| | step type | requirements | statement |
| 0 | instantiation | 1, 2, 3 | , , ⊢  |
| | : , : , :  |
| 1 | reference | 20 | ⊢  |
| 2 | instantiation | 20, 4, 5 | , , ⊢  |
| | : , : , :  |
| 3 | instantiation | 32, 29, 33, 28, 6, 7, 39, 40, 41 | , , ⊢  |
| | : , : , : , : , : , : , :  |
| 4 | instantiation | 20, 8, 9 | , , ⊢  |
| | : , : , :  |
| 5 | instantiation | 32, 15, 28, 34, 10, 11, 39, 40, 41 | , , ⊢  |
| | : , : , : , : , : , : , :  |
| 6 | instantiation | 42 | ⊢  |
| | : , : , : , : , : , : , :  |
| 7 | instantiation | 43 | ⊢  |
| | : , :  |
| 8 | instantiation | 20, 12, 13 | , , ⊢  |
| | : , : , :  |
| 9 | instantiation | 32, 14, 15, 16, 17, 18, 19, 39, 40, 41 | , , ⊢  |
| | : , : , : , : , : , : , :  |
| 10 | instantiation | 27 | ⊢  |
| | : , : , : , : , : , :  |
| 11 | instantiation | 44 | ⊢  |
| | : , : , :  |
| 12 | instantiation | 20, 21, 22 | , , ⊢  |
| | : , : , :  |
| 13 | instantiation | 32, 34, 35, 33, 23, 24, 25, 39, 40, 41 | , , ⊢  |
| | : , : , : , : , : , : , :  |
| 14 | theorem | | ⊢  |
| | proveit.numbers.numerals.decimals.nat4 |
| 15 | theorem | | ⊢  |
| | proveit.numbers.numerals.decimals.nat6 |
| 16 | axiom | | ⊢  |
| | proveit.numbers.number_sets.natural_numbers.zero_in_nats |
| 17 | instantiation | 26 | ⊢  |
| | : , : , : , :  |
| 18 | instantiation | 27 | ⊢  |
| | : , : , : , : , : , :  |
| 19 | theorem | | ⊢  |
| | proveit.core_expr_types.tuples.tuple_len_0_typical_eq |
| 20 | axiom | | ⊢  |
| | proveit.logic.equality.equals_transitivity |
| 21 | instantiation | 32, 28, 33, 29, 30, 31, 39, 40, 41 | , , ⊢  |
| | : , : , : , : , : , : , :  |
| 22 | instantiation | 32, 33, 34, 35, 36, 37, 38, 39, 40, 41 | , , ⊢  |
| | : , : , : , : , : , : , :  |
| 23 | instantiation | 44 | ⊢  |
| | : , : , :  |
| 24 | instantiation | 45 | ⊢  |
| | : , : , : , : , :  |
| 25 | instantiation | 43 | ⊢  |
| | : , :  |
| 26 | theorem | | ⊢  |
| | proveit.numbers.numerals.decimals.tuple_len_4_typical_eq |
| 27 | theorem | | ⊢  |
| | proveit.numbers.numerals.decimals.tuple_len_6_typical_eq |
| 28 | theorem | | ⊢  |
| | proveit.numbers.numerals.decimals.nat1 |
| 29 | theorem | | ⊢  |
| | proveit.numbers.numerals.decimals.nat7 |
| 30 | instantiation | 43 | ⊢  |
| | : , :  |
| 31 | instantiation | 42 | ⊢  |
| | : , : , : , : , : , : , :  |
| 32 | theorem | | ⊢  |
| | proveit.numbers.addition.leftward_commutation |
| 33 | theorem | | ⊢  |
| | proveit.numbers.numerals.decimals.nat2 |
| 34 | theorem | | ⊢  |
| | proveit.numbers.numerals.decimals.nat3 |
| 35 | theorem | | ⊢  |
| | proveit.numbers.numerals.decimals.nat5 |
| 36 | instantiation | 43 | ⊢  |
| | : , :  |
| 37 | instantiation | 44 | ⊢  |
| | : , : , :  |
| 38 | instantiation | 45 | ⊢  |
| | : , : , : , : , :  |
| 39 | assumption | | ⊢  |
| 40 | assumption | | ⊢  |
| 41 | assumption | | ⊢  |
| 42 | theorem | | ⊢  |
| | proveit.numbers.numerals.decimals.tuple_len_7_typical_eq |
| 43 | theorem | | ⊢  |
| | proveit.numbers.numerals.decimals.tuple_len_2_typical_eq |
| 44 | theorem | | ⊢  |
| | proveit.numbers.numerals.decimals.tuple_len_3_typical_eq |
| 45 | theorem | | ⊢  |
| | proveit.numbers.numerals.decimals.tuple_len_5_typical_eq |