| | step type | requirements | statement |
|---|
| 0 | instantiation | 1, 2, 3, 4, 5, 6, 7, 8, 9 | ⊢  |
| |  :  ,  :  ,  :  ,  :  |
| 1 | theorem | | ⊢  |
| | proveit.physics.quantum.circuits.qcircuit_eq |
| 2 | reference | 47 | ⊢  |
| 3 | reference | 68 | ⊢  |
| 4 | instantiation | 91, 10, 12, 13 | ⊢  |
| |  :  ,  :  ,  :  ,  :  |
| 5 | instantiation | 91, 11, 12, 13 | ⊢  |
| | :  , : , : , : |
| 6 | instantiation | 91, 14, 18, 19 | ⊢  |
| | :  , : , : , :  |
| 7 | instantiation | 91, 15, 18, 19 | ⊢  |
| | :  , : , : , : |
| 8 | instantiation | 91, 16, 18, 19 | ⊢  |
| | :  , : , : , : |
| 9 | instantiation | 91, 17, 18, 19 | ⊢  |
| | :  , : , : , : |
| 10 | instantiation | 35, 20, 21, 22, 56, 23, 40, 34, 24* | ⊢  |
| |  :  ,  :  ,  :  ,  :  |
| 11 | instantiation | 35, 25, 26, 27, 28, 40, 41, 34, 29* | ⊢  |
| | :  , :  , :  , :  |
| 12 | instantiation | 102, 30 | ⊢  |
| |  : ,  : |
| 13 | instantiation | 102, 31 | ⊢  |
| | : , : |
| 14 | instantiation | 52, 53 | ⊢  |
| | : ,  :  |
| 15 | instantiation | 35, 36, 32, 119, 109, 40, 34, 64*, 112* | ⊢  |
| | :  , :  , :  , :  |
| 16 | instantiation | 35, 36, 33, 119, 109, 40, 34, 64*, 112* | ⊢  |
| | : , :  , : , : |
| 17 | instantiation | 35, 36, 37, 38, 39, 40, 41, 64*, 65* | ⊢  |
| | : , :  , :  , :  |
| 18 | instantiation | 145 | ⊢  |
| | : |
| 19 | instantiation | 102, 42 | ⊢  |
| | : , : |
| 20 | theorem | | ⊢  |
| | proveit.numbers.numerals.decimals.posnat5 |
| 21 | instantiation | 69 | ⊢  |
| |  : ,  :  ,  :  ,  :  ,  :  |
| 22 | instantiation | 69 | ⊢  |
| | :  , : , : , : ,  : |
| 23 | instantiation | 50, 53, 57 | ⊢  |
| |  :  , :  , : |
| 24 | instantiation | 138, 43, 44 | ⊢  |
| | :  , :  ,  : |
| 25 | theorem | | ⊢  |
| | proveit.numbers.numerals.decimals.posnat6 |
| 26 | instantiation | 77 | ⊢  |
| | : , : , : , : , : , : |
| 27 | instantiation | 77 | ⊢  |
| | : , :  , : , : , : , : |
| 28 | instantiation | 77 | ⊢  |
| | :  , : , : , :  , : , : |
| 29 | instantiation | 138, 45, 59 | ⊢  |
| | :  , :  , : |
| 30 | instantiation | 115, 175, 125, 124, 109, 126, 101, 133, 137 | ⊢  |
| | : , : , :  , :  , : , :  |
| 31 | instantiation | 46, 47, 48, 53 | ⊢  |
| | : , :  , : |
| 32 | instantiation | 142 | ⊢  |
| | : , : |
| 33 | instantiation | 142 | ⊢  |
| | : , : |
| 34 | instantiation | 50, 51, 112 | ⊢  |
| | : , :  , : |
| 35 | theorem | | ⊢  |
| | proveit.core_expr_types.tuples.general_len |
| 36 | theorem | | ⊢  |
| | proveit.numbers.numerals.decimals.posnat2 |
| 37 | instantiation | 142 | ⊢  |
| | : , : |
| 38 | instantiation | 142 | ⊢  |
| | : , : |
| 39 | instantiation | 142 | ⊢  |
| | : , : |
| 40 | instantiation | 50, 49, 64 | ⊢  |
| | : , :  , : |
| 41 | instantiation | 50, 51, 65 | ⊢  |
| | : , :  , : |
| 42 | instantiation | 52, 53 | ⊢  |
| | : , :  |
| 43 | instantiation | 60, 54, 55, 56, 57, 64, 112 | ⊢  |
| | : ,  :  , :  , : |
| 44 | instantiation | 138, 58, 59 | ⊢  |
| | : , : , : |
| 45 | instantiation | 60, 61, 62, 63, 64, 65, 112 | ⊢  |
| | : ,  :  , :  , :  |
| 46 | theorem | | ⊢  |
| | proveit.core_expr_types.tuples.len_of_ranges_with_repeated_indices_from_1 |
| 47 | theorem | | ⊢ |
| | proveit.numbers.numerals.decimals.posnat3 |
| 48 | instantiation | 66, 157 | ⊢  |
| | : ,  :  |
| 49 | instantiation | 173, 67, 172 | ⊢  |
| | :  , :  , : |
| 50 | theorem | | ⊢  |
| | proveit.logic.equality.sub_left_side_into |
| 51 | instantiation | 173, 67, 160 | ⊢  |
| | : , : , : |
| 52 | theorem | | ⊢  |
| | proveit.core_expr_types.tuples.range_from1_len |
| 53 | instantiation | 173, 67, 68 | ⊢  |
| | : , : , : |
| 54 | theorem | | ⊢  |
| | proveit.numbers.numerals.decimals.nat5 |
| 55 | instantiation | 69 | ⊢  |
| | : , : , : , : , : |
| 56 | instantiation | 69 | ⊢  |
| | : , : , : , : , : |
| 57 | instantiation | 138, 70, 71 | ⊢  |
| | : , :  , : |
| 58 | instantiation | 108, 124, 125, 72, 126, 109, 73, 133, 137 | ⊢  |
| | : , : , :  , : , : , :  |
| 59 | instantiation | 91, 74, 75, 76 | ⊢  |
| | : , :  , :  , : |
| 60 | axiom | | ⊢  |
| | proveit.core_expr_types.operations.operands_substitution |
| 61 | theorem | | ⊢  |
| | proveit.numbers.numerals.decimals.nat6 |
| 62 | instantiation | 77 | ⊢  |
| | : , : , : , : , : , : |
| 63 | instantiation | 77 | ⊢  |
| | : , : , : , : , : , : |
| 64 | instantiation | 130, 131, 133, 132 | ⊢  |
| | : , : , : |
| 65 | instantiation | 138, 78, 79 | ⊢  |
| | : , :  , : |
| 66 | theorem | | ⊢  |
| | proveit.core_expr_types.tuples.range_from1_len_typical_eq |
| 67 | theorem | | ⊢  |
| | proveit.numbers.number_sets.natural_numbers.nat_pos_within_nat |
| 68 | instantiation | 80, 172, 160 | ⊢ |
| | : , : |
| 69 | theorem | | ⊢  |
| | proveit.numbers.numerals.decimals.tuple_len_5_typical_eq |
| 70 | instantiation | 108, 124, 125, 126, 109, 127, 133, 137, 128, 131 | ⊢  |
| | : , : , : , : , : , :  |
| 71 | instantiation | 81, 125, 124, 109, 126, 133, 137, 131 | ⊢  |
| | : , : , : , : , : , : , : , : |
| 72 | theorem | | ⊢  |
| | proveit.numbers.numerals.decimals.nat4 |
| 73 | instantiation | 82 | ⊢  |
| | : , : , : , : |
| 74 | instantiation | 138, 83, 84 | ⊢  |
| | : , :  , : |
| 75 | instantiation | 118, 124, 157, 126, 85, 87, 133, 137, 86* | ⊢  |
| | : , : , : , : , :  , :  |
| 76 | instantiation | 118, 175, 157, 124, 87, 126, 88, 137, 89* | ⊢  |
| | : , : , : , :  , : , : |
| 77 | theorem | | ⊢  |
| | proveit.numbers.numerals.decimals.tuple_len_6_typical_eq |
| 78 | instantiation | 150, 90 | ⊢  |
| | :  , :  , :  |
| 79 | instantiation | 91, 92, 93, 94 | ⊢  |
| | : , :  , :  , : |
| 80 | theorem | | ⊢  |
| | proveit.numbers.addition.add_nat_pos_closure_bin |
| 81 | theorem | | ⊢  |
| | proveit.numbers.addition.subtraction.add_cancel_general_rev |
| 82 | theorem | | ⊢  |
| | proveit.numbers.numerals.decimals.tuple_len_4_typical_eq |
| 83 | instantiation | 96, 175, 157, 95, 133, 137 | ⊢  |
| | : , : , : , :  , :  , : , :  |
| 84 | instantiation | 96, 125, 175, 97, 98, 133, 137 | ⊢  |
| | : , : , : , :  , :  , : , : |
| 85 | instantiation | 135 | ⊢  |
| | : , : , : |
| 86 | instantiation | 102, 99, 104* | ⊢  |
| | :  , :  |
| 87 | instantiation | 135 | ⊢  |
| | : , : , : |
| 88 | instantiation | 100, 101, 133 | ⊢  |
| | : , : |
| 89 | instantiation | 102, 103, 104* | ⊢  |
| | :  , :  |
| 90 | instantiation | 105, 133, 131 | ⊢  |
| | : , : |
| 91 | theorem | | ⊢  |
| | proveit.logic.equality.four_chain_transitivity |
| 92 | instantiation | 108, 124, 125, 126, 109, 106, 133, 137, 107, 131 | ⊢  |
| | : , : , : , : , : , :  |
| 93 | instantiation | 108, 125, 175, 109, 110, 133, 137, 122, 128, 131 | ⊢  |
| | : , : , : , : , :  , :  |
| 94 | instantiation | 138, 111, 112 | ⊢  |
| | : , : , : |
| 95 | instantiation | 135 | ⊢  |
| | : , : , : |
| 96 | theorem | | ⊢  |
| | proveit.numbers.addition.leftward_commutation |
| 97 | instantiation | 142 | ⊢  |
| | : , : |
| 98 | instantiation | 142 | ⊢  |
| | : , : |
| 99 | instantiation | 115, 124, 157, 175, 126, 116, 131, 133, 113* | ⊢  |
| | : , : , : , : , :  , : |
| 100 | theorem | | ⊢  |
| | proveit.numbers.multiplication.mult_complex_closure_bin |
| 101 | instantiation | 173, 148, 114 | ⊢  |
| | :  , :  , : |
| 102 | theorem | | ⊢  |
| | proveit.logic.equality.equals_reversal |
| 103 | instantiation | 115, 124, 157, 175, 126, 116, 131, 137, 117* | ⊢  |
| | : , : , : , : , : , : |
| 104 | instantiation | 118, 124, 125, 175, 126, 119, 131, 120* | ⊢  |
| | : , : , : , : , : , : |
| 105 | theorem | | ⊢  |
| | proveit.numbers.negation.distribute_neg_through_binary_sum |
| 106 | instantiation | 142 | ⊢  |
| | : , : |
| 107 | instantiation | 121, 122, 128 | ⊢  |
| | :  , :  |
| 108 | theorem | | ⊢  |
| | proveit.numbers.addition.disassociation |
| 109 | instantiation | 142 | ⊢  |
| | : , : |
| 110 | instantiation | 142 | ⊢  |
| | : , : |
| 111 | instantiation | 123, 124, 175, 125, 126, 127, 133, 137, 128, 131, 129 | ⊢  |
| | : , : , : , : , : , : , : , : |
| 112 | instantiation | 130, 131, 137, 132 | ⊢  |
| | : , : , : |
| 113 | instantiation | 136, 133 | ⊢  |
| | : |
| 114 | instantiation | 173, 155, 134 | ⊢  |
| | :  , : , : |
| 115 | theorem | | ⊢  |
| | proveit.numbers.multiplication.distribute_through_sum |
| 116 | instantiation | 135 | ⊢  |
| | : , : , : |
| 117 | instantiation | 136, 137 | ⊢  |
| | : |
| 118 | theorem | | ⊢  |
| | proveit.numbers.addition.association |
| 119 | instantiation | 142 | ⊢  |
| | : , : |
| 120 | instantiation | 138, 139, 140 | ⊢  |
| | :  , :  , : |
| 121 | theorem | | ⊢  |
| | proveit.numbers.addition.add_complex_closure_bin |
| 122 | instantiation | 173, 148, 141 | ⊢  |
| | : , : , : |
| 123 | theorem | | ⊢  |
| | proveit.numbers.addition.subtraction.add_cancel_general |
| 124 | axiom | | ⊢  |
| | proveit.numbers.number_sets.natural_numbers.zero_in_nats |
| 125 | theorem | | ⊢  |
| | proveit.numbers.numerals.decimals.nat2 |
| 126 | theorem | | ⊢  |
| | proveit.core_expr_types.tuples.tuple_len_0_typical_eq |
| 127 | instantiation | 142 | ⊢  |
| | : , : |
| 128 | instantiation | 173, 148, 143 | ⊢  |
| | : , : , : |
| 129 | instantiation | 145 | ⊢  |
| | : |
| 130 | theorem | | ⊢  |
| | proveit.numbers.addition.subtraction.add_cancel_triple_32 |
| 131 | instantiation | 173, 148, 144 | ⊢  |
| | : , : , : |
| 132 | instantiation | 145 | ⊢  |
| | : |
| 133 | instantiation | 173, 148, 146 | ⊢  |
| | : , : , : |
| 134 | instantiation | 173, 164, 147 | ⊢  |
| | :  , : , : |
| 135 | theorem | | ⊢  |
| | proveit.numbers.numerals.decimals.tuple_len_3_typical_eq |
| 136 | theorem | | ⊢  |
| | proveit.numbers.multiplication.elim_one_left |
| 137 | instantiation | 173, 148, 149 | ⊢  |
| | : , : , : |
| 138 | axiom | | ⊢  |
| | proveit.logic.equality.equals_transitivity |
| 139 | instantiation | 150, 151 | ⊢  |
| | :  , :  , : |
| 140 | theorem | | ⊢  |
| | proveit.numbers.numerals.decimals.add_2_1 |
| 141 | instantiation | 173, 152, 153 | ⊢  |
| | :  , : , : |
| 142 | theorem | | ⊢  |
| | proveit.numbers.numerals.decimals.tuple_len_2_typical_eq |
| 143 | instantiation | 173, 155, 154 | ⊢  |
| | : , : , : |
| 144 | instantiation | 173, 155, 156 | ⊢  |
| | : , : , : |
| 145 | axiom | | ⊢  |
| | proveit.logic.equality.equals_reflexivity |
| 146 | instantiation | 158, 159, 172 | ⊢  |
| | : , : , : |
| 147 | instantiation | 173, 174, 157 | ⊢  |
| | : , : , : |
| 148 | theorem | | ⊢  |
| | proveit.numbers.number_sets.complex_numbers.real_within_complex |
| 149 | instantiation | 158, 159, 160 | ⊢  |
| | : , : , : |
| 150 | axiom | | ⊢  |
| | proveit.logic.equality.substitution |
| 151 | theorem | | ⊢  |
| | proveit.numbers.numerals.decimals.add_1_1 |
| 152 | theorem | | ⊢  |
| | proveit.numbers.number_sets.real_numbers.real_neg_within_real |
| 153 | instantiation | 173, 161, 162 | ⊢  |
| | :  , : , : |
| 154 | instantiation | 173, 164, 163 | ⊢  |
| | : , : , : |
| 155 | theorem | | ⊢  |
| | proveit.numbers.number_sets.real_numbers.rational_within_real |
| 156 | instantiation | 173, 164, 170 | ⊢  |
| | : , : , : |
| 157 | theorem | | ⊢  |
| | proveit.numbers.numerals.decimals.nat3 |
| 158 | theorem | | ⊢  |
| | proveit.logic.sets.inclusion.unfold_subset_eq |
| 159 | instantiation | 165, 166 | ⊢  |
| | : , : |
| 160 | axiom | | ⊢  |
| | proveit.physics.quantum.QPE._s_in_nat_pos |
| 161 | theorem | | ⊢  |
| | proveit.numbers.number_sets.real_numbers.rational_neg_within_real_neg |
| 162 | instantiation | 173, 167, 168 | ⊢  |
| | :  , : , : |
| 163 | instantiation | 169, 170 | ⊢  |
| | : |
| 164 | theorem | | ⊢  |
| | proveit.numbers.number_sets.rational_numbers.int_within_rational |
| 165 | theorem | | ⊢  |
| | proveit.logic.sets.inclusion.relax_proper_subset |
| 166 | theorem | | ⊢  |
| | proveit.numbers.number_sets.real_numbers.nat_pos_within_real |
| 167 | theorem | | ⊢  |
| | proveit.numbers.number_sets.rational_numbers.neg_int_within_rational_neg |
| 168 | instantiation | 171, 172 | ⊢  |
| | : |
| 169 | theorem | | ⊢  |
| | proveit.numbers.negation.int_closure |
| 170 | instantiation | 173, 174, 175 | ⊢  |
| | : , : , : |
| 171 | theorem | | ⊢  |
| | proveit.numbers.negation.int_neg_closure |
| 172 | axiom | | ⊢  |
| | proveit.physics.quantum.QPE._t_in_natural_pos |
| 173 | theorem | | ⊢  |
| | proveit.logic.sets.inclusion.superset_membership_from_proper_subset |
| 174 | theorem | | ⊢  |
| | proveit.numbers.number_sets.integers.nat_within_int |
| 175 | theorem | | ⊢  |
| | proveit.numbers.numerals.decimals.nat1 |
| *equality replacement requirements |
