| | step type | requirements | statement |
| 0 | instantiation | 1, 2, 3, 4 | ⊢  |
| | : , : , : , :  |
| 1 | reference | 5 | ⊢  |
| 2 | instantiation | 5, 6, 7, 8 | ⊢  |
| | : , : , : , :  |
| 3 | instantiation | 21, 97, 16, 10, 23, 17, 24, 11, 50, 38, 9* | ⊢  |
| | : , : , : , : , : , :  |
| 4 | instantiation | 34, 16, 97, 17, 10, 24, 11, 12 | ⊢  |
| | : , : , : , : , : , : , :  |
| 5 | theorem | | ⊢  |
| | proveit.logic.equality.four_chain_transitivity |
| 6 | instantiation | 13, 14, 15 | ⊢  |
| | : , : , :  |
| 7 | instantiation | 21, 16, 97, 99, 17, 18, 19, 57, 36, 37, 62, 50, 38, 20* | ⊢  |
| | : , : , : , : , : , :  |
| 8 | instantiation | 21, 100, 97, 22, 23, 24, 37, 62, 50, 38, 25* | ⊢  |
| | : , : , : , : , : , :  |
| 9 | instantiation | 26, 50, 59, 27, 28, 29*, 30*, 31* | ⊢  |
| | : , : , : , :  |
| 10 | instantiation | 41 | ⊢  |
| | : , :  |
| 11 | instantiation | 53, 62, 32 | ⊢  |
| | : , :  |
| 12 | instantiation | 54, 50, 55, 56 | ⊢  |
| | : , :  |
| 13 | axiom | | ⊢  |
| | proveit.logic.equality.equals_transitivity |
| 14 | instantiation | 34, 100, 103, 33, 57, 37, 36, 50, 62, 38 | ⊢  |
| | : , : , : , : , : , : , :  |
| 15 | instantiation | 34, 103, 100, 35, 57, 36, 37, 50, 62, 38 | ⊢  |
| | : , : , : , : , : , : , :  |
| 16 | axiom | | ⊢  |
| | proveit.numbers.number_sets.natural_numbers.zero_in_nats |
| 17 | theorem | | ⊢  |
| | proveit.core_expr_types.tuples.tuple_len_0_typical_eq |
| 18 | instantiation | 41 | ⊢  |
| | : , :  |
| 19 | instantiation | 39 | ⊢  |
| | : , : , : , :  |
| 20 | instantiation | 43, 57, 86, 83, 40* | ⊢  |
| | : , : , :  |
| 21 | theorem | | ⊢  |
| | proveit.numbers.multiplication.association |
| 22 | instantiation | 41 | ⊢  |
| | : , :  |
| 23 | instantiation | 41 | ⊢  |
| | : , :  |
| 24 | instantiation | 53, 57, 42 | ⊢  |
| | : , :  |
| 25 | instantiation | 43, 62, 83, 86, 44* | ⊢  |
| | : , : , :  |
| 26 | theorem | | ⊢  |
| | proveit.numbers.division.prod_of_fracs |
| 27 | instantiation | 101, 46, 45 | ⊢  |
| | : , : , :  |
| 28 | instantiation | 101, 46, 47 | ⊢  |
| | : , : , :  |
| 29 | instantiation | 48, 50 | ⊢  |
| | :  |
| 30 | instantiation | 49, 50 | ⊢  |
| | :  |
| 31 | instantiation | 51, 55 | ⊢  |
| | :  |
| 32 | instantiation | 58, 60, 59 | ⊢  |
| | : , :  |
| 33 | instantiation | 52 | ⊢  |
| | : , : , :  |
| 34 | theorem | | ⊢  |
| | proveit.numbers.multiplication.leftward_commutation |
| 35 | instantiation | 52 | ⊢  |
| | : , : , :  |
| 36 | instantiation | 53, 57, 60 | ⊢  |
| | : , :  |
| 37 | instantiation | 53, 62, 60 | ⊢  |
| | : , :  |
| 38 | instantiation | 54, 59, 55, 56 | ⊢  |
| | : , :  |
| 39 | theorem | | ⊢  |
| | proveit.numbers.numerals.decimals.tuple_len_4_typical_eq |
| 40 | instantiation | 61, 57 | ⊢  |
| | :  |
| 41 | theorem | | ⊢  |
| | proveit.numbers.numerals.decimals.tuple_len_2_typical_eq |
| 42 | instantiation | 58, 59, 60 | ⊢  |
| | : , :  |
| 43 | theorem | | ⊢  |
| | proveit.numbers.exponentiation.product_of_posnat_powers |
| 44 | instantiation | 61, 62 | ⊢  |
| | :  |
| 45 | instantiation | 101, 64, 63 | ⊢  |
| | : , : , :  |
| 46 | theorem | | ⊢  |
| | proveit.numbers.number_sets.complex_numbers.real_nonzero_within_complex_nonzero |
| 47 | instantiation | 101, 64, 65 | ⊢  |
| | : , : , :  |
| 48 | theorem | | ⊢  |
| | proveit.numbers.division.frac_one_denom |
| 49 | theorem | | ⊢  |
| | proveit.numbers.multiplication.elim_one_right |
| 50 | instantiation | 101, 72, 66 | ⊢  |
| | : , : , :  |
| 51 | theorem | | ⊢  |
| | proveit.numbers.multiplication.elim_one_left |
| 52 | theorem | | ⊢  |
| | proveit.numbers.numerals.decimals.tuple_len_3_typical_eq |
| 53 | theorem | | ⊢  |
| | proveit.numbers.exponentiation.exp_complex_closure |
| 54 | theorem | | ⊢  |
| | proveit.numbers.division.div_complex_closure |
| 55 | instantiation | 101, 72, 67 | ⊢  |
| | : , : , :  |
| 56 | instantiation | 68, 88 | ⊢  |
| | :  |
| 57 | instantiation | 101, 72, 69 | ⊢  |
| | : , : , :  |
| 58 | theorem | | ⊢  |
| | proveit.numbers.addition.add_complex_closure_bin |
| 59 | instantiation | 101, 72, 70 | ⊢  |
| | : , : , :  |
| 60 | instantiation | 101, 72, 71 | ⊢  |
| | : , : , :  |
| 61 | theorem | | ⊢  |
| | proveit.numbers.exponentiation.complex_x_to_first_power_is_x |
| 62 | instantiation | 101, 72, 73 | ⊢  |
| | : , : , :  |
| 63 | instantiation | 101, 75, 74 | ⊢  |
| | : , : , :  |
| 64 | theorem | | ⊢  |
| | proveit.numbers.number_sets.real_numbers.rational_nonzero_within_real_nonzero |
| 65 | instantiation | 101, 75, 76 | ⊢  |
| | : , : , :  |
| 66 | instantiation | 101, 84, 77 | ⊢  |
| | : , : , :  |
| 67 | instantiation | 101, 84, 78 | ⊢  |
| | : , : , :  |
| 68 | theorem | | ⊢  |
| | proveit.numbers.number_sets.natural_numbers.nonzero_if_is_nat_pos |
| 69 | instantiation | 101, 84, 79 | ⊢  |
| | : , : , :  |
| 70 | instantiation | 101, 84, 80 | ⊢  |
| | : , : , :  |
| 71 | instantiation | 81, 82, 83 | ⊢  |
| | : , : , :  |
| 72 | theorem | | ⊢  |
| | proveit.numbers.number_sets.complex_numbers.real_within_complex |
| 73 | instantiation | 101, 84, 85 | ⊢  |
| | : , : , :  |
| 74 | instantiation | 101, 87, 86 | ⊢  |
| | : , : , :  |
| 75 | theorem | | ⊢  |
| | proveit.numbers.number_sets.rational_numbers.nonzero_int_within_rational_nonzero |
| 76 | instantiation | 101, 87, 88 | ⊢  |
| | : , : , :  |
| 77 | instantiation | 101, 95, 89 | ⊢  |
| | : , : , :  |
| 78 | instantiation | 101, 95, 90 | ⊢  |
| | : , : , :  |
| 79 | instantiation | 101, 95, 91 | ⊢  |
| | : , : , :  |
| 80 | instantiation | 101, 95, 92 | ⊢  |
| | : , : , :  |
| 81 | theorem | | ⊢  |
| | proveit.logic.sets.inclusion.unfold_subset_eq |
| 82 | instantiation | 93, 94 | ⊢  |
| | : , :  |
| 83 | assumption | | ⊢  |
| 84 | theorem | | ⊢  |
| | proveit.numbers.number_sets.real_numbers.rational_within_real |
| 85 | instantiation | 101, 95, 96 | ⊢  |
| | : , : , :  |
| 86 | theorem | | ⊢  |
| | proveit.numbers.numerals.decimals.posnat1 |
| 87 | theorem | | ⊢  |
| | proveit.numbers.number_sets.integers.nat_pos_within_nonzero_int |
| 88 | theorem | | ⊢  |
| | proveit.numbers.numerals.decimals.posnat5 |
| 89 | instantiation | 101, 102, 97 | ⊢  |
| | : , : , :  |
| 90 | instantiation | 101, 102, 98 | ⊢  |
| | : , : , :  |
| 91 | instantiation | 101, 102, 99 | ⊢  |
| | : , : , :  |
| 92 | instantiation | 101, 102, 100 | ⊢  |
| | : , : , :  |
| 93 | theorem | | ⊢  |
| | proveit.logic.sets.inclusion.relax_proper_subset |
| 94 | theorem | | ⊢  |
| | proveit.numbers.number_sets.real_numbers.nat_pos_within_real |
| 95 | theorem | | ⊢  |
| | proveit.numbers.number_sets.rational_numbers.int_within_rational |
| 96 | instantiation | 101, 102, 103 | ⊢  |
| | : , : , :  |
| 97 | theorem | | ⊢  |
| | proveit.numbers.numerals.decimals.nat2 |
| 98 | theorem | | ⊢  |
| | proveit.numbers.numerals.decimals.nat5 |
| 99 | theorem | | ⊢  |
| | proveit.numbers.numerals.decimals.nat4 |
| 100 | theorem | | ⊢  |
| | proveit.numbers.numerals.decimals.nat1 |
| 101 | theorem | | ⊢  |
| | proveit.logic.sets.inclusion.superset_membership_from_proper_subset |
| 102 | theorem | | ⊢  |
| | proveit.numbers.number_sets.integers.nat_within_int |
| 103 | theorem | | ⊢  |
| | proveit.numbers.numerals.decimals.nat3 |
| *equality replacement requirements |