| | step type | requirements | statement |
| 0 | instantiation | 1, 2, 3 | , , ⊢  |
| | : , : , :  |
| 1 | reference | 16 | ⊢  |
| 2 | instantiation | 16, 4, 5 | , , ⊢  |
| | : , : , :  |
| 3 | instantiation | 28, 11, 24, 30, 6, 7, 35, 36, 37 | , , ⊢  |
| | : , : , : , : , : , : , :  |
| 4 | instantiation | 16, 8, 9 | , , ⊢  |
| | : , : , :  |
| 5 | instantiation | 28, 10, 11, 12, 13, 14, 15, 35, 36, 37 | , , ⊢  |
| | : , : , : , : , : , : , :  |
| 6 | instantiation | 23 | ⊢  |
| | : , : , : , : , : , :  |
| 7 | instantiation | 40 | ⊢  |
| | : , : , :  |
| 8 | instantiation | 16, 17, 18 | , , ⊢  |
| | : , : , :  |
| 9 | instantiation | 28, 30, 31, 29, 19, 20, 21, 35, 36, 37 | , , ⊢  |
| | : , : , : , : , : , : , :  |
| 10 | theorem | | ⊢  |
| | proveit.numbers.numerals.decimals.nat4 |
| 11 | theorem | | ⊢  |
| | proveit.numbers.numerals.decimals.nat6 |
| 12 | axiom | | ⊢  |
| | proveit.numbers.number_sets.natural_numbers.zero_in_nats |
| 13 | instantiation | 22 | ⊢  |
| | : , : , : , :  |
| 14 | instantiation | 23 | ⊢  |
| | : , : , : , : , : , :  |
| 15 | theorem | | ⊢  |
| | proveit.core_expr_types.tuples.tuple_len_0_typical_eq |
| 16 | axiom | | ⊢  |
| | proveit.logic.equality.equals_transitivity |
| 17 | instantiation | 28, 24, 29, 25, 26, 27, 35, 36, 37 | , , ⊢  |
| | : , : , : , : , : , : , :  |
| 18 | instantiation | 28, 29, 30, 31, 32, 33, 34, 35, 36, 37 | , , ⊢  |
| | : , : , : , : , : , : , :  |
| 19 | instantiation | 40 | ⊢  |
| | : , : , :  |
| 20 | instantiation | 41 | ⊢  |
| | : , : , : , : , :  |
| 21 | instantiation | 39 | ⊢  |
| | : , :  |
| 22 | theorem | | ⊢  |
| | proveit.numbers.numerals.decimals.tuple_len_4_typical_eq |
| 23 | theorem | | ⊢  |
| | proveit.numbers.numerals.decimals.tuple_len_6_typical_eq |
| 24 | theorem | | ⊢  |
| | proveit.numbers.numerals.decimals.nat1 |
| 25 | theorem | | ⊢  |
| | proveit.numbers.numerals.decimals.nat7 |
| 26 | instantiation | 39 | ⊢  |
| | : , :  |
| 27 | instantiation | 38 | ⊢  |
| | : , : , : , : , : , : , :  |
| 28 | theorem | | ⊢  |
| | proveit.numbers.addition.leftward_commutation |
| 29 | theorem | | ⊢  |
| | proveit.numbers.numerals.decimals.nat2 |
| 30 | theorem | | ⊢  |
| | proveit.numbers.numerals.decimals.nat3 |
| 31 | theorem | | ⊢  |
| | proveit.numbers.numerals.decimals.nat5 |
| 32 | instantiation | 39 | ⊢  |
| | : , :  |
| 33 | instantiation | 40 | ⊢  |
| | : , : , :  |
| 34 | instantiation | 41 | ⊢  |
| | : , : , : , : , :  |
| 35 | assumption | | ⊢  |
| 36 | assumption | | ⊢  |
| 37 | assumption | | ⊢  |
| 38 | theorem | | ⊢  |
| | proveit.numbers.numerals.decimals.tuple_len_7_typical_eq |
| 39 | theorem | | ⊢  |
| | proveit.numbers.numerals.decimals.tuple_len_2_typical_eq |
| 40 | theorem | | ⊢  |
| | proveit.numbers.numerals.decimals.tuple_len_3_typical_eq |
| 41 | theorem | | ⊢  |
| | proveit.numbers.numerals.decimals.tuple_len_5_typical_eq |