.tuple_len_0_typical_eq |
| 56 | instantiation | 64 | ⊢  |
| | : , :  |
| 57 | instantiation | 64 | ⊢  |
| | : , :  |
| 58 | theorem | | ⊢  |
| | proveit.numbers.number_sets.complex_numbers.i_is_complex |
| 59 | instantiation | 78, 68, 65 | ⊢  |
| | : , : , :  |
| 60 | instantiation | 78, 72, 66 | ⊢  |
| | : , : , :  |
| 61 | theorem | | ⊢  |
| | proveit.numbers.multiplication.mult_complex_closure_bin |
| 62 | instantiation | 78, 68, 67 | ⊢  |
| | : , : , :  |
| 63 | instantiation | 78, 68, 69 | ⊢  |
| | : , : , :  |
| 64 | theorem | | ⊢  |
| | proveit.numbers.numerals.decimals.tuple_len_2_typical_eq |
| 65 | instantiation | 78, 74, 70 | ⊢  |
| | : , : , :  |
| 66 | instantiation | 78, 76, 71 | ⊢  |
| | : , : , :  |
| 67 | instantiation | 78, 72, 73 | ⊢  |
| | : , : , :  |
| 68 | theorem | | ⊢  |
| | proveit.numbers.number_sets.complex_numbers.real_within_complex |
| 69 | instantiation | 78, 74, 75 | ⊢  |
| | : , : , :  |
| 70 | assumption | | ⊢  |
| 71 | assumption | | ⊢  |
| 72 | theorem | | ⊢  |
| | proveit.numbers.number_sets.real_numbers.rational_within_real |
| 73 | instantiation | 78, 76, 77 | ⊢  |
| | : , : , :  |
| 74 | theorem | | ⊢  |
| | proveit.numbers.number_sets.real_numbers.real_pos_within_real |
| 75 | theorem | | ⊢  |
| | proveit.numbers.number_sets.real_numbers.pi_is_real_pos |
| 76 | theorem | | ⊢  |
| | proveit.numbers.number_sets.rational_numbers.int_within_rational |
| 77 | instantiation | 78, 79, 80 | ⊢  |
| | : , : , :  |
| 78 | theorem | | ⊢  |
| | proveit.logic.sets.inclusion.superset_membership_from_proper_subset |
| 79 | theorem | | ⊢  |
| | proveit.numbers.number_sets.integers.nat_within_int |
| 80 | theorem | | ⊢  |
| | proveit.numbers.numerals.decimals.nat2 |
| *equality replacement requirements |