| | step type | requirements | statement |
| 0 | instantiation | 1, 2, 3 | , , , ⊢  |
| | : , : , :  |
| 1 | reference | 4 | ⊢  |
| 2 | instantiation | 4, 5, 6 | , , , ⊢  |
| | : , : , :  |
| 3 | instantiation | 10, 7, 76, 8, 14, 16, 17, 18, 9, 20, 21 | , , , ⊢  |
| | : , : , : , : , : , : , :  |
| 4 | axiom | | ⊢  |
| | proveit.logic.equality.equals_transitivity |
| 5 | instantiation | 10, 79, 11, 12, 17, 18, 49, 20, 19, 21 | , , , ⊢  |
| | : , : , : , : , : , : , :  |
| 6 | instantiation | 13, 76, 14, 15, 16, 17, 18, 49, 19, 20, 21, 22* | , , , ⊢  |
| | : , : , : , : , : , :  |
| 7 | axiom | | ⊢  |
| | proveit.numbers.number_sets.natural_numbers.zero_in_nats |
| 8 | theorem | | ⊢  |
| | proveit.core_expr_types.tuples.tuple_len_0_typical_eq |
| 9 | instantiation | 29, 23, 51, 30 | ⊢  |
| | : , :  |
| 10 | theorem | | ⊢  |
| | proveit.numbers.multiplication.leftward_commutation |
| 11 | theorem | | ⊢  |
| | proveit.numbers.numerals.decimals.nat1 |
| 12 | instantiation | 24 | ⊢  |
| | : , : , :  |
| 13 | theorem | | ⊢  |
| | proveit.numbers.multiplication.association |
| 14 | instantiation | 25 | ⊢  |
| | : , :  |
| 15 | instantiation | 25 | ⊢  |
| | : , :  |
| 16 | instantiation | 25 | ⊢  |
| | : , :  |
| 17 | instantiation | 77, 60, 26 | ⊢  |
| | : , : , :  |
| 18 | instantiation | 27, 28 | ⊢  |
| | :  |
| 19 | instantiation | 29, 49, 51, 30 | ⊢  |
| | : , :  |
| 20 | instantiation | 31, 32, 49 | ⊢  |
| | : , :  |
| 21 | instantiation | 77, 60, 33 | ⊢  |
| | : , : , :  |
| 22 | instantiation | 34, 49, 35, 36, 37*, 38*, 39* | ⊢  |
| | : , : , : , :  |
| 23 | instantiation | 77, 60, 40 | ⊢  |
| | : , : , :  |
| 24 | theorem | | ⊢  |
| | proveit.numbers.numerals.decimals.tuple_len_3_typical_eq |
| 25 | theorem | | ⊢  |
| | proveit.numbers.numerals.decimals.tuple_len_2_typical_eq |
| 26 | instantiation | 77, 54, 41 | ⊢  |
| | : , : , :  |
| 27 | theorem | | ⊢  |
| | proveit.numbers.exponentiation.sqrt_complex_closure |
| 28 | instantiation | 77, 60, 42 | ⊢  |
| | : , : , :  |
| 29 | theorem | | ⊢  |
| | proveit.numbers.division.div_complex_closure |
| 30 | instantiation | 43, 72 | ⊢  |
| | :  |
| 31 | theorem | | ⊢  |
| | proveit.numbers.exponentiation.exp_complex_closure |
| 32 | instantiation | 77, 60, 44 | ⊢  |
| | : , : , :  |
| 33 | assumption | | ⊢  |
| 34 | theorem | | ⊢  |
| | proveit.numbers.division.prod_of_fracs |
| 35 | instantiation | 77, 46, 45 | ⊢  |
| | : , : , :  |
| 36 | instantiation | 77, 46, 47 | ⊢  |
| | : , : , :  |
| 37 | instantiation | 48, 49 | ⊢  |
| | :  |
| 38 | theorem | | ⊢  |
| | proveit.numbers.numerals.decimals.mult_2_2 |
| 39 | instantiation | 50, 51 | ⊢  |
| | :  |
| 40 | instantiation | 77, 67, 52 | ⊢  |
| | : , : , :  |
| 41 | assumption | | ⊢  |
| 42 | instantiation | 77, 54, 53 | ⊢  |
| | : , : , :  |
| 43 | theorem | | ⊢  |
| | proveit.numbers.number_sets.natural_numbers.nonzero_if_is_nat_pos |
| 44 | instantiation | 77, 54, 55 | ⊢  |
| | : , : , :  |
| 45 | instantiation | 77, 57, 56 | ⊢  |
| | : , : , :  |
| 46 | theorem | | ⊢  |
| | proveit.numbers.number_sets.complex_numbers.real_nonzero_within_complex_nonzero |
| 47 | instantiation | 77, 57, 58 | ⊢  |
| | : , : , :  |
| 48 | theorem | | ⊢  |
| | proveit.numbers.division.frac_one_denom |
| 49 | instantiation | 77, 60, 59 | ⊢  |
| | : , : , :  |
| 50 | theorem | | ⊢  |
| | proveit.numbers.multiplication.elim_one_left |
| 51 | instantiation | 77, 60, 61 | ⊢  |
| | : , : , :  |
| 52 | instantiation | 77, 74, 62 | ⊢  |
| | : , : , :  |
| 53 | assumption | | ⊢  |
| 54 | theorem | | ⊢  |
| | proveit.numbers.number_sets.real_numbers.real_neg_within_real |
| 55 | assumption | | ⊢  |
| 56 | instantiation | 77, 64, 63 | ⊢  |
| | : , : , :  |
| 57 | theorem | | ⊢  |
| | proveit.numbers.number_sets.real_numbers.rational_nonzero_within_real_nonzero |
| 58 | instantiation | 77, 64, 65 | ⊢  |
| | : , : , :  |
| 59 | instantiation | 77, 67, 66 | ⊢  |
| | : , : , :  |
| 60 | theorem | | ⊢  |
| | proveit.numbers.number_sets.complex_numbers.real_within_complex |
| 61 | instantiation | 77, 67, 68 | ⊢  |
| | : , : , :  |
| 62 | instantiation | 77, 78, 69 | ⊢  |
| | : , : , :  |
| 63 | instantiation | 77, 71, 70 | ⊢  |
| | : , : , :  |
| 64 | theorem | | ⊢  |
| | proveit.numbers.number_sets.rational_numbers.nonzero_int_within_rational_nonzero |
| 65 | instantiation | 77, 71, 72 | ⊢  |
| | : , : , :  |
| 66 | instantiation | 77, 74, 73 | ⊢  |
| | : , : , :  |
| 67 | theorem | | ⊢  |
| | proveit.numbers.number_sets.real_numbers.rational_within_real |
| 68 | instantiation | 77, 74, 75 | ⊢  |
| | : , : , :  |
| 69 | theorem | | ⊢  |
| | proveit.numbers.numerals.decimals.nat4 |
| 70 | theorem | | ⊢  |
| | proveit.numbers.numerals.decimals.posnat1 |
| 71 | theorem | | ⊢  |
| | proveit.numbers.number_sets.integers.nat_pos_within_nonzero_int |
| 72 | theorem | | ⊢  |
| | proveit.numbers.numerals.decimals.posnat3 |
| 73 | instantiation | 77, 78, 76 | ⊢  |
| | : , : , :  |
| 74 | theorem | | ⊢  |
| | proveit.numbers.number_sets.rational_numbers.int_within_rational |
| 75 | instantiation | 77, 78, 79 | ⊢  |
| | : , : , :  |
| 76 | theorem | | ⊢  |
| | proveit.numbers.numerals.decimals.nat2 |
| 77 | theorem | | ⊢  |
| | proveit.logic.sets.inclusion.superset_membership_from_proper_subset |
| 78 | theorem | | ⊢  |
| | proveit.numbers.number_sets.integers.nat_within_int |
| 79 | theorem | | ⊢  |
| | proveit.numbers.numerals.decimals.nat3 |
| *equality replacement requirements |