| | step type | requirements | statement |
| 0 | instantiation | 1, 2 | , , ⊢  |
| | : , :  |
| 1 | theorem | | ⊢  |
| | proveit.logic.equality.equals_reversal |
| 2 | instantiation | 3, 4, 5, 6, 7, 8 | , , ⊢  |
| | : , : , :  |
| 3 | theorem | | ⊢  |
| | proveit.numbers.exponentiation.real_power_of_product |
| 4 | instantiation | 10, 20, 9 | ⊢  |
| | : , :  |
| 5 | instantiation | 10, 20, 15 | ⊢  |
| | : , :  |
| 6 | instantiation | 76, 69, 11 | ⊢  |
| | : , : , :  |
| 7 | instantiation | 12, 13, 14 | ⊢  |
| | : , : , :  |
| 8 | instantiation | 19, 20, 15, 22 | ⊢  |
| | : , :  |
| 9 | instantiation | 31, 16, 17 | ⊢  |
| | : , : , :  |
| 10 | theorem | | ⊢  |
| | proveit.numbers.exponentiation.exp_complex_closure |
| 11 | instantiation | 76, 74, 18 | ⊢  |
| | : , : , :  |
| 12 | theorem | | ⊢  |
| | proveit.logic.equality.sub_left_side_into |
| 13 | instantiation | 19, 20, 21, 22 | ⊢  |
| | : , :  |
| 14 | instantiation | 23, 24 | ⊢  |
| | : , : , :  |
| 15 | instantiation | 31, 25, 26 | ⊢  |
| | : , : , :  |
| 16 | instantiation | 59, 50, 27 | ⊢  |
| | : , :  |
| 17 | instantiation | 42, 28, 29 | ⊢  |
| | : , : , :  |
| 18 | assumption | | ⊢  |
| 19 | theorem | | ⊢  |
| | proveit.numbers.exponentiation.exp_not_eq_zero |
| 20 | instantiation | 76, 66, 30 | ⊢  |
| | : , : , :  |
| 21 | instantiation | 31, 32, 33 | ⊢  |
| | : , : , :  |
| 22 | instantiation | 34, 35 | ⊢  |
| | :  |
| 23 | axiom | | ⊢  |
| | proveit.logic.equality.substitution |
| 24 | instantiation | 36, 78, 49, 52, 54, 53, 60, 61, 57, 56 | ⊢  |
| | : , : , : , : , : , : , :  |
| 25 | instantiation | 59, 50, 37 | ⊢  |
| | : , :  |
| 26 | instantiation | 42, 38, 39 | ⊢  |
| | : , : , :  |
| 27 | instantiation | 59, 57, 56 | ⊢  |
| | : , :  |
| 28 | instantiation | 51, 49, 78, 52, 40, 53, 50, 57, 56 | ⊢  |
| | : , : , : , : , : , :  |
| 29 | instantiation | 51, 52, 78, 53, 54, 40, 60, 61, 57, 56 | ⊢  |
| | : , : , : , : , : , :  |
| 30 | instantiation | 76, 71, 46 | ⊢  |
| | : , : , :  |
| 31 | theorem | | ⊢  |
| | proveit.logic.equality.sub_right_side_into |
| 32 | instantiation | 59, 50, 41 | ⊢  |
| | : , :  |
| 33 | instantiation | 42, 43, 44 | ⊢  |
| | : , : , :  |
| 34 | theorem | | ⊢  |
| | proveit.numbers.number_sets.real_numbers.nonzero_if_in_real_nonzero |
| 35 | instantiation | 76, 45, 46 | ⊢  |
| | : , : , :  |
| 36 | theorem | | ⊢  |
| | proveit.numbers.multiplication.leftward_commutation |
| 37 | instantiation | 59, 57, 48 | ⊢  |
| | : , :  |
| 38 | instantiation | 51, 49, 78, 52, 47, 53, 50, 57, 48 | ⊢  |
| | : , : , : , : , : , :  |
| 39 | instantiation | 51, 52, 78, 53, 54, 47, 60, 61, 57, 48 | ⊢  |
| | : , : , : , : , : , :  |
| 40 | instantiation | 62 | ⊢  |
| | : , :  |
| 41 | instantiation | 59, 56, 57 | ⊢  |
| | : , :  |
| 42 | axiom | | ⊢  |
| | proveit.logic.equality.equals_transitivity |
| 43 | instantiation | 51, 49, 78, 52, 55, 53, 50, 56, 57 | ⊢  |
| | : , : , : , : , : , :  |
| 44 | instantiation | 51, 52, 78, 53, 54, 55, 60, 61, 56, 57 | ⊢  |
| | : , : , : , : , : , :  |
| 45 | theorem | | ⊢  |
| | proveit.numbers.number_sets.real_numbers.real_pos_within_real_nonzero |
| 46 | theorem | | ⊢  |
| | proveit.numbers.number_sets.real_numbers.e_is_real_pos |
| 47 | instantiation | 62 | ⊢  |
| | : , :  |
| 48 | instantiation | 76, 66, 58 | ⊢  |
| | : , : , :  |
| 49 | theorem | | ⊢  |
| | proveit.numbers.numerals.decimals.nat1 |
| 50 | instantiation | 59, 60, 61 | ⊢  |
| | : , :  |
| 51 | theorem | | ⊢  |
| | proveit.numbers.multiplication.disassociation |
| 52 | axiom | | ⊢  |
| | proveit.numbers.number_sets.natural_numbers.zero_in_nats |
| 53 | theorem | | ⊢  |
| | proveit.core_expr_types.tuples.tuple_len_0_typical_eq |
| 54 | instantiation | 62 | ⊢  |
| | : , :  |
| 55 | instantiation | 62 | ⊢  |
| | : , :  |
| 56 | instantiation | 76, 66, 63 | ⊢  |
| | : , : , :  |
| 57 | theorem | | ⊢  |
| | proveit.numbers.number_sets.complex_numbers.i_is_complex |
| 58 | instantiation | 76, 71, 64 | ⊢  |
| | : , : , :  |
| 59 | theorem | | ⊢  |
| | proveit.numbers.multiplication.mult_complex_closure_bin |
| 60 | instantiation | 76, 66, 65 | ⊢  |
| | : , : , :  |
| 61 | instantiation | 76, 66, 67 | ⊢  |
| | : , : , :  |
| 62 | theorem | | ⊢  |
| | proveit.numbers.numerals.decimals.tuple_len_2_typical_eq |
| 63 | instantiation | 76, 69, 68 | ⊢  |
| | : , : , :  |
| 64 | assumption | | ⊢  |
| 65 | instantiation | 76, 69, 70 | ⊢  |
| | : , : , :  |
| 66 | theorem | | ⊢  |
| | proveit.numbers.number_sets.complex_numbers.real_within_complex |
| 67 | instantiation | 76, 71, 72 | ⊢  |
| | : , : , :  |
| 68 | instantiation | 76, 74, 73 | ⊢  |
| | : , : , :  |
| 69 | theorem | | ⊢  |
| | proveit.numbers.number_sets.real_numbers.rational_within_real |
| 70 | instantiation | 76, 74, 75 | ⊢  |
| | : , : , :  |
| 71 | theorem | | ⊢  |
| | proveit.numbers.number_sets.real_numbers.real_pos_within_real |
| 72 | theorem | | ⊢  |
| | proveit.numbers.number_sets.real_numbers.pi_is_real_pos |
| 73 | assumption | | ⊢  |
| 74 | theorem | | ⊢  |
| | proveit.numbers.number_sets.rational_numbers.int_within_rational |
| 75 | instantiation | 76, 77, 78 | ⊢  |
| | : , : , :  |
| 76 | theorem | | ⊢  |
| | proveit.logic.sets.inclusion.superset_membership_from_proper_subset |
| 77 | theorem | | ⊢  |
| | proveit.numbers.number_sets.integers.nat_within_int |
| 78 | theorem | | ⊢  |
| | proveit.numbers.numerals.decimals.nat2 |