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