| | step type | requirements | statement |
| 0 | instantiation | 1, 2 | , , , ⊢  |
| | : , :  |
| 1 | theorem | | ⊢  |
| | proveit.logic.equality.equals_reversal |
| 2 | instantiation | 5, 3, 4 | , , , ⊢  |
| | : , : , :  |
| 3 | instantiation | 5, 6, 7 | , , , ⊢  |
| | : , : , :  |
| 4 | instantiation | 11, 8, 77, 9, 15, 17, 18, 19, 10, 21, 22 | , , , ⊢  |
| | : , : , : , : , : , : , :  |
| 5 | axiom | | ⊢  |
| | proveit.logic.equality.equals_transitivity |
| 6 | instantiation | 11, 80, 12, 13, 18, 19, 50, 21, 20, 22 | , , , ⊢  |
| | : , : , : , : , : , : , :  |
| 7 | instantiation | 14, 77, 15, 16, 17, 18, 19, 50, 20, 21, 22, 23* | , , , ⊢  |
| | : , : , : , : , : , :  |
| 8 | axiom | | ⊢  |
| | proveit.numbers.number_sets.natural_numbers.zero_in_nats |
| 9 | theorem | | ⊢  |
| | proveit.core_expr_types.tuples.tuple_len_0_typical_eq |
| 10 | instantiation | 30, 24, 52, 31 | ⊢  |
| | : , :  |
| 11 | theorem | | ⊢  |
| | proveit.numbers.multiplication.leftward_commutation |
| 12 | theorem | | ⊢  |
| | proveit.numbers.numerals.decimals.nat1 |
| 13 | instantiation | 25 | ⊢  |
| | : , : , :  |
| 14 | theorem | | ⊢  |
| | proveit.numbers.multiplication.association |
| 15 | instantiation | 26 | ⊢  |
| | : , :  |
| 16 | instantiation | 26 | ⊢  |
| | : , :  |
| 17 | instantiation | 26 | ⊢  |
| | : , :  |
| 18 | instantiation | 78, 61, 27 | ⊢  |
| | : , : , :  |
| 19 | instantiation | 28, 29 | ⊢  |
| | :  |
| 20 | instantiation | 30, 50, 52, 31 | ⊢  |
| | : , :  |
| 21 | instantiation | 32, 33, 50 | ⊢  |
| | : , :  |
| 22 | instantiation | 78, 61, 34 | ⊢  |
| | : , : , :  |
| 23 | instantiation | 35, 50, 36, 37, 38*, 39*, 40* | ⊢  |
| | : , : , : , :  |
| 24 | instantiation | 78, 61, 41 | ⊢  |
| | : , : , :  |
| 25 | theorem | | ⊢  |
| | proveit.numbers.numerals.decimals.tuple_len_3_typical_eq |
| 26 | theorem | | ⊢  |
| | proveit.numbers.numerals.decimals.tuple_len_2_typical_eq |
| 27 | instantiation | 78, 55, 42 | ⊢  |
| | : , : , :  |
| 28 | theorem | | ⊢  |
| | proveit.numbers.exponentiation.sqrt_complex_closure |
| 29 | instantiation | 78, 61, 43 | ⊢  |
| | : , : , :  |
| 30 | theorem | | ⊢  |
| | proveit.numbers.division.div_complex_closure |
| 31 | instantiation | 44, 73 | ⊢  |
| | :  |
| 32 | theorem | | ⊢  |
| | proveit.numbers.exponentiation.exp_complex_closure |
| 33 | instantiation | 78, 61, 45 | ⊢  |
| | : , : , :  |
| 34 | assumption | | ⊢  |
| 35 | theorem | | ⊢  |
| | proveit.numbers.division.prod_of_fracs |
| 36 | instantiation | 78, 47, 46 | ⊢  |
| | : , : , :  |
| 37 | instantiation | 78, 47, 48 | ⊢  |
| | : , : , :  |
| 38 | instantiation | 49, 50 | ⊢  |
| | :  |
| 39 | theorem | | ⊢  |
| | proveit.numbers.numerals.decimals.mult_2_2 |
| 40 | instantiation | 51, 52 | ⊢  |
| | :  |
| 41 | instantiation | 78, 68, 53 | ⊢  |
| | : , : , :  |
| 42 | assumption | | ⊢  |
| 43 | instantiation | 78, 55, 54 | ⊢  |
| | : , : , :  |
| 44 | theorem | | ⊢  |
| | proveit.numbers.number_sets.natural_numbers.nonzero_if_is_nat_pos |
| 45 | instantiation | 78, 55, 56 | ⊢  |
| | : , : , :  |
| 46 | instantiation | 78, 58, 57 | ⊢  |
| | : , : , :  |
| 47 | theorem | | ⊢  |
| | proveit.numbers.number_sets.complex_numbers.real_nonzero_within_complex_nonzero |
| 48 | instantiation | 78, 58, 59 | ⊢  |
| | : , : , :  |
| 49 | theorem | | ⊢  |
| | proveit.numbers.division.frac_one_denom |
| 50 | instantiation | 78, 61, 60 | ⊢  |
| | : , : , :  |
| 51 | theorem | | ⊢  |
| | proveit.numbers.multiplication.elim_one_left |
| 52 | instantiation | 78, 61, 62 | ⊢  |
| | : , : , :  |
| 53 | instantiation | 78, 75, 63 | ⊢  |
| | : , : , :  |
| 54 | assumption | | ⊢  |
| 55 | theorem | | ⊢  |
| | proveit.numbers.number_sets.real_numbers.real_neg_within_real |
| 56 | assumption | | ⊢  |
| 57 | instantiation | 78, 65, 64 | ⊢  |
| | : , : , :  |
| 58 | theorem | | ⊢  |
| | proveit.numbers.number_sets.real_numbers.rational_nonzero_within_real_nonzero |
| 59 | instantiation | 78, 65, 66 | ⊢  |
| | : , : , :  |
| 60 | instantiation | 78, 68, 67 | ⊢  |
| | : , : , :  |
| 61 | theorem | | ⊢  |
| | proveit.numbers.number_sets.complex_numbers.real_within_complex |
| 62 | instantiation | 78, 68, 69 | ⊢  |
| | : , : , :  |
| 63 | instantiation | 78, 79, 70 | ⊢  |
| | : , : , :  |
| 64 | instantiation | 78, 72, 71 | ⊢  |
| | : , : , :  |
| 65 | theorem | | ⊢  |
| | proveit.numbers.number_sets.rational_numbers.nonzero_int_within_rational_nonzero |
| 66 | instantiation | 78, 72, 73 | ⊢  |
| | : , : , :  |
| 67 | instantiation | 78, 75, 74 | ⊢  |
| | : , : , :  |
| 68 | theorem | | ⊢  |
| | proveit.numbers.number_sets.real_numbers.rational_within_real |
| 69 | instantiation | 78, 75, 76 | ⊢  |
| | : , : , :  |
| 70 | theorem | | ⊢  |
| | proveit.numbers.numerals.decimals.nat4 |
| 71 | theorem | | ⊢  |
| | proveit.numbers.numerals.decimals.posnat1 |
| 72 | theorem | | ⊢  |
| | proveit.numbers.number_sets.integers.nat_pos_within_nonzero_int |
| 73 | theorem | | ⊢  |
| | proveit.numbers.numerals.decimals.posnat3 |
| 74 | instantiation | 78, 79, 77 | ⊢  |
| | : , : , :  |
| 75 | theorem | | ⊢  |
| | proveit.numbers.number_sets.rational_numbers.int_within_rational |
| 76 | instantiation | 78, 79, 80 | ⊢  |
| | : , : , :  |
| 77 | theorem | | ⊢  |
| | proveit.numbers.numerals.decimals.nat2 |
| 78 | theorem | | ⊢  |
| | proveit.logic.sets.inclusion.superset_membership_from_proper_subset |
| 79 | theorem | | ⊢  |
| | proveit.numbers.number_sets.integers.nat_within_int |
| 80 | theorem | | ⊢  |
| | proveit.numbers.numerals.decimals.nat3 |
| *equality replacement requirements |