| | step type | requirements | statement |
| 0 | instantiation | 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13* | , , , ⊢  |
| | : , : , : , : , : , :  |
| 1 | theorem | | ⊢  |
| | proveit.numbers.addition.association |
| 2 | reference | 37 | ⊢  |
| 3 | reference | 82 | ⊢  |
| 4 | theorem | | ⊢  |
| | proveit.numbers.numerals.decimals.nat4 |
| 5 | reference | 38 | ⊢  |
| 6 | instantiation | 64 | ⊢  |
| | : , :  |
| 7 | instantiation | 14 | ⊢  |
| | : , : , : , :  |
| 8 | reference | 52 | ⊢  |
| 9 | instantiation | 50, 15 | ⊢  |
| | :  |
| 10 | instantiation | 85, 77, 16 | ⊢  |
| | : , : , :  |
| 11 | instantiation | 85, 77, 17 | ⊢  |
| | : , : , :  |
| 12 | instantiation | 22, 66, 18 | ⊢  |
| | : , :  |
| 13 | instantiation | 46, 19, 20, 21* | ⊢  |
| | : , : , :  |
| 14 | theorem | | ⊢  |
| | proveit.numbers.numerals.decimals.tuple_len_4_typical_eq |
| 15 | instantiation | 22, 51, 52 | ⊢  |
| | : , :  |
| 16 | instantiation | 85, 71, 23 | ⊢  |
| | : , : , :  |
| 17 | instantiation | 85, 71, 24 | ⊢  |
| | : , : , :  |
| 18 | instantiation | 85, 77, 25 | ⊢  |
| | : , : , :  |
| 19 | instantiation | 26, 27 | ⊢  |
| | : , : , :  |
| 20 | instantiation | 34, 28 | ⊢  |
| | : , :  |
| 21 | instantiation | 29, 84, 30, 79, 31*, 32*, 33* | ⊢  |
| | : , : , : , :  |
| 22 | theorem | | ⊢  |
| | proveit.numbers.multiplication.mult_complex_closure_bin |
| 23 | assumption | | ⊢  |
| 24 | assumption | | ⊢  |
| 25 | assumption | | ⊢  |
| 26 | axiom | | ⊢  |
| | proveit.logic.equality.substitution |
| 27 | instantiation | 34, 35 | ⊢  |
| | : , :  |
| 28 | instantiation | 36, 37, 82, 87, 38, 39, 75, 40, 52, 41* | ⊢  |
| | : , : , : , : , : , :  |
| 29 | theorem | | ⊢  |
| | proveit.numbers.addition.rational_pair_addition |
| 30 | instantiation | 42, 84 | ⊢  |
| | :  |
| 31 | instantiation | 43, 75, 44 | ⊢  |
| | :  |
| 32 | instantiation | 45, 75, 66, 62 | ⊢  |
| | : , :  |
| 33 | instantiation | 46, 47, 48 | ⊢  |
| | : , : , :  |
| 34 | theorem | | ⊢  |
| | proveit.logic.equality.equals_reversal |
| 35 | instantiation | 49, 51, 52 | ⊢  |
| | : , :  |
| 36 | theorem | | ⊢  |
| | proveit.numbers.multiplication.distribute_through_sum |
| 37 | axiom | | ⊢  |
| | proveit.numbers.number_sets.natural_numbers.zero_in_nats |
| 38 | theorem | | ⊢  |
| | proveit.core_expr_types.tuples.tuple_len_0_typical_eq |
| 39 | instantiation | 64 | ⊢  |
| | : , :  |
| 40 | instantiation | 50, 51 | ⊢  |
| | :  |
| 41 | instantiation | 65, 52 | ⊢  |
| | :  |
| 42 | theorem | | ⊢  |
| | proveit.numbers.negation.int_closure |
| 43 | theorem | | ⊢  |
| | proveit.numbers.division.frac_cancel_complete |
| 44 | instantiation | 69, 53 | ⊢  |
| | :  |
| 45 | theorem | | ⊢  |
| | proveit.numbers.division.neg_frac_neg_numerator |
| 46 | axiom | | ⊢  |
| | proveit.logic.equality.equals_transitivity |
| 47 | instantiation | 54, 82, 55, 56, 57, 58 | ⊢  |
| | : , : , : , :  |
| 48 | instantiation | 59, 75, 66, 60 | ⊢  |
| | : , : , :  |
| 49 | theorem | | ⊢  |
| | proveit.numbers.negation.neg_times_pos |
| 50 | theorem | | ⊢  |
| | proveit.numbers.negation.complex_closure |
| 51 | instantiation | 61, 75, 66, 62 | ⊢  |
| | : , :  |
| 52 | instantiation | 85, 77, 63 | ⊢  |
| | : , : , :  |
| 53 | theorem | | ⊢  |
| | proveit.numbers.numerals.decimals.posnat1 |
| 54 | axiom | | ⊢  |
| | proveit.core_expr_types.operations.operands_substitution |
| 55 | instantiation | 64 | ⊢  |
| | : , :  |
| 56 | instantiation | 64 | ⊢  |
| | : , :  |
| 57 | instantiation | 65, 66 | ⊢  |
| | :  |
| 58 | instantiation | 67, 75, 68* | ⊢  |
| | : , :  |
| 59 | theorem | | ⊢  |
| | proveit.numbers.addition.subtraction.subtract_from_add |
| 60 | theorem | | ⊢  |
| | proveit.numbers.numerals.decimals.add_1_1 |
| 61 | theorem | | ⊢  |
| | proveit.numbers.division.div_complex_closure |
| 62 | instantiation | 69, 70 | ⊢  |
| | :  |
| 63 | instantiation | 85, 71, 72 | ⊢  |
| | : , : , :  |
| 64 | theorem | | ⊢  |
| | proveit.numbers.numerals.decimals.tuple_len_2_typical_eq |
| 65 | theorem | | ⊢  |
| | proveit.numbers.multiplication.elim_one_left |
| 66 | instantiation | 85, 77, 73 | ⊢  |
| | : , : , :  |
| 67 | theorem | | ⊢  |
| | proveit.numbers.negation.pos_times_neg |
| 68 | instantiation | 74, 75 | ⊢  |
| | :  |
| 69 | theorem | | ⊢  |
| | proveit.numbers.number_sets.natural_numbers.nonzero_if_is_nat_pos |
| 70 | theorem | | ⊢  |
| | proveit.numbers.numerals.decimals.posnat2 |
| 71 | theorem | | ⊢  |
| | proveit.numbers.number_sets.real_numbers.real_neg_within_real |
| 72 | assumption | | ⊢  |
| 73 | instantiation | 85, 80, 76 | ⊢  |
| | : , : , :  |
| 74 | theorem | | ⊢  |
| | proveit.numbers.multiplication.elim_one_right |
| 75 | instantiation | 85, 77, 78 | ⊢  |
| | : , : , :  |
| 76 | instantiation | 85, 83, 79 | ⊢  |
| | : , : , :  |
| 77 | theorem | | ⊢  |
| | proveit.numbers.number_sets.complex_numbers.real_within_complex |
| 78 | instantiation | 85, 80, 81 | ⊢  |
| | : , : , :  |
| 79 | instantiation | 85, 86, 82 | ⊢  |
| | : , : , :  |
| 80 | theorem | | ⊢  |
| | proveit.numbers.number_sets.real_numbers.rational_within_real |
| 81 | instantiation | 85, 83, 84 | ⊢  |
| | : , : , :  |
| 82 | theorem | | ⊢  |
| | proveit.numbers.numerals.decimals.nat2 |
| 83 | theorem | | ⊢  |
| | proveit.numbers.number_sets.rational_numbers.int_within_rational |
| 84 | instantiation | 85, 86, 87 | ⊢  |
| | : , : , :  |
| 85 | theorem | | ⊢  |
| | proveit.logic.sets.inclusion.superset_membership_from_proper_subset |
| 86 | theorem | | ⊢  |
| | proveit.numbers.number_sets.integers.nat_within_int |
| 87 | theorem | | ⊢  |
| | proveit.numbers.numerals.decimals.nat1 |
| *equality replacement requirements |