| | step type | requirements | statement |
| 0 | instantiation | 1, 2, 3 | , ⊢  |
| | : , : , :  |
| 1 | reference | 32 | ⊢  |
| 2 | instantiation | 4, 5 | , ⊢  |
| | : , : , :  |
| 3 | instantiation | 6, 7 | , ⊢  |
| | : , :  |
| 4 | axiom | | ⊢  |
| | proveit.logic.equality.substitution |
| 5 | instantiation | 32, 8, 9 | , ⊢  |
| | : , : , :  |
| 6 | theorem | | ⊢  |
| | proveit.logic.equality.equals_reversal |
| 7 | instantiation | 10, 11, 12, 13 | , ⊢  |
| | : , :  |
| 8 | instantiation | 14, 15, 38, 41, 16, 42, 49, 50, 45, 20, 46 | , ⊢  |
| | : , : , : , : , : , : , :  |
| 9 | instantiation | 17, 41, 18, 38, 42, 19, 49, 50, 45, 46, 20 | , ⊢  |
| | : , : , : , : , : , :  |
| 10 | instantiation | 21, 47 | ⊢  |
| | :  |
| 11 | instantiation | 64, 54, 22 | ⊢  |
| | : , : , :  |
| 12 | instantiation | 23, 24, 25 | ⊢  |
| | : , : , :  |
| 13 | instantiation | 26, 27 | ⊢  |
| | :  |
| 14 | theorem | | ⊢  |
| | proveit.numbers.multiplication.rightward_commutation |
| 15 | theorem | | ⊢  |
| | proveit.numbers.numerals.decimals.nat3 |
| 16 | instantiation | 28 | ⊢  |
| | : , : , :  |
| 17 | theorem | | ⊢  |
| | proveit.numbers.multiplication.association |
| 18 | theorem | | ⊢  |
| | proveit.numbers.numerals.decimals.nat4 |
| 19 | instantiation | 29 | ⊢  |
| | : , : , : , :  |
| 20 | instantiation | 64, 54, 30 | ⊢  |
| | : , : , :  |
| 21 | theorem | | ⊢  |
| | proveit.numbers.exponentiation.int_exp_of_exp |
| 22 | instantiation | 64, 59, 36 | ⊢  |
| | : , : , :  |
| 23 | theorem | | ⊢  |
| | proveit.logic.equality.sub_right_side_into |
| 24 | instantiation | 48, 39, 31 | ⊢  |
| | : , :  |
| 25 | instantiation | 32, 33, 34 | ⊢  |
| | : , : , :  |
| 26 | theorem | | ⊢  |
| | proveit.numbers.number_sets.real_numbers.nonzero_if_in_real_nonzero |
| 27 | instantiation | 64, 35, 36 | ⊢  |
| | : , : , :  |
| 28 | theorem | | ⊢  |
| | proveit.numbers.numerals.decimals.tuple_len_3_typical_eq |
| 29 | theorem | | ⊢  |
| | proveit.numbers.numerals.decimals.tuple_len_4_typical_eq |
| 30 | instantiation | 64, 57, 37 | ⊢  |
| | : , : , :  |
| 31 | instantiation | 48, 45, 46 | ⊢  |
| | : , :  |
| 32 | axiom | | ⊢  |
| | proveit.logic.equality.equals_transitivity |
| 33 | instantiation | 40, 38, 66, 41, 44, 42, 39, 45, 46 | ⊢  |
| | : , : , : , : , : , :  |
| 34 | instantiation | 40, 41, 66, 42, 43, 44, 49, 50, 45, 46 | ⊢  |
| | : , : , : , : , : , :  |
| 35 | theorem | | ⊢  |
| | proveit.numbers.number_sets.real_numbers.real_pos_within_real_nonzero |
| 36 | theorem | | ⊢  |
| | proveit.numbers.number_sets.real_numbers.e_is_real_pos |
| 37 | instantiation | 64, 62, 47 | ⊢  |
| | : , : , :  |
| 38 | theorem | | ⊢  |
| | proveit.numbers.numerals.decimals.nat1 |
| 39 | instantiation | 48, 49, 50 | ⊢  |
| | : , :  |
| 40 | theorem | | ⊢  |
| | proveit.numbers.multiplication.disassociation |
| 41 | axiom | | ⊢  |
| | proveit.numbers.number_sets.natural_numbers.zero_in_nats |
| 42 | theorem | | ⊢  |
| | proveit.core_expr_types.tuples.tuple_len_0_typical_eq |
| 43 | instantiation | 51 | ⊢  |
| | : , :  |
| 44 | instantiation | 51 | ⊢  |
| | : , :  |
| 45 | theorem | | ⊢  |
| | proveit.numbers.number_sets.complex_numbers.i_is_complex |
| 46 | instantiation | 64, 54, 52 | ⊢  |
| | : , : , :  |
| 47 | assumption | | ⊢  |
| 48 | theorem | | ⊢  |
| | proveit.numbers.multiplication.mult_complex_closure_bin |
| 49 | instantiation | 64, 54, 53 | ⊢  |
| | : , : , :  |
| 50 | instantiation | 64, 54, 55 | ⊢  |
| | : , : , :  |
| 51 | theorem | | ⊢  |
| | proveit.numbers.numerals.decimals.tuple_len_2_typical_eq |
| 52 | instantiation | 64, 57, 56 | ⊢  |
| | : , : , :  |
| 53 | instantiation | 64, 57, 58 | ⊢  |
| | : , : , :  |
| 54 | theorem | | ⊢  |
| | proveit.numbers.number_sets.complex_numbers.real_within_complex |
| 55 | instantiation | 64, 59, 60 | ⊢  |
| | : , : , :  |
| 56 | instantiation | 64, 62, 61 | ⊢  |
| | : , : , :  |
| 57 | theorem | | ⊢  |
| | proveit.numbers.number_sets.real_numbers.rational_within_real |
| 58 | instantiation | 64, 62, 63 | ⊢  |
| | : , : , :  |
| 59 | theorem | | ⊢  |
| | proveit.numbers.number_sets.real_numbers.real_pos_within_real |
| 60 | theorem | | ⊢  |
| | proveit.numbers.number_sets.real_numbers.pi_is_real_pos |
| 61 | assumption | | ⊢  |
| 62 | theorem | | ⊢  |
| | proveit.numbers.number_sets.rational_numbers.int_within_rational |
| 63 | instantiation | 64, 65, 66 | ⊢  |
| | : , : , :  |
| 64 | theorem | | ⊢  |
| | proveit.logic.sets.inclusion.superset_membership_from_proper_subset |
| 65 | theorem | | ⊢  |
| | proveit.numbers.number_sets.integers.nat_within_int |
| 66 | theorem | | ⊢  |
| | proveit.numbers.numerals.decimals.nat2 |