| | step type | requirements | statement |
|---|
| 0 | instantiation | 1, 2, 3, 4* | ⊢  |
| |  :  ,  :  ,  :  |
| 1 | reference | 53 | ⊢  |
| 2 | instantiation | 53, 5, 6 | ⊢  |
| | :  , :  , :  |
| 3 | instantiation | 47, 109, 87, 36, 73, 38, 39, 71, 7*, 8* | ⊢  |
| |  :  ,  :  ,  : ,  :  ,  :  ,  :  |
| 4 | instantiation | 49, 9, 10 | ⊢  |
| | :  , :  ,  :  |
| 5 | instantiation | 27, 11 | ⊢  |
| | : , :  |
| 6 | instantiation | 47, 109, 87, 66, 36, 67, 74, 38, 39, 12* | ⊢  |
| | : , : , :  , :  , : , :  |
| 7 | instantiation | 49, 13, 14 | ⊢  |
| | :  , :  , :  |
| 8 | instantiation | 15, 109, 73, 71 | ⊢  |
| | : , : , : , : |
| 9 | instantiation | 35, 66, 87, 67, 16, 36, 19, 38, 39 | ⊢  |
| | : , : , : , : , :  , : |
| 10 | instantiation | 17, 109, 87, 18, 19, 38, 39, 20* | ⊢  |
| | : , : , : , :  , :  , :  |
| 11 | instantiation | 57, 74, 58, 21*, 60* | ⊢  |
| | :  ,  : ,  : |
| 12 | instantiation | 49, 22, 23 | ⊢  |
| | :  , :  , : |
| 13 | instantiation | 65, 109, 87, 62, 73, 71 | ⊢  |
| | : , : , : , : , :  , : |
| 14 | instantiation | 49, 24, 25 | ⊢  |
| | : , :  , : |
| 15 | theorem | | ⊢  |
| | proveit.numbers.multiplication.elim_one_any |
| 16 | instantiation | 75 | ⊢  |
| | : , :  |
| 17 | theorem | | ⊢  |
| | proveit.numbers.addition.association |
| 18 | instantiation | 75 | ⊢  |
| | : , : |
| 19 | instantiation | 107, 78, 26 | ⊢  |
| |  :  ,  :  , : |
| 20 | instantiation | 27, 28, 29* | ⊢  |
| | :  , :  |
| 21 | instantiation | 70, 74 | ⊢  |
| | : |
| 22 | instantiation | 30, 87, 31, 32, 33, 34 | ⊢  |
| | : ,  :  , :  , :  |
| 23 | instantiation | 35, 109, 87, 66, 36, 67, 37, 38, 39 | ⊢  |
| | : , : , : , :  , : , : |
| 24 | instantiation | 41, 66, 87, 67, 48, 42, 73, 71, 40* | ⊢  |
| | : , : , : , : , :  , :  |
| 25 | instantiation | 41, 109, 87, 66, 42, 67, 43, 71, 44* | ⊢  |
| | : , : , : , :  , : , : |
| 26 | instantiation | 45, 56, 46 | ⊢  |
| | :  , :  |
| 27 | theorem | | ⊢  |
| | proveit.logic.equality.equals_reversal |
| 28 | instantiation | 47, 66, 87, 109, 67, 48, 73, 71 | ⊢  |
| | : , : , : , : , : , : |
| 29 | theorem | | ⊢  |
| | proveit.numbers.numerals.decimals.add_2_2 |
| 30 | axiom | | ⊢  |
| | proveit.core_expr_types.operations.operands_substitution |
| 31 | instantiation | 75 | ⊢  |
| | :  , :  |
| 32 | instantiation | 75 | ⊢  |
| | : , : |
| 33 | instantiation | 49, 50, 51 | ⊢  |
| | : , :  , : |
| 34 | instantiation | 52, 74 | ⊢  |
| | : |
| 35 | theorem | | ⊢  |
| | proveit.numbers.addition.disassociation |
| 36 | instantiation | 75 | ⊢  |
| | : , : |
| 37 | instantiation | 53, 54, 55 | ⊢  |
| | :  , :  , : |
| 38 | instantiation | 107, 78, 83 | ⊢  |
| | : , : , : |
| 39 | instantiation | 107, 78, 101 | ⊢  |
| | : , : , : |
| 40 | theorem | | ⊢  |
| | proveit.numbers.numerals.decimals.mult_2_2 |
| 41 | theorem | | ⊢  |
| | proveit.numbers.multiplication.association |
| 42 | instantiation | 75 | ⊢  |
| | :  , : |
| 43 | instantiation | 107, 78, 56 | ⊢  |
| | : , : , : |
| 44 | instantiation | 57, 71, 58, 59*, 60* | ⊢  |
| | : , : , : |
| 45 | theorem | | ⊢  |
| | proveit.numbers.multiplication.mult_real_closure_bin |
| 46 | instantiation | 61, 94, 87 | ⊢  |
| | : , : |
| 47 | theorem | | ⊢  |
| | proveit.numbers.multiplication.distribute_through_sum |
| 48 | instantiation | 75 | ⊢  |
| | : , : |
| 49 | axiom | | ⊢  |
| | proveit.logic.equality.equals_transitivity |
| 50 | instantiation | 65, 109, 87, 66, 62, 67, 74, 73, 71 | ⊢  |
| | : , : , : , : , : , : |
| 51 | instantiation | 63, 66, 109, 67, 74, 73, 71 | ⊢  |
| | : , : , : , : , : , : ,  : |
| 52 | theorem | | ⊢  |
| | proveit.numbers.multiplication.elim_one_right |
| 53 | theorem | | ⊢ |
| | proveit.logic.equality.sub_right_side_into |
| 54 | instantiation | 72, 64, 71 | ⊢  |
| | :  , : |
| 55 | instantiation | 65, 66, 87, 109, 67, 68, 73, 74, 71 | ⊢  |
| | : , : , : , : , :  , : |
| 56 | instantiation | 107, 103, 69 | ⊢  |
| | :  , : , : |
| 57 | theorem | | ⊢  |
| | proveit.numbers.exponentiation.product_of_posnat_powers |
| 58 | theorem | | ⊢  |
| | proveit.numbers.numerals.decimals.posnat1 |
| 59 | instantiation | 70, 71 | ⊢  |
| | : |
| 60 | theorem | | ⊢  |
| | proveit.numbers.numerals.decimals.add_1_1 |
| 61 | theorem | | ⊢  |
| | proveit.numbers.exponentiation.exp_real_closure_nat_power |
| 62 | instantiation | 75 | ⊢  |
| | : , : |
| 63 | theorem | | ⊢  |
| | proveit.numbers.multiplication.leftward_commutation |
| 64 | instantiation | 72, 73, 74 | ⊢  |
| | : , : |
| 65 | theorem | | ⊢  |
| | proveit.numbers.multiplication.disassociation |
| 66 | axiom | | ⊢  |
| | proveit.numbers.number_sets.natural_numbers.zero_in_nats |
| 67 | theorem | | ⊢  |
| | proveit.core_expr_types.tuples.tuple_len_0_typical_eq |
| 68 | instantiation | 75 | ⊢  |
| | : , : |
| 69 | instantiation | 107, 105, 76 | ⊢  |
| | :  , : , : |
| 70 | theorem | | ⊢  |
| | proveit.numbers.exponentiation.complex_x_to_first_power_is_x |
| 71 | instantiation | 107, 78, 94 | ⊢  |
| | : , : , : |
| 72 | theorem | | ⊢  |
| | proveit.numbers.multiplication.mult_complex_closure_bin |
| 73 | instantiation | 107, 78, 77 | ⊢  |
| | : , : , : |
| 74 | instantiation | 107, 78, 79 | ⊢  |
| | : , : , : |
| 75 | theorem | | ⊢  |
| | proveit.numbers.numerals.decimals.tuple_len_2_typical_eq |
| 76 | instantiation | 107, 108, 80 | ⊢  |
| | :  , : , : |
| 77 | instantiation | 107, 103, 81 | ⊢  |
| | : , : , : |
| 78 | theorem | | ⊢  |
| | proveit.numbers.number_sets.complex_numbers.real_within_complex |
| 79 | instantiation | 82, 83, 101 | ⊢  |
| | : , : |
| 80 | theorem | | ⊢  |
| | proveit.numbers.numerals.decimals.nat4 |
| 81 | instantiation | 107, 105, 84 | ⊢  |
| | : , : , : |
| 82 | theorem | | ⊢  |
| | proveit.numbers.addition.add_real_closure_bin |
| 83 | instantiation | 107, 85, 86 | ⊢  |
| | :  , : , : |
| 84 | instantiation | 107, 108, 87 | ⊢  |
| | : , : , : |
| 85 | theorem | | ⊢  |
| | proveit.numbers.number_sets.real_numbers.real_pos_within_real |
| 86 | instantiation | 88, 89, 90 | ⊢  |
| | : , : |
| 87 | theorem | | ⊢  |
| | proveit.numbers.numerals.decimals.nat2 |
| 88 | theorem | | ⊢  |
| | proveit.numbers.multiplication.mult_real_pos_closure_bin |
| 89 | instantiation | 107, 91, 92 | ⊢  |
| | :  , : , : |
| 90 | instantiation | 93, 94, 95 | ⊢  |
| | : |
| 91 | theorem | | ⊢  |
| | proveit.numbers.number_sets.real_numbers.rational_pos_within_real_pos |
| 92 | instantiation | 107, 96, 97 | ⊢  |
| | :  , : , : |
| 93 | theorem | | ⊢  |
| | proveit.numbers.number_sets.real_numbers.pos_real_is_real_pos |
| 94 | instantiation | 98, 100, 101, 102 | ⊢  |
| | : , : , : |
| 95 | instantiation | 99, 100, 101, 102 | ⊢  |
| | : , : , : |
| 96 | theorem | | ⊢  |
| | proveit.numbers.number_sets.rational_numbers.nat_pos_within_rational_pos |
| 97 | theorem | | ⊢  |
| | proveit.numbers.numerals.decimals.posnat2 |
| 98 | theorem | | ⊢  |
| | proveit.numbers.number_sets.real_numbers.all_in_interval_oc__is__real |
| 99 | theorem | | ⊢  |
| | proveit.numbers.number_sets.real_numbers.interval_oc_lower_bound |
| 100 | theorem | | ⊢  |
| | proveit.numbers.number_sets.real_numbers.zero_is_real |
| 101 | instantiation | 107, 103, 104 | ⊢  |
| | : , : , : |
| 102 | axiom | | ⊢  |
| | proveit.physics.quantum.QPE._eps_in_interval |
| 103 | theorem | | ⊢  |
| | proveit.numbers.number_sets.real_numbers.rational_within_real |
| 104 | instantiation | 107, 105, 106 | ⊢  |
| | : , : , : |
| 105 | theorem | | ⊢  |
| | proveit.numbers.number_sets.rational_numbers.int_within_rational |
| 106 | instantiation | 107, 108, 109 | ⊢  |
| | : , : , : |
| 107 | theorem | | ⊢  |
| | proveit.logic.sets.inclusion.superset_membership_from_proper_subset |
| 108 | theorem | | ⊢  |
| | proveit.numbers.number_sets.integers.nat_within_int |
| 109 | theorem | | ⊢  |
| | proveit.numbers.numerals.decimals.nat1 |
| *equality replacement requirements |
