| | step type | requirements | statement |
| 0 | instantiation | 1, 2, 3, 4 | , , , , , ⊢  |
| | : , : , : , :  |
| 1 | reference | 5 | ⊢  |
| 2 | instantiation | 5, 6, 7, 8 | , , , , , ⊢  |
| | : , : , : , :  |
| 3 | instantiation | 31, 46, 65, 9, 48, 10, 11, 50, 32, 24, 60, 25, 26, 27, 28, 12* | , , , , , ⊢  |
| | : , : , : , : , : , :  |
| 4 | instantiation | 31, 47, 21, 13, 14, 23, 15, 24, 60, 25, 26, 27, 28, 16* | , , , , , ⊢  |
| | : , : , : , : , : , :  |
| 5 | theorem | | ⊢  |
| | proveit.logic.equality.four_chain_transitivity |
| 6 | instantiation | 20, 70, 18, 47, 19, 17, 50, 24, 60, 25, 26, 27, 28, 32 | , , , , , ⊢  |
| | : , : , : , : , : , : , :  |
| 7 | instantiation | 20, 47, 18, 70, 49, 19, 50, 24, 60, 25, 26, 27, 28, 32 | , , , , , ⊢  |
| | : , : , : , : , : , : , :  |
| 8 | instantiation | 20, 62, 21, 46, 22, 23, 48, 50, 32, 24, 60, 25, 26, 27, 28 | , , , , , ⊢  |
| | : , : , : , : , : , : , :  |
| 9 | theorem | | ⊢  |
| | proveit.numbers.numerals.decimals.nat7 |
| 10 | instantiation | 29 | ⊢  |
| | : , : , :  |
| 11 | instantiation | 30 | ⊢  |
| | : , : , : , : , : , : , :  |
| 12 | instantiation | 31, 46, 47, 70, 48, 49, 50, 32, 33* | ⊢  |
| | : , : , : , : , : , :  |
| 13 | instantiation | 56 | ⊢  |
| | : , :  |
| 14 | instantiation | 56 | ⊢  |
| | : , :  |
| 15 | instantiation | 68, 57, 34 | ⊢  |
| | : , : , :  |
| 16 | instantiation | 35, 36, 54* | ⊢  |
| | : , :  |
| 17 | instantiation | 56 | ⊢  |
| | : , :  |
| 18 | theorem | | ⊢  |
| | proveit.numbers.numerals.decimals.nat6 |
| 19 | instantiation | 37 | ⊢  |
| | : , : , : , : , : , :  |
| 20 | theorem | | ⊢  |
| | proveit.numbers.addition.leftward_commutation |
| 21 | theorem | | ⊢  |
| | proveit.numbers.numerals.decimals.nat4 |
| 22 | instantiation | 38 | ⊢  |
| | : , : , : , : , :  |
| 23 | instantiation | 39 | ⊢  |
| | : , : , : , :  |
| 24 | assumption | | ⊢  |
| 25 | assumption | | ⊢  |
| 26 | assumption | | ⊢  |
| 27 | assumption | | ⊢  |
| 28 | assumption | | ⊢  |
| 29 | theorem | | ⊢  |
| | proveit.numbers.numerals.decimals.tuple_len_3_typical_eq |
| 30 | theorem | | ⊢  |
| | proveit.numbers.numerals.decimals.tuple_len_7_typical_eq |
| 31 | theorem | | ⊢  |
| | proveit.numbers.addition.association |
| 32 | instantiation | 68, 57, 40 | ⊢  |
| | : , : , :  |
| 33 | instantiation | 41, 42, 43 | ⊢  |
| | : , : , :  |
| 34 | instantiation | 68, 63, 44 | ⊢  |
| | : , : , :  |
| 35 | theorem | | ⊢  |
| | proveit.logic.equality.equals_reversal |
| 36 | instantiation | 45, 46, 47, 70, 48, 49, 50, 60, 51* | ⊢  |
| | : , : , : , : , : , :  |
| 37 | theorem | | ⊢  |
| | proveit.numbers.numerals.decimals.tuple_len_6_typical_eq |
| 38 | theorem | | ⊢  |
| | proveit.numbers.numerals.decimals.tuple_len_5_typical_eq |
| 39 | theorem | | ⊢  |
| | proveit.numbers.numerals.decimals.tuple_len_4_typical_eq |
| 40 | instantiation | 68, 63, 52 | ⊢  |
| | : , : , :  |
| 41 | axiom | | ⊢  |
| | proveit.logic.equality.equals_transitivity |
| 42 | instantiation | 53, 54 | ⊢  |
| | : , : , :  |
| 43 | theorem | | ⊢  |
| | proveit.numbers.numerals.decimals.add_2_3 |
| 44 | instantiation | 68, 66, 55 | ⊢  |
| | : , : , :  |
| 45 | theorem | | ⊢  |
| | proveit.numbers.multiplication.distribute_through_sum |
| 46 | axiom | | ⊢  |
| | proveit.numbers.number_sets.natural_numbers.zero_in_nats |
| 47 | theorem | | ⊢  |
| | proveit.numbers.numerals.decimals.nat2 |
| 48 | theorem | | ⊢  |
| | proveit.core_expr_types.tuples.tuple_len_0_typical_eq |
| 49 | instantiation | 56 | ⊢  |
| | : , :  |
| 50 | instantiation | 68, 57, 58 | ⊢  |
| | : , : , :  |
| 51 | instantiation | 59, 60 | ⊢  |
| | :  |
| 52 | instantiation | 68, 66, 61 | ⊢  |
| | : , : , :  |
| 53 | axiom | | ⊢  |
| | proveit.logic.equality.substitution |
| 54 | theorem | | ⊢  |
| | proveit.numbers.numerals.decimals.add_1_1 |
| 55 | instantiation | 68, 69, 62 | ⊢  |
| | : , : , :  |
| 56 | theorem | | ⊢  |
| | proveit.numbers.numerals.decimals.tuple_len_2_typical_eq |
| 57 | theorem | | ⊢  |
| | proveit.numbers.number_sets.complex_numbers.real_within_complex |
| 58 | instantiation | 68, 63, 64 | ⊢  |
| | : , : , :  |
| 59 | theorem | | ⊢  |
| | proveit.numbers.multiplication.elim_one_left |
| 60 | assumption | | ⊢  |
| 61 | instantiation | 68, 69, 65 | ⊢  |
| | : , : , :  |
| 62 | theorem | | ⊢  |
| | proveit.numbers.numerals.decimals.nat5 |
| 63 | theorem | | ⊢  |
| | proveit.numbers.number_sets.real_numbers.rational_within_real |
| 64 | instantiation | 68, 66, 67 | ⊢  |
| | : , : , :  |
| 65 | theorem | | ⊢  |
| | proveit.numbers.numerals.decimals.nat3 |
| 66 | theorem | | ⊢  |
| | proveit.numbers.number_sets.rational_numbers.int_within_rational |
| 67 | instantiation | 68, 69, 70 | ⊢  |
| | : , : , :  |
| 68 | theorem | | ⊢  |
| | proveit.logic.sets.inclusion.superset_membership_from_proper_subset |
| 69 | theorem | | ⊢  |
| | proveit.numbers.number_sets.integers.nat_within_int |
| 70 | theorem | | ⊢  |
| | proveit.numbers.numerals.decimals.nat1 |
| *equality replacement requirements |