| | step type | requirements | statement |
|---|
| 0 | instantiation | 1, 2, 3, 4, 5, 6, 7, 8, 9, 10 | ⊢  |
| |  :  ,  :  ,  :  ,  :  |
| 1 | theorem | | ⊢  |
| | proveit.physics.quantum.circuits.qcircuit_eq |
| 2 | reference | 53 | ⊢  |
| 3 | instantiation | 86, 11, 12 | ⊢  |
| |  :  ,  :  |
| 4 | instantiation | 143, 13, 14 | ⊢  |
| |  : ,  :  ,  :  |
| 5 | instantiation | 97, 15, 17, 18 | ⊢  |
| | :  , :  ,  :  ,  :  |
| 6 | instantiation | 97, 16, 17, 18 | ⊢  |
| | :  , : , : , : |
| 7 | instantiation | 97, 19, 23, 24 | ⊢  |
| | :  , : , : , :  |
| 8 | instantiation | 97, 20, 23, 24 | ⊢  |
| | :  , : , : , : |
| 9 | instantiation | 97, 21, 23, 24 | ⊢  |
| | :  , : , : , : |
| 10 | instantiation | 97, 22, 23, 24 | ⊢  |
| | :  , : , : , : |
| 11 | instantiation | 56, 175, 70 | ⊢  |
| |  :  , : , :  |
| 12 | instantiation | 56, 163, 118 | ⊢  |
| | : , : , :  |
| 13 | instantiation | 154, 70 | ⊢  |
| |  :  , : , : |
| 14 | instantiation | 154, 118 | ⊢  |
| | :  , : , : |
| 15 | instantiation | 41, 25, 26, 27, 28, 46, 39, 47, 29, 30* | ⊢  |
| |  :  ,  :  ,  :  ,  :  |
| 16 | instantiation | 41, 31, 32, 33, 34, 46, 39, 47, 35* | ⊢  |
| | :  , :  , :  , :  |
| 17 | instantiation | 108, 36 | ⊢  |
| | : , : |
| 18 | instantiation | 108, 37 | ⊢  |
| | : , : |
| 19 | instantiation | 41, 42, 38, 125, 115, 46, 39, 70*, 118* | ⊢  |
| | :  , :  , :  , :  |
| 20 | instantiation | 41, 42, 40, 44, 45, 46, 47, 70*, 71* | ⊢  |
| | : , :  , :  , :  |
| 21 | instantiation | 58, 59 | ⊢  |
| | : , :  |
| 22 | instantiation | 41, 42, 43, 44, 45, 46, 47, 70*, 71* | ⊢  |
| | : , :  , : , : |
| 23 | instantiation | 150 | ⊢  |
| | : |
| 24 | instantiation | 108, 48 | ⊢  |
| | : , : |
| 25 | theorem | | ⊢  |
| | proveit.numbers.numerals.decimals.posnat5 |
| 26 | instantiation | 75 | ⊢  |
| |  :  ,  :  ,  :  ,  : ,  : |
| 27 | instantiation | 75 | ⊢  |
| | :  , : , : , :  ,  : |
| 28 | instantiation | 75 | ⊢  |
| | : , : , : , : , : |
| 29 | instantiation | 56, 59, 63 | ⊢  |
| | :  , :  , : |
| 30 | instantiation | 143, 49, 50 | ⊢  |
| | :  , :  , : |
| 31 | theorem | | ⊢  |
| | proveit.numbers.numerals.decimals.posnat6 |
| 32 | instantiation | 83 | ⊢  |
| | : , : , : , : , : , : |
| 33 | instantiation | 83 | ⊢  |
| | : , : , : , : , : , : |
| 34 | instantiation | 83 | ⊢  |
| | : , : , : , : , : , : |
| 35 | instantiation | 143, 51, 65 | ⊢  |
| | :  , :  , : |
| 36 | instantiation | 121, 178, 131, 130, 115, 132, 107, 138, 142 | ⊢  |
| | : , : , :  , :  , : , :  |
| 37 | instantiation | 52, 53, 54, 59 | ⊢  |
| | : , :  , : |
| 38 | instantiation | 147 | ⊢  |
| | : , : |
| 39 | instantiation | 56, 57, 118 | ⊢  |
| | : , : , : |
| 40 | instantiation | 147 | ⊢  |
| | : , : |
| 41 | theorem | | ⊢  |
| | proveit.core_expr_types.tuples.general_len |
| 42 | theorem | | ⊢  |
| | proveit.numbers.numerals.decimals.posnat2 |
| 43 | instantiation | 147 | ⊢  |
| | : , : |
| 44 | instantiation | 147 | ⊢  |
| | : , : |
| 45 | instantiation | 147 | ⊢  |
| | : , : |
| 46 | instantiation | 56, 55, 70 | ⊢  |
| | : , : , : |
| 47 | instantiation | 56, 57, 71 | ⊢  |
| | : , :  , : |
| 48 | instantiation | 58, 59 | ⊢  |
| | : , :  |
| 49 | instantiation | 66, 60, 61, 62, 70, 118, 71, 63 | ⊢  |
| | : ,  :  , :  , :  |
| 50 | instantiation | 143, 64, 65 | ⊢  |
| | : , : , : |
| 51 | instantiation | 66, 67, 68, 69, 70, 118, 71 | ⊢  |
| | : ,  :  , :  , :  |
| 52 | theorem | | ⊢  |
| | proveit.core_expr_types.tuples.len_of_ranges_with_repeated_indices_from_1 |
| 53 | theorem | | ⊢ |
| | proveit.numbers.numerals.decimals.posnat3 |
| 54 | instantiation | 72, 160 | ⊢  |
| | : ,  :  |
| 55 | instantiation | 176, 73, 175 | ⊢  |
| | :  , :  , : |
| 56 | theorem | | ⊢  |
| | proveit.logic.equality.sub_left_side_into |
| 57 | instantiation | 176, 73, 163 | ⊢  |
| | : , : , : |
| 58 | theorem | | ⊢  |
| | proveit.core_expr_types.tuples.range_from1_len |
| 59 | instantiation | 176, 73, 74 | ⊢  |
| | : , : , : |
| 60 | theorem | | ⊢  |
| | proveit.numbers.numerals.decimals.nat5 |
| 61 | instantiation | 75 | ⊢  |
| | : , : , : , : , : |
| 62 | instantiation | 75 | ⊢  |
| | : , : , : , : , : |
| 63 | instantiation | 143, 76, 77 | ⊢  |
| | : , :  , : |
| 64 | instantiation | 114, 78, 131, 130, 79, 115, 132, 138, 142 | ⊢  |
| | :  , : , : , :  , : , : |
| 65 | instantiation | 97, 80, 81, 82 | ⊢  |
| | : , :  , :  , : |
| 66 | axiom | | ⊢  |
| | proveit.core_expr_types.operations.operands_substitution |
| 67 | theorem | | ⊢  |
| | proveit.numbers.numerals.decimals.nat6 |
| 68 | instantiation | 83 | ⊢  |
| | : , : , : , : , : , : |
| 69 | instantiation | 83 | ⊢  |
| | : , : , : , : , : , : |
| 70 | instantiation | 136, 149, 138, 137 | ⊢  |
| | : , : , : |
| 71 | instantiation | 143, 84, 85 | ⊢  |
| | : , :  , : |
| 72 | theorem | | ⊢  |
| | proveit.core_expr_types.tuples.range_from1_len_typical_eq |
| 73 | theorem | | ⊢  |
| | proveit.numbers.number_sets.natural_numbers.nat_pos_within_nat |
| 74 | instantiation | 86, 175, 163 | ⊢  |
| | : , : |
| 75 | theorem | | ⊢  |
| | proveit.numbers.numerals.decimals.tuple_len_5_typical_eq |
| 76 | instantiation | 114, 130, 131, 132, 115, 133, 138, 142, 134, 149 | ⊢  |
| | : , : , : , : , : , :  |
| 77 | instantiation | 87, 131, 130, 115, 132, 138, 142, 149 | ⊢  |
| | : , : , : , : , : , : , : , : |
| 78 | theorem | | ⊢  |
| | proveit.numbers.numerals.decimals.nat4 |
| 79 | instantiation | 88 | ⊢  |
| | : , : , : , : |
| 80 | instantiation | 143, 89, 90 | ⊢  |
| | : , :  , : |
| 81 | instantiation | 124, 130, 160, 132, 91, 93, 138, 142, 92* | ⊢  |
| | : , : , : , : , :  , :  |
| 82 | instantiation | 124, 178, 160, 130, 93, 132, 94, 142, 95* | ⊢  |
| | : , : , : , :  , : , : |
| 83 | theorem | | ⊢  |
| | proveit.numbers.numerals.decimals.tuple_len_6_typical_eq |
| 84 | instantiation | 154, 96 | ⊢  |
| | :  , :  , :  |
| 85 | instantiation | 97, 98, 99, 100 | ⊢  |
| | : , :  , :  , : |
| 86 | theorem | | ⊢  |
| | proveit.numbers.addition.add_nat_pos_closure_bin |
| 87 | theorem | | ⊢  |
| | proveit.numbers.addition.subtraction.add_cancel_general_rev |
| 88 | theorem | | ⊢  |
| | proveit.numbers.numerals.decimals.tuple_len_4_typical_eq |
| 89 | instantiation | 102, 178, 160, 101, 138, 142 | ⊢  |
| | : , : , : , :  , :  , : , :  |
| 90 | instantiation | 102, 131, 178, 103, 104, 138, 142 | ⊢  |
| | : , : , : , :  , :  , : , : |
| 91 | instantiation | 140 | ⊢  |
| | : , : , : |
| 92 | instantiation | 108, 105, 110* | ⊢  |
| | :  , :  |
| 93 | instantiation | 140 | ⊢  |
| | : , : , : |
| 94 | instantiation | 106, 107, 138 | ⊢  |
| | : , : |
| 95 | instantiation | 108, 109, 110* | ⊢  |
| | :  , :  |
| 96 | instantiation | 111, 138, 149 | ⊢  |
| | : , : |
| 97 | theorem | | ⊢  |
| | proveit.logic.equality.four_chain_transitivity |
| 98 | instantiation | 114, 130, 131, 132, 115, 112, 138, 142, 113, 149 | ⊢  |
| | : , : , : , : , : , :  |
| 99 | instantiation | 114, 131, 178, 115, 116, 138, 142, 128, 134, 149 | ⊢  |
| | : , : , : , : , :  , :  |
| 100 | instantiation | 143, 117, 118 | ⊢  |
| | : , : , : |
| 101 | instantiation | 140 | ⊢  |
| | : , : , : |
| 102 | theorem | | ⊢  |
| | proveit.numbers.addition.leftward_commutation |
| 103 | instantiation | 147 | ⊢  |
| | : , : |
| 104 | instantiation | 147 | ⊢  |
| | : , : |
| 105 | instantiation | 121, 130, 160, 178, 132, 122, 149, 138, 119* | ⊢  |
| | : , : , : , : , :  , : |
| 106 | theorem | | ⊢  |
| | proveit.numbers.multiplication.mult_complex_closure_bin |
| 107 | instantiation | 176, 158, 120 | ⊢  |
| | :  , :  , : |
| 108 | theorem | | ⊢  |
| | proveit.logic.equality.equals_reversal |
| 109 | instantiation | 121, 130, 160, 178, 132, 122, 149, 142, 123* | ⊢  |
| | : , : , : , : , : , : |
| 110 | instantiation | 124, 130, 131, 178, 132, 125, 149, 126* | ⊢  |
| | : , : , : , : , : , : |
| 111 | theorem | | ⊢  |
| | proveit.numbers.negation.distribute_neg_through_binary_sum |
| 112 | instantiation | 147 | ⊢  |
| | : , : |
| 113 | instantiation | 127, 128, 134 | ⊢  |
| | :  , :  |
| 114 | theorem | | ⊢  |
| | proveit.numbers.addition.disassociation |
| 115 | instantiation | 147 | ⊢  |
| | : , : |
| 116 | instantiation | 147 | ⊢  |
| | : , : |
| 117 | instantiation | 129, 130, 178, 131, 132, 133, 138, 142, 134, 149, 135 | ⊢  |
| | : , : , : , : , : , : , : , : |
| 118 | instantiation | 136, 149, 142, 137 | ⊢  |
| | : , : , : |
| 119 | instantiation | 141, 138 | ⊢  |
| | : |
| 120 | instantiation | 176, 166, 139 | ⊢  |
| | :  , : , : |
| 121 | theorem | | ⊢  |
| | proveit.numbers.multiplication.distribute_through_sum |
| 122 | instantiation | 140 | ⊢  |
| | : , : , : |
| 123 | instantiation | 141, 142 | ⊢  |
| | : |
| 124 | theorem | | ⊢  |
| | proveit.numbers.addition.association |
| 125 | instantiation | 147 | ⊢  |
| | : , : |
| 126 | instantiation | 143, 144, 145 | ⊢  |
| | :  , :  , : |
| 127 | theorem | | ⊢  |
| | proveit.numbers.addition.add_complex_closure_bin |
| 128 | instantiation | 176, 158, 146 | ⊢  |
| | : , : , : |
| 129 | theorem | | ⊢  |
| | proveit.numbers.addition.subtraction.add_cancel_general |
| 130 | axiom | | ⊢  |
| | proveit.numbers.number_sets.natural_numbers.zero_in_nats |
| 131 | theorem | | ⊢  |
| | proveit.numbers.numerals.decimals.nat2 |
| 132 | theorem | | ⊢  |
| | proveit.core_expr_types.tuples.tuple_len_0_typical_eq |
| 133 | instantiation | 147 | ⊢  |
| | : , : |
| 134 | instantiation | 148, 149 | ⊢  |
| | : |
| 135 | instantiation | 150 | ⊢  |
| | : |
| 136 | theorem | | ⊢  |
| | proveit.numbers.addition.subtraction.add_cancel_triple_32 |
| 137 | instantiation | 150 | ⊢  |
| | : |
| 138 | instantiation | 176, 158, 151 | ⊢  |
| | : , : , : |
| 139 | instantiation | 176, 172, 152 | ⊢  |
| | :  , : , : |
| 140 | theorem | | ⊢  |
| | proveit.numbers.numerals.decimals.tuple_len_3_typical_eq |
| 141 | theorem | | ⊢  |
| | proveit.numbers.multiplication.elim_one_left |
| 142 | instantiation | 176, 158, 153 | ⊢  |
| | : , : , : |
| 143 | axiom | | ⊢  |
| | proveit.logic.equality.equals_transitivity |
| 144 | instantiation | 154, 155 | ⊢  |
| | :  , :  , : |
| 145 | theorem | | ⊢  |
| | proveit.numbers.numerals.decimals.add_2_1 |
| 146 | instantiation | 176, 156, 157 | ⊢  |
| | :  , : , : |
| 147 | theorem | | ⊢  |
| | proveit.numbers.numerals.decimals.tuple_len_2_typical_eq |
| 148 | theorem | | ⊢  |
| | proveit.numbers.negation.complex_closure |
| 149 | instantiation | 176, 158, 159 | ⊢  |
| | : , : , : |
| 150 | axiom | | ⊢  |
| | proveit.logic.equality.equals_reflexivity |
| 151 | instantiation | 161, 162, 175 | ⊢  |
| | : , : , : |
| 152 | instantiation | 176, 177, 160 | ⊢  |
| | : , : , : |
| 153 | instantiation | 161, 162, 163 | ⊢  |
| | : , : , : |
| 154 | axiom | | ⊢  |
| | proveit.logic.equality.substitution |
| 155 | theorem | | ⊢  |
| | proveit.numbers.numerals.decimals.add_1_1 |
| 156 | theorem | | ⊢  |
| | proveit.numbers.number_sets.real_numbers.real_neg_within_real |
| 157 | instantiation | 176, 164, 165 | ⊢  |
| | :  , : , : |
| 158 | theorem | | ⊢  |
| | proveit.numbers.number_sets.complex_numbers.real_within_complex |
| 159 | instantiation | 176, 166, 167 | ⊢  |
| | : , : , : |
| 160 | theorem | | ⊢  |
| | proveit.numbers.numerals.decimals.nat3 |
| 161 | theorem | | ⊢  |
| | proveit.logic.sets.inclusion.unfold_subset_eq |
| 162 | instantiation | 168, 169 | ⊢  |
| | : , : |
| 163 | axiom | | ⊢  |
| | proveit.physics.quantum.QPE._s_in_nat_pos |
| 164 | theorem | | ⊢  |
| | proveit.numbers.number_sets.real_numbers.rational_neg_within_real_neg |
| 165 | instantiation | 176, 170, 171 | ⊢  |
| | :  , : , : |
| 166 | theorem | | ⊢  |
| | proveit.numbers.number_sets.real_numbers.rational_within_real |
| 167 | instantiation | 176, 172, 173 | ⊢  |
| | : , : , : |
| 168 | theorem | | ⊢  |
| | proveit.logic.sets.inclusion.relax_proper_subset |
| 169 | theorem | | ⊢  |
| | proveit.numbers.number_sets.real_numbers.nat_pos_within_real |
| 170 | theorem | | ⊢  |
| | proveit.numbers.number_sets.rational_numbers.neg_int_within_rational_neg |
| 171 | instantiation | 174, 175 | ⊢  |
| | : |
| 172 | theorem | | ⊢  |
| | proveit.numbers.number_sets.rational_numbers.int_within_rational |
| 173 | instantiation | 176, 177, 178 | ⊢  |
| | : , : , : |
| 174 | theorem | | ⊢  |
| | proveit.numbers.negation.int_neg_closure |
| 175 | axiom | | ⊢  |
| | proveit.physics.quantum.QPE._t_in_natural_pos |
| 176 | theorem | | ⊢  |
| | proveit.logic.sets.inclusion.superset_membership_from_proper_subset |
| 177 | theorem | | ⊢  |
| | proveit.numbers.number_sets.integers.nat_within_int |
| 178 | theorem | | ⊢  |
| | proveit.numbers.numerals.decimals.nat1 |
| *equality replacement requirements |
