| | step type | requirements | statement |
| 0 | instantiation | 1, 2, 3, 4, 5, 6, 7, 8 | , , , , ⊢  |
| | : , : , : , : , : , :  |
| 1 | theorem | | ⊢  |
| | proveit.numbers.multiplication.association |
| 2 | reference | 59 | ⊢  |
| 3 | reference | 90 | ⊢  |
| 4 | instantiation | 71 | ⊢  |
| | : , :  |
| 5 | instantiation | 12, 13, 9 | ⊢  |
| | : , :  |
| 6 | instantiation | 12, 13, 10 | , ⊢  |
| | : , :  |
| 7 | instantiation | 12, 13, 11 | , ⊢  |
| | : , :  |
| 8 | instantiation | 12, 13, 14 | ⊢  |
| | : , :  |
| 9 | instantiation | 43, 15, 16 | ⊢  |
| | : , : , :  |
| 10 | instantiation | 43, 17, 18 | , ⊢  |
| | : , : , :  |
| 11 | instantiation | 43, 19, 20 | , ⊢  |
| | : , : , :  |
| 12 | theorem | | ⊢  |
| | proveit.numbers.exponentiation.exp_complex_closure |
| 13 | instantiation | 88, 76, 21 | ⊢  |
| | : , : , :  |
| 14 | instantiation | 43, 22, 23 | ⊢  |
| | : , : , :  |
| 15 | instantiation | 68, 48, 24 | ⊢  |
| | : , :  |
| 16 | instantiation | 35, 25, 26 | ⊢  |
| | : , : , :  |
| 17 | instantiation | 68, 48, 27 | , ⊢  |
| | : , :  |
| 18 | instantiation | 35, 28, 29 | , ⊢  |
| | : , : , :  |
| 19 | instantiation | 68, 48, 30 | , ⊢  |
| | : , :  |
| 20 | instantiation | 35, 31, 32 | , ⊢  |
| | : , : , :  |
| 21 | instantiation | 88, 83, 33 | ⊢  |
| | : , : , :  |
| 22 | instantiation | 68, 48, 34 | ⊢  |
| | : , :  |
| 23 | instantiation | 35, 36, 37 | ⊢  |
| | : , : , :  |
| 24 | instantiation | 68, 69, 39 | ⊢  |
| | : , :  |
| 25 | instantiation | 57, 59, 90, 58, 38, 60, 48, 69, 39 | ⊢  |
| | : , : , : , : , : , :  |
| 26 | instantiation | 57, 58, 90, 60, 49, 38, 63, 64, 69, 39 | ⊢  |
| | : , : , : , : , : , :  |
| 27 | instantiation | 43, 40, 41 | , ⊢  |
| | : , : , :  |
| 28 | instantiation | 57, 59, 46, 58, 42, 60, 48, 69, 66, 55 | , ⊢  |
| | : , : , : , : , : , :  |
| 29 | instantiation | 57, 58, 90, 46, 60, 49, 42, 63, 64, 69, 66, 55 | , ⊢  |
| | : , : , : , : , : , :  |
| 30 | instantiation | 43, 44, 45 | , ⊢  |
| | : , : , :  |
| 31 | instantiation | 57, 59, 46, 58, 47, 60, 48, 69, 70, 66 | , ⊢  |
| | : , : , : , : , : , :  |
| 32 | instantiation | 57, 58, 90, 46, 60, 49, 47, 63, 64, 69, 70, 66 | , ⊢  |
| | : , : , : , : , : , :  |
| 33 | theorem | | ⊢  |
| | proveit.numbers.number_sets.real_numbers.e_is_real_pos |
| 34 | instantiation | 68, 69, 51 | ⊢  |
| | : , :  |
| 35 | axiom | | ⊢  |
| | proveit.logic.equality.equals_transitivity |
| 36 | instantiation | 57, 59, 90, 58, 50, 60, 48, 69, 51 | ⊢  |
| | : , : , : , : , : , :  |
| 37 | instantiation | 57, 58, 90, 60, 49, 50, 63, 64, 69, 51 | ⊢  |
| | : , : , : , : , : , :  |
| 38 | instantiation | 71 | ⊢  |
| | : , :  |
| 39 | instantiation | 88, 76, 52 | ⊢  |
| | : , : , :  |
| 40 | instantiation | 68, 53, 55 | , ⊢  |
| | : , :  |
| 41 | instantiation | 57, 58, 90, 59, 60, 54, 69, 66, 55 | , ⊢  |
| | : , : , : , : , : , :  |
| 42 | instantiation | 62 | ⊢  |
| | : , : , :  |
| 43 | theorem | | ⊢  |
| | proveit.logic.equality.sub_right_side_into |
| 44 | instantiation | 68, 56, 66 | , ⊢  |
| | : , :  |
| 45 | instantiation | 57, 58, 90, 59, 60, 61, 69, 70, 66 | , ⊢  |
| | : , : , : , : , : , :  |
| 46 | theorem | | ⊢  |
| | proveit.numbers.numerals.decimals.nat3 |
| 47 | instantiation | 62 | ⊢  |
| | : , : , :  |
| 48 | instantiation | 68, 63, 64 | ⊢  |
| | : , :  |
| 49 | instantiation | 71 | ⊢  |
| | : , :  |
| 50 | instantiation | 71 | ⊢  |
| | : , :  |
| 51 | instantiation | 88, 76, 65 | ⊢  |
| | : , : , :  |
| 52 | assumption | | ⊢  |
| 53 | instantiation | 68, 69, 66 | ⊢  |
| | : , :  |
| 54 | instantiation | 71 | ⊢  |
| | : , :  |
| 55 | instantiation | 88, 76, 67 | ⊢  |
| | : , : , :  |
| 56 | instantiation | 68, 69, 70 | ⊢  |
| | : , :  |
| 57 | theorem | | ⊢  |
| | proveit.numbers.multiplication.disassociation |
| 58 | axiom | | ⊢  |
| | proveit.numbers.number_sets.natural_numbers.zero_in_nats |
| 59 | theorem | | ⊢  |
| | proveit.numbers.numerals.decimals.nat1 |
| 60 | theorem | | ⊢  |
| | proveit.core_expr_types.tuples.tuple_len_0_typical_eq |
| 61 | instantiation | 71 | ⊢  |
| | : , :  |
| 62 | theorem | | ⊢  |
| | proveit.numbers.numerals.decimals.tuple_len_3_typical_eq |
| 63 | instantiation | 88, 76, 72 | ⊢  |
| | : , : , :  |
| 64 | instantiation | 88, 76, 73 | ⊢  |
| | : , : , :  |
| 65 | assumption | | ⊢  |
| 66 | instantiation | 88, 76, 74 | ⊢  |
| | : , : , :  |
| 67 | instantiation | 88, 80, 75 | ⊢  |
| | : , : , :  |
| 68 | theorem | | ⊢  |
| | proveit.numbers.multiplication.mult_complex_closure_bin |
| 69 | theorem | | ⊢  |
| | proveit.numbers.number_sets.complex_numbers.i_is_complex |
| 70 | instantiation | 88, 76, 77 | ⊢  |
| | : , : , :  |
| 71 | theorem | | ⊢  |
| | proveit.numbers.numerals.decimals.tuple_len_2_typical_eq |
| 72 | instantiation | 88, 80, 78 | ⊢  |
| | : , : , :  |
| 73 | instantiation | 88, 83, 79 | ⊢  |
| | : , : , :  |
| 74 | instantiation | 88, 80, 81 | ⊢  |
| | : , : , :  |
| 75 | instantiation | 88, 86, 82 | ⊢  |
| | : , : , :  |
| 76 | theorem | | ⊢  |
| | proveit.numbers.number_sets.complex_numbers.real_within_complex |
| 77 | instantiation | 88, 83, 84 | ⊢  |
| | : , : , :  |
| 78 | instantiation | 88, 86, 85 | ⊢  |
| | : , : , :  |
| 79 | theorem | | ⊢  |
| | proveit.numbers.number_sets.real_numbers.pi_is_real_pos |
| 80 | theorem | | ⊢  |
| | proveit.numbers.number_sets.real_numbers.rational_within_real |
| 81 | instantiation | 88, 86, 87 | ⊢  |
| | : , : , :  |
| 82 | assumption | | ⊢  |
| 83 | theorem | | ⊢  |
| | proveit.numbers.number_sets.real_numbers.real_pos_within_real |
| 84 | assumption | | ⊢  |
| 85 | instantiation | 88, 89, 90 | ⊢  |
| | : , : , :  |
| 86 | theorem | | ⊢  |
| | proveit.numbers.number_sets.rational_numbers.int_within_rational |
| 87 | assumption | | ⊢  |
| 88 | theorem | | ⊢  |
| | proveit.logic.sets.inclusion.superset_membership_from_proper_subset |
| 89 | theorem | | ⊢  |
| | proveit.numbers.number_sets.integers.nat_within_int |
| 90 | theorem | | ⊢  |
| | proveit.numbers.numerals.decimals.nat2 |