| | step type | requirements | statement |
| 0 | instantiation | 1, 2, 3 | , , ⊢  |
| | : , : , :  |
| 1 | reference | 62 | ⊢  |
| 2 | instantiation | 62, 4, 5 | , , ⊢  |
| | : , : , :  |
| 3 | instantiation | 47, 66, 48, 6, 12, 49, 13, 7, 42, 8* | , , ⊢  |
| | : , : , : , : , : , :  |
| 4 | instantiation | 62, 9, 10 | , , ⊢  |
| | : , : , :  |
| 5 | instantiation | 47, 76, 66, 11, 12, 13, 54, 42, 14* | , , ⊢  |
| | : , : , : , : , : , :  |
| 6 | instantiation | 59 | ⊢  |
| | : , :  |
| 7 | instantiation | 24, 15, 54 | ⊢  |
| | : , :  |
| 8 | instantiation | 36, 16, 70* | ⊢  |
| | : , :  |
| 9 | instantiation | 17, 18, 19, 20 | , , ⊢  |
| | : , : , : , :  |
| 10 | instantiation | 47, 48, 71, 34, 49, 21, 22, 58, 54, 42, 23* | , , ⊢  |
| | : , : , : , : , : , :  |
| 11 | instantiation | 59 | ⊢  |
| | : , :  |
| 12 | instantiation | 59 | ⊢  |
| | : , :  |
| 13 | instantiation | 24, 25, 58 | ⊢  |
| | : , :  |
| 14 | instantiation | 36, 26, 70* | ⊢  |
| | : , :  |
| 15 | instantiation | 74, 60, 27 | ⊢  |
| | : , : , :  |
| 16 | instantiation | 44, 48, 66, 76, 49, 50, 51, 42, 28* | ⊢  |
| | : , : , : , : , : , :  |
| 17 | theorem | | ⊢  |
| | proveit.logic.equality.four_chain_transitivity |
| 18 | instantiation | 33, 76, 66, 71, 29, 30, 58, 54, 42 | , , ⊢  |
| | : , : , : , : , : , : , :  |
| 19 | instantiation | 33, 66, 71, 76, 31, 32, 58, 54, 42 | , , ⊢  |
| | : , : , : , : , : , : , :  |
| 20 | instantiation | 33, 34, 76, 35, 58, 54, 42 | , , ⊢  |
| | : , : , : , : , : , : , :  |
| 21 | instantiation | 56 | ⊢  |
| | : , : , :  |
| 22 | instantiation | 43 | ⊢  |
| | : , : , : , :  |
| 23 | instantiation | 36, 37, 38* | ⊢  |
| | : , :  |
| 24 | theorem | | ⊢  |
| | proveit.numbers.multiplication.mult_complex_closure_bin |
| 25 | instantiation | 74, 60, 39 | ⊢  |
| | : , : , :  |
| 26 | instantiation | 44, 48, 66, 76, 49, 50, 51, 54, 40* | ⊢  |
| | : , : , : , : , : , :  |
| 27 | instantiation | 74, 67, 41 | ⊢  |
| | : , : , :  |
| 28 | instantiation | 57, 42 | ⊢  |
| | :  |
| 29 | instantiation | 59 | ⊢  |
| | : , :  |
| 30 | instantiation | 56 | ⊢  |
| | : , : , :  |
| 31 | instantiation | 59 | ⊢  |
| | : , :  |
| 32 | instantiation | 56 | ⊢  |
| | : , : , :  |
| 33 | theorem | | ⊢  |
| | proveit.numbers.addition.leftward_commutation |
| 34 | theorem | | ⊢  |
| | proveit.numbers.numerals.decimals.nat4 |
| 35 | instantiation | 43 | ⊢  |
| | : , : , : , :  |
| 36 | theorem | | ⊢  |
| | proveit.logic.equality.equals_reversal |
| 37 | instantiation | 44, 48, 71, 76, 49, 45, 51, 58, 46* | ⊢  |
| | : , : , : , : , : , :  |
| 38 | instantiation | 47, 48, 66, 76, 49, 50, 51, 52* | ⊢  |
| | : , : , : , : , : , :  |
| 39 | instantiation | 74, 67, 53 | ⊢  |
| | : , : , :  |
| 40 | instantiation | 57, 54 | ⊢  |
| | :  |
| 41 | instantiation | 74, 72, 55 | ⊢  |
| | : , : , :  |
| 42 | assumption | | ⊢  |
| 43 | theorem | | ⊢  |
| | proveit.numbers.numerals.decimals.tuple_len_4_typical_eq |
| 44 | theorem | | ⊢  |
| | proveit.numbers.multiplication.distribute_through_sum |
| 45 | instantiation | 56 | ⊢  |
| | : , : , :  |
| 46 | instantiation | 57, 58 | ⊢  |
| | :  |
| 47 | theorem | | ⊢  |
| | proveit.numbers.addition.association |
| 48 | axiom | | ⊢  |
| | proveit.numbers.number_sets.natural_numbers.zero_in_nats |
| 49 | theorem | | ⊢  |
| | proveit.core_expr_types.tuples.tuple_len_0_typical_eq |
| 50 | instantiation | 59 | ⊢  |
| | : , :  |
| 51 | instantiation | 74, 60, 61 | ⊢  |
| | : , : , :  |
| 52 | instantiation | 62, 63, 64 | ⊢  |
| | : , : , :  |
| 53 | instantiation | 74, 72, 65 | ⊢  |
| | : , : , :  |
| 54 | assumption | | ⊢  |
| 55 | instantiation | 74, 75, 66 | ⊢  |
| | : , : , :  |
| 56 | theorem | | ⊢  |
| | proveit.numbers.numerals.decimals.tuple_len_3_typical_eq |
| 57 | theorem | | ⊢  |
| | proveit.numbers.multiplication.elim_one_left |
| 58 | assumption | | ⊢  |
| 59 | theorem | | ⊢  |
| | proveit.numbers.numerals.decimals.tuple_len_2_typical_eq |
| 60 | theorem | | ⊢  |
| | proveit.numbers.number_sets.complex_numbers.real_within_complex |
| 61 | instantiation | 74, 67, 68 | ⊢  |
| | : , : , :  |
| 62 | axiom | | ⊢  |
| | proveit.logic.equality.equals_transitivity |
| 63 | instantiation | 69, 70 | ⊢  |
| | : , : , :  |
| 64 | theorem | | ⊢  |
| | proveit.numbers.numerals.decimals.add_2_1 |
| 65 | instantiation | 74, 75, 71 | ⊢  |
| | : , : , :  |
| 66 | theorem | | ⊢  |
| | proveit.numbers.numerals.decimals.nat2 |
| 67 | theorem | | ⊢  |
| | proveit.numbers.number_sets.real_numbers.rational_within_real |
| 68 | instantiation | 74, 72, 73 | ⊢  |
| | : , : , :  |
| 69 | axiom | | ⊢  |
| | proveit.logic.equality.substitution |
| 70 | theorem | | ⊢  |
| | proveit.numbers.numerals.decimals.add_1_1 |
| 71 | theorem | | ⊢  |
| | proveit.numbers.numerals.decimals.nat3 |
| 72 | theorem | | ⊢  |
| | proveit.numbers.number_sets.rational_numbers.int_within_rational |
| 73 | instantiation | 74, 75, 76 | ⊢  |
| | : , : , :  |
| 74 | theorem | | ⊢  |
| | proveit.logic.sets.inclusion.superset_membership_from_proper_subset |
| 75 | theorem | | ⊢  |
| | proveit.numbers.number_sets.integers.nat_within_int |
| 76 | theorem | | ⊢  |
| | proveit.numbers.numerals.decimals.nat1 |
| *equality replacement requirements |