| | step type | requirements | statement |
| 0 | instantiation | 1, 2, 3 | , , , , , ⊢  |
| | : , : , :  |
| 1 | reference | 46 | ⊢  |
| 2 | instantiation | 4, 70, 14, 5, 6, 55, 29, 65, 30, 31, 32, 33, 37 | , , , , , ⊢  |
| | : , : , : , :  |
| 3 | instantiation | 10, 7, 8, 9 | , , , , , ⊢  |
| | : , : , : , :  |
| 4 | theorem | | ⊢  |
| | proveit.numbers.addition.elim_zero_any |
| 5 | instantiation | 34 | ⊢  |
| | : , : , :  |
| 6 | instantiation | 35 | ⊢  |
| | : , : , : , : , : , : , :  |
| 7 | instantiation | 10, 11, 12, 13 | , , , , , ⊢  |
| | : , : , : , :  |
| 8 | instantiation | 36, 51, 70, 14, 53, 15, 16, 55, 37, 29, 65, 30, 31, 32, 33, 17* | , , , , , ⊢  |
| | : , : , : , : , : , :  |
| 9 | instantiation | 36, 52, 26, 18, 19, 28, 20, 29, 65, 30, 31, 32, 33, 21* | , , , , , ⊢  |
| | : , : , : , : , : , :  |
| 10 | theorem | | ⊢  |
| | proveit.logic.equality.four_chain_transitivity |
| 11 | instantiation | 25, 75, 23, 52, 24, 22, 55, 29, 65, 30, 31, 32, 33, 37 | , , , , , ⊢  |
| | : , : , : , : , : , : , :  |
| 12 | instantiation | 25, 52, 23, 75, 54, 24, 55, 29, 65, 30, 31, 32, 33, 37 | , , , , , ⊢  |
| | : , : , : , : , : , : , :  |
| 13 | instantiation | 25, 67, 26, 51, 27, 28, 53, 55, 37, 29, 65, 30, 31, 32, 33 | , , , , , ⊢  |
| | : , : , : , : , : , : , :  |
| 14 | theorem | | ⊢  |
| | proveit.numbers.numerals.decimals.nat7 |
| 15 | instantiation | 34 | ⊢  |
| | : , : , :  |
| 16 | instantiation | 35 | ⊢  |
| | : , : , : , : , : , : , :  |
| 17 | instantiation | 36, 51, 52, 75, 53, 54, 55, 37, 38* | ⊢  |
| | : , : , : , : , : , :  |
| 18 | instantiation | 61 | ⊢  |
| | : , :  |
| 19 | instantiation | 61 | ⊢  |
| | : , :  |
| 20 | instantiation | 73, 62, 39 | ⊢  |
| | : , : , :  |
| 21 | instantiation | 40, 41, 59* | ⊢  |
| | : , :  |
| 22 | instantiation | 61 | ⊢  |
| | : , :  |
| 23 | theorem | | ⊢  |
| | proveit.numbers.numerals.decimals.nat6 |
| 24 | instantiation | 42 | ⊢  |
| | : , : , : , : , : , :  |
| 25 | theorem | | ⊢  |
| | proveit.numbers.addition.leftward_commutation |
| 26 | theorem | | ⊢  |
| | proveit.numbers.numerals.decimals.nat4 |
| 27 | instantiation | 43 | ⊢  |
| | : , : , : , : , :  |
| 28 | instantiation | 44 | ⊢  |
| | : , : , : , :  |
| 29 | assumption | | ⊢  |
| 30 | assumption | | ⊢  |
| 31 | assumption | | ⊢  |
| 32 | assumption | | ⊢  |
| 33 | assumption | | ⊢  |
| 34 | theorem | | ⊢  |
| | proveit.numbers.numerals.decimals.tuple_len_3_typical_eq |
| 35 | theorem | | ⊢  |
| | proveit.numbers.numerals.decimals.tuple_len_7_typical_eq |
| 36 | theorem | | ⊢  |
| | proveit.numbers.addition.association |
| 37 | instantiation | 73, 62, 45 | ⊢  |
| | : , : , :  |
| 38 | instantiation | 46, 47, 48 | ⊢  |
| | : , : , :  |
| 39 | instantiation | 73, 68, 49 | ⊢  |
| | : , : , :  |
| 40 | theorem | | ⊢  |
| | proveit.logic.equality.equals_reversal |
| 41 | instantiation | 50, 51, 52, 75, 53, 54, 55, 65, 56* | ⊢  |
| | : , : , : , : , : , :  |
| 42 | theorem | | ⊢  |
| | proveit.numbers.numerals.decimals.tuple_len_6_typical_eq |
| 43 | theorem | | ⊢  |
| | proveit.numbers.numerals.decimals.tuple_len_5_typical_eq |
| 44 | theorem | | ⊢  |
| | proveit.numbers.numerals.decimals.tuple_len_4_typical_eq |
| 45 | instantiation | 73, 68, 57 | ⊢  |
| | : , : , :  |
| 46 | axiom | | ⊢  |
| | proveit.logic.equality.equals_transitivity |
| 47 | instantiation | 58, 59 | ⊢  |
| | : , : , :  |
| 48 | theorem | | ⊢  |
| | proveit.numbers.numerals.decimals.add_2_3 |
| 49 | instantiation | 73, 71, 60 | ⊢  |
| | : , : , :  |
| 50 | theorem | | ⊢  |
| | proveit.numbers.multiplication.distribute_through_sum |
| 51 | axiom | | ⊢  |
| | proveit.numbers.number_sets.natural_numbers.zero_in_nats |
| 52 | theorem | | ⊢  |
| | proveit.numbers.numerals.decimals.nat2 |
| 53 | theorem | | ⊢  |
| | proveit.core_expr_types.tuples.tuple_len_0_typical_eq |
| 54 | instantiation | 61 | ⊢  |
| | : , :  |
| 55 | instantiation | 73, 62, 63 | ⊢  |
| | : , : , :  |
| 56 | instantiation | 64, 65 | ⊢  |
| | :  |
| 57 | instantiation | 73, 71, 66 | ⊢  |
| | : , : , :  |
| 58 | axiom | | ⊢  |
| | proveit.logic.equality.substitution |
| 59 | theorem | | ⊢  |
| | proveit.numbers.numerals.decimals.add_1_1 |
| 60 | instantiation | 73, 74, 67 | ⊢  |
| | : , : , :  |
| 61 | theorem | | ⊢  |
| | proveit.numbers.numerals.decimals.tuple_len_2_typical_eq |
| 62 | theorem | | ⊢  |
| | proveit.numbers.number_sets.complex_numbers.real_within_complex |
| 63 | instantiation | 73, 68, 69 | ⊢  |
| | : , : , :  |
| 64 | theorem | | ⊢  |
| | proveit.numbers.multiplication.elim_one_left |
| 65 | assumption | | ⊢  |
| 66 | instantiation | 73, 74, 70 | ⊢  |
| | : , : , :  |
| 67 | theorem | | ⊢  |
| | proveit.numbers.numerals.decimals.nat5 |
| 68 | theorem | | ⊢  |
| | proveit.numbers.number_sets.real_numbers.rational_within_real |
| 69 | instantiation | 73, 71, 72 | ⊢  |
| | : , : , :  |
| 70 | theorem | | ⊢  |
| | proveit.numbers.numerals.decimals.nat3 |
| 71 | theorem | | ⊢  |
| | proveit.numbers.number_sets.rational_numbers.int_within_rational |
| 72 | instantiation | 73, 74, 75 | ⊢  |
| | : , : , :  |
| 73 | theorem | | ⊢  |
| | proveit.logic.sets.inclusion.superset_membership_from_proper_subset |
| 74 | theorem | | ⊢  |
| | proveit.numbers.number_sets.integers.nat_within_int |
| 75 | theorem | | ⊢  |
| | proveit.numbers.numerals.decimals.nat1 |
| *equality replacement requirements |