| | step type | requirements | statement |
| 0 | instantiation | 1, 2, 3 | , , ⊢  |
| | : , : , :  |
| 1 | reference | 8 | ⊢  |
| 2 | instantiation | 8, 4, 5 | , , ⊢  |
| | : , : , :  |
| 3 | instantiation | 17, 6, 50, 20, 7, 13, 23, 24, 25, 26, 29, 27, 28 | , , ⊢  |
| | : , : , : , : , : , : , :  |
| 4 | instantiation | 8, 9, 10 | , , ⊢  |
| | : , : , :  |
| 5 | instantiation | 17, 11, 50, 49, 12, 13, 24, 25, 26, 29, 27, 28 | , , ⊢  |
| | : , : , : , : , : , : , :  |
| 6 | theorem | | ⊢  |
| | proveit.numbers.numerals.decimals.nat7 |
| 7 | instantiation | 14 | ⊢  |
| | : , : , : , : , : , : , :  |
| 8 | axiom | | ⊢  |
| | proveit.logic.equality.equals_transitivity |
| 9 | instantiation | 17, 49, 18, 15, 16, 24, 25, 26, 27, 28, 29 | , , ⊢  |
| | : , : , : , : , : , : , :  |
| 10 | instantiation | 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29 | , , ⊢  |
| | : , : , : , : , : , : , :  |
| 11 | theorem | | ⊢  |
| | proveit.numbers.numerals.decimals.nat6 |
| 12 | instantiation | 30 | ⊢  |
| | : , : , : , : , : , :  |
| 13 | instantiation | 31 | ⊢  |
| | : , :  |
| 14 | theorem | | ⊢  |
| | proveit.numbers.numerals.decimals.tuple_len_7_typical_eq |
| 15 | instantiation | 32 | ⊢  |
| | : , : , : , :  |
| 16 | instantiation | 32 | ⊢  |
| | : , : , : , :  |
| 17 | theorem | | ⊢  |
| | proveit.numbers.addition.leftward_commutation |
| 18 | theorem | | ⊢  |
| | proveit.numbers.numerals.decimals.nat4 |
| 19 | theorem | | ⊢  |
| | proveit.numbers.numerals.decimals.nat5 |
| 20 | axiom | | ⊢  |
| | proveit.numbers.number_sets.natural_numbers.zero_in_nats |
| 21 | instantiation | 32 | ⊢  |
| | : , : , : , :  |
| 22 | instantiation | 33 | ⊢  |
| | : , : , : , : , :  |
| 23 | theorem | | ⊢  |
| | proveit.core_expr_types.tuples.tuple_len_0_typical_eq |
| 24 | instantiation | 51, 39, 34 | ⊢  |
| | : , : , :  |
| 25 | instantiation | 51, 39, 35 | ⊢  |
| | : , : , :  |
| 26 | instantiation | 51, 39, 36 | ⊢  |
| | : , : , :  |
| 27 | instantiation | 51, 39, 37 | ⊢  |
| | : , : , :  |
| 28 | instantiation | 51, 39, 38 | ⊢  |
| | : , : , :  |
| 29 | instantiation | 51, 39, 40 | ⊢  |
| | : , : , :  |
| 30 | theorem | | ⊢  |
| | proveit.numbers.numerals.decimals.tuple_len_6_typical_eq |
| 31 | theorem | | ⊢  |
| | proveit.numbers.numerals.decimals.tuple_len_2_typical_eq |
| 32 | theorem | | ⊢  |
| | proveit.numbers.numerals.decimals.tuple_len_4_typical_eq |
| 33 | theorem | | ⊢  |
| | proveit.numbers.numerals.decimals.tuple_len_5_typical_eq |
| 34 | assumption | | ⊢  |
| 35 | instantiation | 51, 43, 41 | ⊢  |
| | : , : , :  |
| 36 | instantiation | 51, 43, 42 | ⊢  |
| | : , : , :  |
| 37 | assumption | | ⊢  |
| 38 | assumption | | ⊢  |
| 39 | theorem | | ⊢  |
| | proveit.numbers.number_sets.complex_numbers.real_within_complex |
| 40 | instantiation | 51, 43, 44 | ⊢  |
| | : , : , :  |
| 41 | instantiation | 51, 47, 45 | ⊢  |
| | : , : , :  |
| 42 | instantiation | 51, 47, 46 | ⊢  |
| | : , : , :  |
| 43 | theorem | | ⊢  |
| | proveit.numbers.number_sets.real_numbers.rational_within_real |
| 44 | instantiation | 51, 47, 48 | ⊢  |
| | : , : , :  |
| 45 | instantiation | 51, 52, 49 | ⊢  |
| | : , : , :  |
| 46 | instantiation | 51, 52, 50 | ⊢  |
| | : , : , :  |
| 47 | theorem | | ⊢  |
| | proveit.numbers.number_sets.rational_numbers.int_within_rational |
| 48 | instantiation | 51, 52, 53 | ⊢  |
| | : , : , :  |
| 49 | theorem | | ⊢  |
| | proveit.numbers.numerals.decimals.nat1 |
| 50 | theorem | | ⊢  |
| | proveit.numbers.numerals.decimals.nat2 |
| 51 | theorem | | ⊢  |
| | proveit.logic.sets.inclusion.superset_membership_from_proper_subset |
| 52 | theorem | | ⊢  |
| | proveit.numbers.number_sets.integers.nat_within_int |
| 53 | theorem | | ⊢  |
| | proveit.numbers.numerals.decimals.nat3 |