| | step type | requirements | statement |
| 0 | instantiation | 1, 2, 3, 4, 5, 6*, 7* | , ⊢  |
| | : , : , :  |
| 1 | theorem | | ⊢  |
| | proveit.numbers.addition.strong_bound_via_left_term_bound |
| 2 | instantiation | 120, 115, 8 | ⊢  |
| | : , : , :  |
| 3 | reference | 11 | ⊢  |
| 4 | instantiation | 9, 12, 13 | ⊢  |
| | : , :  |
| 5 | instantiation | 10, 11, 12, 13, 14, 15 | , ⊢  |
| | : , : , :  |
| 6 | instantiation | 16, 17 | ⊢  |
| | : , :  |
| 7 | instantiation | 75, 18, 19 | ⊢  |
| | : , : , :  |
| 8 | instantiation | 120, 118, 45 | ⊢  |
| | : , : , :  |
| 9 | theorem | | ⊢  |
| | proveit.numbers.addition.add_real_closure_bin |
| 10 | theorem | | ⊢  |
| | proveit.numbers.ordering.less_add_right |
| 11 | instantiation | 20, 61, 60 | ⊢  |
| | : , :  |
| 12 | instantiation | 20, 61, 23 | ⊢  |
| | : , :  |
| 13 | instantiation | 120, 115, 21 | ⊢  |
| | : , : , :  |
| 14 | instantiation | 22, 61, 60, 23, 24, 25 | , ⊢  |
| | : , : , :  |
| 15 | instantiation | 26, 27 | ⊢  |
| | : , :  |
| 16 | theorem | | ⊢  |
| | proveit.logic.equality.equals_reversal |
| 17 | instantiation | 48, 28 | ⊢  |
| | : , : , :  |
| 18 | instantiation | 48, 29 | ⊢  |
| | : , : , :  |
| 19 | theorem | | ⊢  |
| | proveit.numbers.numerals.decimals.add_2_3 |
| 20 | theorem | | ⊢  |
| | proveit.numbers.multiplication.mult_real_closure_bin |
| 21 | instantiation | 120, 85, 32 | ⊢  |
| | : , : , :  |
| 22 | theorem | | ⊢  |
| | proveit.numbers.multiplication.strong_bound_via_right_factor_bound |
| 23 | instantiation | 120, 115, 30 | ⊢  |
| | : , : , :  |
| 24 | assumption | | ⊢  |
| 25 | instantiation | 31, 86 | ⊢  |
| | :  |
| 26 | theorem | | ⊢  |
| | proveit.numbers.ordering.relax_less |
| 27 | instantiation | 31, 32 | ⊢  |
| | :  |
| 28 | instantiation | 33, 51, 102, 34, 35* | ⊢  |
| | : , :  |
| 29 | instantiation | 75, 36, 37 | ⊢  |
| | : , : , :  |
| 30 | instantiation | 120, 118, 44 | ⊢  |
| | : , : , :  |
| 31 | theorem | | ⊢  |
| | proveit.numbers.number_sets.rational_numbers.positive_if_in_rational_pos |
| 32 | instantiation | 97, 38, 99 | ⊢  |
| | : , :  |
| 33 | theorem | | ⊢  |
| | proveit.numbers.division.div_as_mult |
| 34 | instantiation | 39, 108 | ⊢  |
| | :  |
| 35 | instantiation | 75, 40, 41 | ⊢  |
| | : , : , :  |
| 36 | instantiation | 48, 42 | ⊢  |
| | : , : , :  |
| 37 | instantiation | 43, 44, 119, 45, 46* | ⊢  |
| | : , : , : , :  |
| 38 | instantiation | 120, 107, 47 | ⊢  |
| | : , : , :  |
| 39 | theorem | | ⊢  |
| | proveit.numbers.number_sets.natural_numbers.nonzero_if_is_nat_pos |
| 40 | instantiation | 48, 49 | ⊢  |
| | : , : , :  |
| 41 | instantiation | 50, 51, 52 | ⊢  |
| | : , :  |
| 42 | instantiation | 81, 52 | ⊢  |
| | :  |
| 43 | theorem | | ⊢  |
| | proveit.numbers.addition.rational_pair_addition |
| 44 | instantiation | 120, 121, 53 | ⊢  |
| | : , : , :  |
| 45 | instantiation | 120, 121, 54 | ⊢  |
| | : , : , :  |
| 46 | instantiation | 75, 55, 56 | ⊢  |
| | : , : , :  |
| 47 | theorem | | ⊢  |
| | proveit.numbers.numerals.decimals.posnat3 |
| 48 | axiom | | ⊢  |
| | proveit.logic.equality.substitution |
| 49 | instantiation | 57, 58, 113, 59* | ⊢  |
| | : , :  |
| 50 | theorem | | ⊢  |
| | proveit.numbers.multiplication.commutation |
| 51 | instantiation | 120, 109, 60 | ⊢  |
| | : , : , :  |
| 52 | instantiation | 120, 109, 61 | ⊢  |
| | : , : , :  |
| 53 | theorem | | ⊢  |
| | proveit.numbers.numerals.decimals.nat1 |
| 54 | theorem | | ⊢  |
| | proveit.numbers.numerals.decimals.nat3 |
| 55 | instantiation | 87, 122, 62, 63, 64, 65 | ⊢  |
| | : , : , : , :  |
| 56 | instantiation | 66, 67, 68, 102, 69*, 70*, 71* | ⊢  |
| | : , : , :  |
| 57 | theorem | | ⊢  |
| | proveit.numbers.exponentiation.neg_power_as_div |
| 58 | instantiation | 120, 79, 72 | ⊢  |
| | : , : , :  |
| 59 | instantiation | 73, 102 | ⊢  |
| | :  |
| 60 | assumption | | ⊢  |
| 61 | instantiation | 120, 115, 74 | ⊢  |
| | : , : , :  |
| 62 | instantiation | 100 | ⊢  |
| | : , :  |
| 63 | instantiation | 100 | ⊢  |
| | : , :  |
| 64 | instantiation | 75, 76, 77 | ⊢  |
| | : , : , :  |
| 65 | theorem | | ⊢  |
| | proveit.numbers.numerals.decimals.mult_2_2 |
| 66 | theorem | | ⊢  |
| | proveit.numbers.division.frac_cancel_left |
| 67 | instantiation | 120, 79, 78 | ⊢  |
| | : , : , :  |
| 68 | instantiation | 120, 79, 80 | ⊢  |
| | : , : , :  |
| 69 | theorem | | ⊢  |
| | proveit.numbers.numerals.decimals.mult_4_2 |
| 70 | instantiation | 81, 82 | ⊢  |
| | :  |
| 71 | instantiation | 83, 102 | ⊢  |
| | :  |
| 72 | instantiation | 120, 93, 84 | ⊢  |
| | : , : , :  |
| 73 | theorem | | ⊢  |
| | proveit.numbers.exponentiation.complex_x_to_first_power_is_x |
| 74 | instantiation | 120, 85, 86 | ⊢  |
| | : , : , :  |
| 75 | axiom | | ⊢  |
| | proveit.logic.equality.equals_transitivity |
| 76 | instantiation | 87, 122, 88, 89, 90, 91 | ⊢  |
| | : , : , : , :  |
| 77 | theorem | | ⊢  |
| | proveit.numbers.numerals.decimals.add_2_6 |
| 78 | instantiation | 120, 93, 92 | ⊢  |
| | : , : , :  |
| 79 | theorem | | ⊢  |
| | proveit.numbers.number_sets.complex_numbers.real_nonzero_within_complex_nonzero |
| 80 | instantiation | 120, 93, 94 | ⊢  |
| | : , : , :  |
| 81 | theorem | | ⊢  |
| | proveit.numbers.multiplication.elim_one_right |
| 82 | instantiation | 120, 109, 95 | ⊢  |
| | : , : , :  |
| 83 | theorem | | ⊢  |
| | proveit.numbers.division.frac_one_denom |
| 84 | instantiation | 120, 104, 96 | ⊢  |
| | : , : , :  |
| 85 | theorem | | ⊢  |
| | proveit.numbers.number_sets.rational_numbers.rational_pos_within_rational |
| 86 | instantiation | 97, 98, 99 | ⊢  |
| | : , :  |
| 87 | axiom | | ⊢  |
| | proveit.core_expr_types.operations.operands_substitution |
| 88 | instantiation | 100 | ⊢  |
| | : , :  |
| 89 | instantiation | 100 | ⊢  |
| | : , :  |
| 90 | instantiation | 101, 102 | ⊢  |
| | :  |
| 91 | theorem | | ⊢  |
| | proveit.numbers.numerals.decimals.mult_2_3 |
| 92 | instantiation | 120, 104, 103 | ⊢  |
| | : , : , :  |
| 93 | theorem | | ⊢  |
| | proveit.numbers.number_sets.real_numbers.rational_nonzero_within_real_nonzero |
| 94 | instantiation | 120, 104, 105 | ⊢  |
| | : , : , :  |
| 95 | instantiation | 120, 115, 106 | ⊢  |
| | : , : , :  |
| 96 | instantiation | 120, 112, 108 | ⊢  |
| | : , : , :  |
| 97 | theorem | | ⊢  |
| | proveit.numbers.division.div_rational_pos_closure |
| 98 | instantiation | 120, 107, 113 | ⊢  |
| | : , : , :  |
| 99 | instantiation | 120, 107, 108 | ⊢  |
| | : , : , :  |
| 100 | theorem | | ⊢  |
| | proveit.numbers.numerals.decimals.tuple_len_2_typical_eq |
| 101 | theorem | | ⊢  |
| | proveit.numbers.multiplication.elim_one_left |
| 102 | instantiation | 120, 109, 110 | ⊢  |
| | : , : , :  |
| 103 | instantiation | 120, 112, 111 | ⊢  |
| | : , : , :  |
| 104 | theorem | | ⊢  |
| | proveit.numbers.number_sets.rational_numbers.nonzero_int_within_rational_nonzero |
| 105 | instantiation | 120, 112, 113 | ⊢  |
| | : , : , :  |
| 106 | instantiation | 120, 118, 114 | ⊢  |
| | : , : , :  |
| 107 | theorem | | ⊢  |
| | proveit.numbers.number_sets.rational_numbers.nat_pos_within_rational_pos |
| 108 | theorem | | ⊢  |
| | proveit.numbers.numerals.decimals.posnat2 |
| 109 | theorem | | ⊢  |
| | proveit.numbers.number_sets.complex_numbers.real_within_complex |
| 110 | instantiation | 120, 115, 116 | ⊢  |
| | : , : , :  |
| 111 | theorem | | ⊢  |
| | proveit.numbers.numerals.decimals.posnat4 |
| 112 | theorem | | ⊢  |
| | proveit.numbers.number_sets.integers.nat_pos_within_nonzero_int |
| 113 | theorem | | ⊢  |
| | proveit.numbers.numerals.decimals.posnat1 |
| 114 | instantiation | 120, 121, 117 | ⊢  |
| | : , : , :  |
| 115 | theorem | | ⊢  |
| | proveit.numbers.number_sets.real_numbers.rational_within_real |
| 116 | instantiation | 120, 118, 119 | ⊢  |
| | : , : , :  |
| 117 | theorem | | ⊢  |
| | proveit.numbers.numerals.decimals.nat4 |
| 118 | theorem | | ⊢  |
| | proveit.numbers.number_sets.rational_numbers.int_within_rational |
| 119 | instantiation | 120, 121, 122 | ⊢  |
| | : , : , :  |
| 120 | theorem | | ⊢  |
| | proveit.logic.sets.inclusion.superset_membership_from_proper_subset |
| 121 | theorem | | ⊢  |
| | proveit.numbers.number_sets.integers.nat_within_int |
| 122 | theorem | | ⊢  |
| | proveit.numbers.numerals.decimals.nat2 |
| *equality replacement requirements |