| | step type | requirements | statement |
| 0 | instantiation | 1, 2, 3 | , , ⊢  |
| | : , : , :  |
| 1 | reference | 35 | ⊢  |
| 2 | instantiation | 35, 4, 5 | , , ⊢  |
| | : , : , :  |
| 3 | instantiation | 6, 42, 43, 69, 44, 7, 12, 13, 31 | , , ⊢  |
| | : , : , : , : , : , :  |
| 4 | instantiation | 35, 8, 9 | , , ⊢  |
| | : , : , :  |
| 5 | instantiation | 10, 69, 43, 42, 11, 44, 12, 13, 31 | , , ⊢  |
| | : , : , : , : , : , :  |
| 6 | theorem | | ⊢  |
| | proveit.numbers.multiplication.association |
| 7 | instantiation | 53 | ⊢  |
| | : , :  |
| 8 | instantiation | 35, 14, 15 | , , ⊢  |
| | : , : , :  |
| 9 | instantiation | 19, 16 | , ⊢  |
| | : , : , :  |
| 10 | theorem | | ⊢  |
| | proveit.numbers.multiplication.disassociation |
| 11 | instantiation | 53 | ⊢  |
| | : , :  |
| 12 | instantiation | 17, 27, 48 | , ⊢  |
| | : , :  |
| 13 | instantiation | 17, 31, 18 | , ⊢  |
| | : , :  |
| 14 | instantiation | 19, 20 | , ⊢  |
| | : , : , :  |
| 15 | instantiation | 21, 27, 31, 62 | , , ⊢  |
| | : , : , :  |
| 16 | instantiation | 22, 50, 56, 25, 60, 23, 24* | , ⊢  |
| | : , : , : , :  |
| 17 | theorem | | ⊢  |
| | proveit.numbers.exponentiation.exp_complex_closure |
| 18 | instantiation | 67, 59, 25 | ⊢  |
| | : , : , :  |
| 19 | axiom | | ⊢  |
| | proveit.logic.equality.substitution |
| 20 | instantiation | 26, 31, 27 | , ⊢  |
| | : , :  |
| 21 | theorem | | ⊢  |
| | proveit.numbers.exponentiation.pos_power_of_product |
| 22 | theorem | | ⊢  |
| | proveit.numbers.exponentiation.exp_factored_real |
| 23 | instantiation | 28, 29 | ⊢  |
| | : , :  |
| 24 | instantiation | 30, 31 | ⊢  |
| | :  |
| 25 | instantiation | 32, 56, 33 | ⊢  |
| | : , :  |
| 26 | theorem | | ⊢  |
| | proveit.numbers.multiplication.commutation |
| 27 | instantiation | 67, 59, 34 | ⊢  |
| | : , : , :  |
| 28 | theorem | | ⊢  |
| | proveit.logic.equality.equals_reversal |
| 29 | instantiation | 35, 36, 37 | ⊢  |
| | : , : , :  |
| 30 | theorem | | ⊢  |
| | proveit.numbers.exponentiation.complex_x_to_first_power_is_x |
| 31 | instantiation | 67, 59, 38 | ⊢  |
| | : , : , :  |
| 32 | theorem | | ⊢  |
| | proveit.numbers.addition.add_real_closure_bin |
| 33 | instantiation | 67, 63, 39 | ⊢  |
| | : , : , :  |
| 34 | instantiation | 67, 63, 40 | ⊢  |
| | : , : , :  |
| 35 | axiom | | ⊢  |
| | proveit.logic.equality.equals_transitivity |
| 36 | instantiation | 41, 42, 43, 69, 44, 45, 48, 46, 55 | ⊢  |
| | : , : , : , : , : , :  |
| 37 | instantiation | 47, 55, 48, 49 | ⊢  |
| | : , : , :  |
| 38 | instantiation | 67, 61, 50 | ⊢  |
| | : , : , :  |
| 39 | instantiation | 67, 65, 51 | ⊢  |
| | : , : , :  |
| 40 | instantiation | 67, 65, 52 | ⊢  |
| | : , : , :  |
| 41 | theorem | | ⊢  |
| | proveit.numbers.addition.disassociation |
| 42 | axiom | | ⊢  |
| | proveit.numbers.number_sets.natural_numbers.zero_in_nats |
| 43 | theorem | | ⊢  |
| | proveit.numbers.numerals.decimals.nat2 |
| 44 | theorem | | ⊢  |
| | proveit.core_expr_types.tuples.tuple_len_0_typical_eq |
| 45 | instantiation | 53 | ⊢  |
| | : , :  |
| 46 | instantiation | 54, 55 | ⊢  |
| | :  |
| 47 | theorem | | ⊢  |
| | proveit.numbers.addition.subtraction.add_cancel_triple_32 |
| 48 | instantiation | 67, 59, 56 | ⊢  |
| | : , : , :  |
| 49 | instantiation | 57 | ⊢  |
| | :  |
| 50 | assumption | | ⊢  |
| 51 | instantiation | 58, 66 | ⊢  |
| | :  |
| 52 | assumption | | ⊢  |
| 53 | theorem | | ⊢  |
| | proveit.numbers.numerals.decimals.tuple_len_2_typical_eq |
| 54 | theorem | | ⊢  |
| | proveit.numbers.negation.complex_closure |
| 55 | instantiation | 67, 59, 60 | ⊢  |
| | : , : , :  |
| 56 | instantiation | 67, 61, 62 | ⊢  |
| | : , : , :  |
| 57 | axiom | | ⊢  |
| | proveit.logic.equality.equals_reflexivity |
| 58 | theorem | | ⊢  |
| | proveit.numbers.negation.int_closure |
| 59 | theorem | | ⊢  |
| | proveit.numbers.number_sets.complex_numbers.real_within_complex |
| 60 | instantiation | 67, 63, 64 | ⊢  |
| | : , : , :  |
| 61 | theorem | | ⊢  |
| | proveit.numbers.number_sets.real_numbers.real_pos_within_real |
| 62 | assumption | | ⊢  |
| 63 | theorem | | ⊢  |
| | proveit.numbers.number_sets.real_numbers.rational_within_real |
| 64 | instantiation | 67, 65, 66 | ⊢  |
| | : , : , :  |
| 65 | theorem | | ⊢  |
| | proveit.numbers.number_sets.rational_numbers.int_within_rational |
| 66 | instantiation | 67, 68, 69 | ⊢  |
| | : , : , :  |
| 67 | theorem | | ⊢  |
| | proveit.logic.sets.inclusion.superset_membership_from_proper_subset |
| 68 | theorem | | ⊢  |
| | proveit.numbers.number_sets.integers.nat_within_int |
| 69 | theorem | | ⊢  |
| | proveit.numbers.numerals.decimals.nat1 |
| *equality replacement requirements |