| | step type | requirements | statement |
| 0 | instantiation | 1, 2, 3*, 4* | ⊢  |
| | :  |
| 1 | theorem | | ⊢  |
| | proveit.numbers.numerals.decimals.md_only_nine_add_one |
| 2 | theorem | | ⊢  |
| | proveit.numbers.numerals.decimals.posnat9 |
| 3 | instantiation | 8, 24, 25, 26, 5, 6, 7 | ⊢  |
| | : , : , : , : , : , : , :  |
| 4 | instantiation | 8, 20, 25, 24, 9, 26, 10, 11, 12 | ⊢  |
| | : , : , : , : , : , : , :  |
| 5 | instantiation | 29 | ⊢  |
| | : , : , : , : , : , : , : , : , :  |
| 6 | instantiation | 15, 13, 17 | ⊢  |
| | : , : , :  |
| 7 | instantiation | 18 | ⊢  |
| | :  |
| 8 | theorem | | ⊢  |
| | proveit.numbers.numerals.decimals.deci_sequence_reduction_ER |
| 9 | instantiation | 29 | ⊢  |
| | : , : , : , : , : , : , : , : , :  |
| 10 | instantiation | 15, 14, 17 | ⊢  |
| | : , : , :  |
| 11 | instantiation | 15, 16, 17 | ⊢  |
| | : , : , :  |
| 12 | instantiation | 18 | ⊢  |
| | :  |
| 13 | instantiation | 23, 25, 24, 19, 26 | ⊢  |
| | : , : , : , : , :  |
| 14 | instantiation | 23, 20, 21, 22 | ⊢  |
| | : , : , : , : , :  |
| 15 | theorem | | ⊢  |
| | proveit.logic.equality.sub_left_side_into |
| 16 | instantiation | 23, 24, 25, 26, 27 | ⊢  |
| | : , : , : , : , :  |
| 17 | theorem | | ⊢  |
| | proveit.numbers.numerals.decimals.N_leq_9_enumSet |
| 18 | theorem | | ⊢  |
| | proveit.numbers.numerals.decimals.reduce_9_repeats |
| 19 | instantiation | 29 | ⊢  |
| | : , : , : , : , : , : , : , : , :  |
| 20 | theorem | | ⊢  |
| | proveit.numbers.numerals.decimals.nat1 |
| 21 | theorem | | ⊢  |
| | proveit.numbers.numerals.decimals.nat8 |
| 22 | instantiation | 28 | ⊢  |
| | : , : , : , : , : , : , : , :  |
| 23 | theorem | | ⊢  |
| | proveit.logic.sets.enumeration.in_enumerated_set |
| 24 | axiom | | ⊢  |
| | proveit.numbers.number_sets.natural_numbers.zero_in_nats |
| 25 | theorem | | ⊢  |
| | proveit.numbers.numerals.decimals.nat9 |
| 26 | theorem | | ⊢  |
| | proveit.core_expr_types.tuples.tuple_len_0_typical_eq |
| 27 | instantiation | 29 | ⊢  |
| | : , : , : , : , : , : , : , : , :  |
| 28 | theorem | | ⊢  |
| | proveit.numbers.numerals.decimals.tuple_len_8_typical_eq |
| 29 | theorem | | ⊢  |
| | proveit.numbers.numerals.decimals.tuple_len_9_typical_eq |
| *equality replacement requirements |