| | step type | requirements | statement |
| 0 | instantiation | 1, 2, 3 | , ⊢  |
| | : , : , :  |
| 1 | axiom | | ⊢  |
| | proveit.logic.equality.equals_transitivity |
| 2 | instantiation | 4, 55, 56, 5, 38, 39, 42, 21, 22, 6 | , ⊢  |
| | : , : , : , : , : , : , : , :  |
| 3 | instantiation | 7, 8, 9, 10 | , ⊢  |
| | : , : , : , :  |
| 4 | theorem | | ⊢  |
| | proveit.numbers.addition.subtraction.add_cancel_general |
| 5 | instantiation | 11 | ⊢  |
| | : , : , :  |
| 6 | instantiation | 12 | ⊢  |
| | :  |
| 7 | theorem | | ⊢  |
| | proveit.logic.equality.four_chain_transitivity |
| 8 | instantiation | 13, 59, 34, 14, 19, 35, 38, 42, 21, 22 | , ⊢  |
| | : , : , : , : , : , : , :  |
| 9 | instantiation | 17, 55, 59, 15, 19, 38, 42, 21, 22, 16* | , ⊢  |
| | : , : , : , : , : , :  |
| 10 | instantiation | 17, 59, 34, 18, 19, 35, 38, 20, 21, 22, 23* | , ⊢  |
| | : , : , : , : , : , :  |
| 11 | theorem | | ⊢  |
| | proveit.numbers.numerals.decimals.tuple_len_3_typical_eq |
| 12 | axiom | | ⊢  |
| | proveit.logic.equality.equals_reflexivity |
| 13 | theorem | | ⊢  |
| | proveit.numbers.addition.leftward_commutation |
| 14 | instantiation | 43 | ⊢  |
| | : , :  |
| 15 | instantiation | 43 | ⊢  |
| | : , :  |
| 16 | instantiation | 27, 24, 25* | ⊢  |
| | : , :  |
| 17 | theorem | | ⊢  |
| | proveit.numbers.addition.association |
| 18 | instantiation | 43 | ⊢  |
| | : , :  |
| 19 | instantiation | 43 | ⊢  |
| | : , :  |
| 20 | instantiation | 26, 38, 42 | ⊢  |
| | : , :  |
| 21 | instantiation | 26, 37, 39 | ⊢  |
| | : , :  |
| 22 | instantiation | 26, 38, 39 | ⊢  |
| | : , :  |
| 23 | instantiation | 27, 28, 29* | ⊢  |
| | : , :  |
| 24 | instantiation | 33, 34, 59, 55, 35, 30, 31, 42, 32* | ⊢  |
| | : , : , : , : , : , :  |
| 25 | theorem | | ⊢  |
| | proveit.numbers.numerals.decimals.add_1_1 |
| 26 | theorem | | ⊢  |
| | proveit.numbers.multiplication.mult_complex_closure_bin |
| 27 | theorem | | ⊢  |
| | proveit.logic.equality.equals_reversal |
| 28 | instantiation | 33, 34, 59, 55, 35, 36, 37, 38, 39 | ⊢  |
| | : , : , : , : , : , :  |
| 29 | theorem | | ⊢  |
| | proveit.numbers.numerals.decimals.add_3_2 |
| 30 | instantiation | 43 | ⊢  |
| | : , :  |
| 31 | instantiation | 57, 45, 40 | ⊢  |
| | : , : , :  |
| 32 | instantiation | 41, 42 | ⊢  |
| | :  |
| 33 | theorem | | ⊢  |
| | proveit.numbers.multiplication.distribute_through_sum |
| 34 | axiom | | ⊢  |
| | proveit.numbers.number_sets.natural_numbers.zero_in_nats |
| 35 | theorem | | ⊢  |
| | proveit.core_expr_types.tuples.tuple_len_0_typical_eq |
| 36 | instantiation | 43 | ⊢  |
| | : , :  |
| 37 | instantiation | 57, 45, 44 | ⊢  |
| | : , : , :  |
| 38 | instantiation | 57, 45, 46 | ⊢  |
| | : , : , :  |
| 39 | assumption | | ⊢  |
| 40 | instantiation | 57, 49, 47 | ⊢  |
| | : , : , :  |
| 41 | theorem | | ⊢  |
| | proveit.numbers.multiplication.elim_one_left |
| 42 | assumption | | ⊢  |
| 43 | theorem | | ⊢  |
| | proveit.numbers.numerals.decimals.tuple_len_2_typical_eq |
| 44 | instantiation | 57, 49, 48 | ⊢  |
| | : , : , :  |
| 45 | theorem | | ⊢  |
| | proveit.numbers.number_sets.complex_numbers.real_within_complex |
| 46 | instantiation | 57, 49, 50 | ⊢  |
| | : , : , :  |
| 47 | instantiation | 57, 53, 51 | ⊢  |
| | : , : , :  |
| 48 | instantiation | 57, 53, 52 | ⊢  |
| | : , : , :  |
| 49 | theorem | | ⊢  |
| | proveit.numbers.number_sets.real_numbers.rational_within_real |
| 50 | instantiation | 57, 53, 54 | ⊢  |
| | : , : , :  |
| 51 | instantiation | 57, 58, 55 | ⊢  |
| | : , : , :  |
| 52 | instantiation | 57, 58, 56 | ⊢  |
| | : , : , :  |
| 53 | theorem | | ⊢  |
| | proveit.numbers.number_sets.rational_numbers.int_within_rational |
| 54 | instantiation | 57, 58, 59 | ⊢  |
| | : , : , :  |
| 55 | theorem | | ⊢  |
| | proveit.numbers.numerals.decimals.nat1 |
| 56 | theorem | | ⊢  |
| | proveit.numbers.numerals.decimals.nat3 |
| 57 | theorem | | ⊢  |
| | proveit.logic.sets.inclusion.superset_membership_from_proper_subset |
| 58 | theorem | | ⊢  |
| | proveit.numbers.number_sets.integers.nat_within_int |
| 59 | theorem | | ⊢  |
| | proveit.numbers.numerals.decimals.nat2 |
| *equality replacement requirements |