| | step type | requirements | statement |
| 0 | instantiation | 1, 2, 3 | , , , ⊢  |
| | : , : , :  |
| 1 | reference | 18 | ⊢  |
| 2 | instantiation | 27, 4 | ⊢  |
| | : , : , :  |
| 3 | instantiation | 18, 5, 6 | , , , ⊢  |
| | : , : , :  |
| 4 | instantiation | 7, 30, 54, 46, 8* | ⊢  |
| | : , :  |
| 5 | instantiation | 9, 77, 74, 10, 14, 50, 15, 16 | , , , ⊢  |
| | : , : , : , : , : , : , :  |
| 6 | instantiation | 11, 74, 77, 12, 13, 14, 50, 15, 16, 17* | , , , ⊢  |
| | : , : , : , : , : , :  |
| 7 | theorem | | ⊢  |
| | proveit.numbers.division.div_as_mult |
| 8 | instantiation | 18, 19, 20 | ⊢  |
| | : , : , :  |
| 9 | theorem | | ⊢  |
| | proveit.numbers.addition.leftward_commutation |
| 10 | instantiation | 48 | ⊢  |
| | : , :  |
| 11 | theorem | | ⊢  |
| | proveit.numbers.addition.association |
| 12 | instantiation | 48 | ⊢  |
| | : , :  |
| 13 | instantiation | 48 | ⊢  |
| | : , :  |
| 14 | instantiation | 75, 62, 21 | ⊢  |
| | : , : , :  |
| 15 | instantiation | 23, 54, 22 | ⊢  |
| | : , :  |
| 16 | instantiation | 23, 31, 30 | ⊢  |
| | : , :  |
| 17 | instantiation | 24, 25, 26* | ⊢  |
| | : , :  |
| 18 | axiom | | ⊢  |
| | proveit.logic.equality.equals_transitivity |
| 19 | instantiation | 27, 28 | ⊢  |
| | : , : , :  |
| 20 | instantiation | 29, 30, 31 | ⊢  |
| | : , :  |
| 21 | instantiation | 75, 55, 32 | ⊢  |
| | : , : , :  |
| 22 | instantiation | 75, 62, 33 | ⊢  |
| | : , : , :  |
| 23 | theorem | | ⊢  |
| | proveit.numbers.multiplication.mult_complex_closure_bin |
| 24 | theorem | | ⊢  |
| | proveit.logic.equality.equals_reversal |
| 25 | instantiation | 34, 35, 77, 74, 36, 37, 45, 50, 38* | ⊢  |
| | : , : , : , : , : , :  |
| 26 | theorem | | ⊢  |
| | proveit.numbers.numerals.decimals.add_1_1 |
| 27 | axiom | | ⊢  |
| | proveit.logic.equality.substitution |
| 28 | instantiation | 39, 40, 41, 42* | ⊢  |
| | : , :  |
| 29 | theorem | | ⊢  |
| | proveit.numbers.multiplication.commutation |
| 30 | instantiation | 75, 62, 43 | ⊢  |
| | : , : , :  |
| 31 | instantiation | 44, 45, 54, 46 | ⊢  |
| | : , :  |
| 32 | assumption | | ⊢  |
| 33 | instantiation | 75, 55, 47 | ⊢  |
| | : , : , :  |
| 34 | theorem | | ⊢  |
| | proveit.numbers.multiplication.distribute_through_sum |
| 35 | axiom | | ⊢  |
| | proveit.numbers.number_sets.natural_numbers.zero_in_nats |
| 36 | theorem | | ⊢  |
| | proveit.core_expr_types.tuples.tuple_len_0_typical_eq |
| 37 | instantiation | 48 | ⊢  |
| | : , :  |
| 38 | instantiation | 49, 50 | ⊢  |
| | :  |
| 39 | theorem | | ⊢  |
| | proveit.numbers.exponentiation.neg_power_as_div |
| 40 | instantiation | 75, 51, 52 | ⊢  |
| | : , : , :  |
| 41 | theorem | | ⊢  |
| | proveit.numbers.numerals.decimals.posnat1 |
| 42 | instantiation | 53, 54 | ⊢  |
| | :  |
| 43 | instantiation | 75, 55, 56 | ⊢  |
| | : , : , :  |
| 44 | theorem | | ⊢  |
| | proveit.numbers.division.div_complex_closure |
| 45 | instantiation | 75, 62, 57 | ⊢  |
| | : , : , :  |
| 46 | instantiation | 58, 71 | ⊢  |
| | :  |
| 47 | assumption | | ⊢  |
| 48 | theorem | | ⊢  |
| | proveit.numbers.numerals.decimals.tuple_len_2_typical_eq |
| 49 | theorem | | ⊢  |
| | proveit.numbers.multiplication.elim_one_left |
| 50 | instantiation | 75, 62, 59 | ⊢  |
| | : , : , :  |
| 51 | theorem | | ⊢  |
| | proveit.numbers.number_sets.complex_numbers.real_nonzero_within_complex_nonzero |
| 52 | instantiation | 75, 60, 61 | ⊢  |
| | : , : , :  |
| 53 | theorem | | ⊢  |
| | proveit.numbers.exponentiation.complex_x_to_first_power_is_x |
| 54 | instantiation | 75, 62, 63 | ⊢  |
| | : , : , :  |
| 55 | theorem | | ⊢  |
| | proveit.numbers.number_sets.real_numbers.real_neg_within_real |
| 56 | assumption | | ⊢  |
| 57 | instantiation | 75, 67, 64 | ⊢  |
| | : , : , :  |
| 58 | theorem | | ⊢  |
| | proveit.numbers.number_sets.natural_numbers.nonzero_if_is_nat_pos |
| 59 | assumption | | ⊢  |
| 60 | theorem | | ⊢  |
| | proveit.numbers.number_sets.real_numbers.rational_nonzero_within_real_nonzero |
| 61 | instantiation | 75, 65, 66 | ⊢  |
| | : , : , :  |
| 62 | theorem | | ⊢  |
| | proveit.numbers.number_sets.complex_numbers.real_within_complex |
| 63 | instantiation | 75, 67, 68 | ⊢  |
| | : , : , :  |
| 64 | instantiation | 75, 72, 69 | ⊢  |
| | : , : , :  |
| 65 | theorem | | ⊢  |
| | proveit.numbers.number_sets.rational_numbers.nonzero_int_within_rational_nonzero |
| 66 | instantiation | 75, 70, 71 | ⊢  |
| | : , : , :  |
| 67 | theorem | | ⊢  |
| | proveit.numbers.number_sets.real_numbers.rational_within_real |
| 68 | instantiation | 75, 72, 73 | ⊢  |
| | : , : , :  |
| 69 | instantiation | 75, 76, 74 | ⊢  |
| | : , : , :  |
| 70 | theorem | | ⊢  |
| | proveit.numbers.number_sets.integers.nat_pos_within_nonzero_int |
| 71 | theorem | | ⊢  |
| | proveit.numbers.numerals.decimals.posnat2 |
| 72 | theorem | | ⊢  |
| | proveit.numbers.number_sets.rational_numbers.int_within_rational |
| 73 | instantiation | 75, 76, 77 | ⊢  |
| | : , : , :  |
| 74 | theorem | | ⊢  |
| | proveit.numbers.numerals.decimals.nat1 |
| 75 | theorem | | ⊢  |
| | proveit.logic.sets.inclusion.superset_membership_from_proper_subset |
| 76 | theorem | | ⊢  |
| | proveit.numbers.number_sets.integers.nat_within_int |
| 77 | theorem | | ⊢  |
| | proveit.numbers.numerals.decimals.nat2 |
| *equality replacement requirements |