| | step type | requirements | statement |
| 0 | instantiation | 1, 2, 3 | , , ⊢  |
| | : , : , :  |
| 1 | reference | 39 | ⊢  |
| 2 | instantiation | 39, 4, 5 | , , ⊢  |
| | : , : , :  |
| 3 | instantiation | 24, 67, 6, 7, 8, 17, 9, 49, 18, 10* | , , ⊢  |
| | : , : , : , : , : , :  |
| 4 | instantiation | 24, 44, 68, 11, 45, 12, 13, 26, 27, 28, 60, 49, 18, 14* | , , ⊢  |
| | : , : , : , : , : , :  |
| 5 | instantiation | 24, 74, 67, 69, 15, 16, 17, 60, 49, 18, 19* | , , ⊢  |
| | : , : , : , : , : , :  |
| 6 | instantiation | 56 | ⊢  |
| | : , :  |
| 7 | instantiation | 56 | ⊢  |
| | : , :  |
| 8 | instantiation | 56 | ⊢  |
| | : , :  |
| 9 | instantiation | 20, 26, 60 | ⊢  |
| | : , :  |
| 10 | instantiation | 32, 21, 34* | ⊢  |
| | : , :  |
| 11 | theorem | | ⊢  |
| | proveit.numbers.numerals.decimals.nat6 |
| 12 | instantiation | 22 | ⊢  |
| | : , : , :  |
| 13 | instantiation | 23 | ⊢  |
| | : , : , : , : , : , :  |
| 14 | instantiation | 24, 44, 67, 74, 45, 25, 26, 27, 28, 29* | ⊢  |
| | : , : , : , : , : , :  |
| 15 | instantiation | 56 | ⊢  |
| | : , :  |
| 16 | instantiation | 30 | ⊢  |
| | : , : , : , :  |
| 17 | instantiation | 72, 57, 31 | ⊢  |
| | : , : , :  |
| 18 | assumption | | ⊢  |
| 19 | instantiation | 32, 33, 34* | ⊢  |
| | : , :  |
| 20 | theorem | | ⊢  |
| | proveit.numbers.multiplication.mult_complex_closure_bin |
| 21 | instantiation | 43, 44, 67, 74, 45, 46, 47, 49, 35* | ⊢  |
| | : , : , : , : , : , :  |
| 22 | theorem | | ⊢  |
| | proveit.numbers.numerals.decimals.tuple_len_3_typical_eq |
| 23 | theorem | | ⊢  |
| | proveit.numbers.numerals.decimals.tuple_len_6_typical_eq |
| 24 | theorem | | ⊢  |
| | proveit.numbers.addition.association |
| 25 | instantiation | 56 | ⊢  |
| | : , :  |
| 26 | instantiation | 72, 57, 36 | ⊢  |
| | : , : , :  |
| 27 | instantiation | 72, 57, 37 | ⊢  |
| | : , : , :  |
| 28 | instantiation | 72, 57, 38 | ⊢  |
| | : , : , :  |
| 29 | instantiation | 39, 40, 41 | ⊢  |
| | : , : , :  |
| 30 | theorem | | ⊢  |
| | proveit.numbers.numerals.decimals.tuple_len_4_typical_eq |
| 31 | instantiation | 72, 65, 42 | ⊢  |
| | : , : , :  |
| 32 | theorem | | ⊢  |
| | proveit.logic.equality.equals_reversal |
| 33 | instantiation | 43, 44, 67, 74, 45, 46, 47, 60, 48* | ⊢  |
| | : , : , : , : , : , :  |
| 34 | theorem | | ⊢  |
| | proveit.numbers.numerals.decimals.add_1_1 |
| 35 | instantiation | 59, 49 | ⊢  |
| | :  |
| 36 | instantiation | 72, 65, 50 | ⊢  |
| | : , : , :  |
| 37 | instantiation | 72, 65, 51 | ⊢  |
| | : , : , :  |
| 38 | instantiation | 72, 65, 52 | ⊢  |
| | : , : , :  |
| 39 | axiom | | ⊢  |
| | proveit.logic.equality.equals_transitivity |
| 40 | instantiation | 53, 54 | ⊢  |
| | : , : , :  |
| 41 | theorem | | ⊢  |
| | proveit.numbers.numerals.decimals.add_5_4 |
| 42 | instantiation | 72, 70, 55 | ⊢  |
| | : , : , :  |
| 43 | theorem | | ⊢  |
| | proveit.numbers.multiplication.distribute_through_sum |
| 44 | axiom | | ⊢  |
| | proveit.numbers.number_sets.natural_numbers.zero_in_nats |
| 45 | theorem | | ⊢  |
| | proveit.core_expr_types.tuples.tuple_len_0_typical_eq |
| 46 | instantiation | 56 | ⊢  |
| | : , :  |
| 47 | instantiation | 72, 57, 58 | ⊢  |
| | : , : , :  |
| 48 | instantiation | 59, 60 | ⊢  |
| | :  |
| 49 | assumption | | ⊢  |
| 50 | instantiation | 72, 70, 61 | ⊢  |
| | : , : , :  |
| 51 | instantiation | 72, 70, 62 | ⊢  |
| | : , : , :  |
| 52 | instantiation | 72, 70, 63 | ⊢  |
| | : , : , :  |
| 53 | axiom | | ⊢  |
| | proveit.logic.equality.substitution |
| 54 | theorem | | ⊢  |
| | proveit.numbers.numerals.decimals.add_2_3 |
| 55 | instantiation | 72, 73, 64 | ⊢  |
| | : , : , :  |
| 56 | theorem | | ⊢  |
| | proveit.numbers.numerals.decimals.tuple_len_2_typical_eq |
| 57 | theorem | | ⊢  |
| | proveit.numbers.number_sets.complex_numbers.real_within_complex |
| 58 | instantiation | 72, 65, 66 | ⊢  |
| | : , : , :  |
| 59 | theorem | | ⊢  |
| | proveit.numbers.multiplication.elim_one_left |
| 60 | assumption | | ⊢  |
| 61 | instantiation | 72, 73, 67 | ⊢  |
| | : , : , :  |
| 62 | instantiation | 72, 73, 68 | ⊢  |
| | : , : , :  |
| 63 | instantiation | 72, 73, 69 | ⊢  |
| | : , : , :  |
| 64 | theorem | | ⊢  |
| | proveit.numbers.numerals.decimals.nat9 |
| 65 | theorem | | ⊢  |
| | proveit.numbers.number_sets.real_numbers.rational_within_real |
| 66 | instantiation | 72, 70, 71 | ⊢  |
| | : , : , :  |
| 67 | theorem | | ⊢  |
| | proveit.numbers.numerals.decimals.nat2 |
| 68 | theorem | | ⊢  |
| | proveit.numbers.numerals.decimals.nat3 |
| 69 | theorem | | ⊢  |
| | proveit.numbers.numerals.decimals.nat4 |
| 70 | theorem | | ⊢  |
| | proveit.numbers.number_sets.rational_numbers.int_within_rational |
| 71 | instantiation | 72, 73, 74 | ⊢  |
| | : , : , :  |
| 72 | theorem | | ⊢  |
| | proveit.logic.sets.inclusion.superset_membership_from_proper_subset |
| 73 | theorem | | ⊢  |
| | proveit.numbers.number_sets.integers.nat_within_int |
| 74 | theorem | | ⊢  |
| | proveit.numbers.numerals.decimals.nat1 |
| *equality replacement requirements |