| | step type | requirements | statement |
|---|
| 0 | modus ponens | 1, 2 |  ⊢  |
| 1 | instantiation | 3, 26, 133, 81, 61, 82, 4* | ⊢  |
| |  :  ,  :  ,  :  ,  :  ,  :  ,  :  ,  :  ,  :  |
| 2 | instantiation | 50, 5, 6 | ⊢  |
| |  :  ,  :  ,  :  |
| 3 | theorem | | ⊢  |
| | proveit.physics.quantum.algebra.qmult_distribution_over_summation |
| 4 | instantiation | 64, 7, 8 | ⊢  |
| | :  , :  ,  :  |
| 5 | instantiation | 46, 89, 90, 57, 9 | ⊢  |
| |  :  ,  :  , :  ,  :  |
| 6 | instantiation | 59, 60, 61 | ⊢  |
| | : , : ,  : |
| 7 | instantiation | 10, 11, 12*, 13* | ⊢  |
| |  :  ,  :  ,  :  |
| 8 | modus ponens | 14, 15 | ⊢  |
| 9 | modus ponens | 16, 17 | ⊢  |
| 10 | axiom | | ⊢  |
| | proveit.logic.equality.substitution |
| 11 | modus ponens | 18, 19 | ⊢  |
| 12 | instantiation | 20, 121 | ⊢  |
| |  :  ,  : |
| 13 | instantiation | 20, 121 | ⊢  |
| | :  , : |
| 14 | instantiation | 21, 26 | ⊢  |
| | : , : , : , : |
| 15 | generalization | 22 | ⊢  |
| 16 | instantiation | 23, 26, 29 | ⊢  |
| | : ,  : , : , : ,  : , : |
| 17 | generalization | 24 | ⊢  |
| 18 | instantiation | 25, 26 | ⊢  |
| |  : , : ,  : , : , : , : ,  : |
| 19 | generalization | 27 | ⊢  |
| 20 | theorem | | ⊢  |
| | proveit.core_expr_types.conditionals.satisfied_condition_reduction |
| 21 | axiom | | ⊢  |
| | proveit.linear_algebra.addition.scalar_sum_extends_number_sum |
| 22 | instantiation | 94, 44, 45 | , ⊢  |
| | :  , :  |
| 23 | theorem | | ⊢  |
| | proveit.linear_algebra.addition.summation_closure |
| 24 | instantiation | 28, 29, 44, 58 | ⊢  |
| | : , : , : , :  |
| 25 | theorem | | ⊢  |
| | proveit.core_expr_types.lambda_maps.general_lambda_substitution |
| 26 | theorem | | ⊢  |
| | proveit.numbers.numerals.decimals.posnat1 |
| 27 | instantiation | 30, 31, 32, 33 | , ⊢  |
| | : , :  , :  ,  : |
| 28 | theorem | | ⊢  |
| | proveit.linear_algebra.scalar_multiplication.scalar_mult_closure |
| 29 | instantiation | 34, 115 | ⊢  |
| | :  |
| 30 | theorem | | ⊢  |
| | proveit.logic.equality.four_chain_transitivity |
| 31 | instantiation | 35, 44, 133, 81, 61, 82, 40 | , ⊢  |
| |  : ,  : , : , : , : , : |
| 32 | instantiation | 36, 133, 138, 44, 61, 40 | , ⊢  |
| | : , : , : , : , :  |
| 33 | instantiation | 37, 38, 44, 39, 40, 41* | , ⊢  |
| | :  , : , :  |
| 34 | theorem | | ⊢  |
| | proveit.linear_algebra.complex_vec_set_is_vec_space |
| 35 | theorem | | ⊢  |
| | proveit.physics.quantum.algebra.scalar_mult_absorption |
| 36 | theorem | | ⊢  |
| | proveit.physics.quantum.algebra.qmult_pulling_scalar_out_front |
| 37 | theorem | | ⊢  |
| | proveit.physics.quantum.algebra.scalar_mult_factorization |
| 38 | theorem | | ⊢  |
| | proveit.numbers.numerals.decimals.posnat3 |
| 39 | instantiation | 87 | ⊢  |
| | :  , :  , : |
| 40 | instantiation | 50, 42, 52 | , ⊢  |
| | : , : , :  |
| 41 | instantiation | 43, 44, 45 | , ⊢  |
| | : , : |
| 42 | instantiation | 46, 89, 90, 57, 58 | , ⊢  |
| | : , : , : , : |
| 43 | axiom | | ⊢  |
| | proveit.linear_algebra.scalar_multiplication.scalar_mult_extends_number_mult |
| 44 | instantiation | 47, 48, 49 | ⊢  |
| | :  , :  |
| 45 | instantiation | 50, 51, 52 | , ⊢  |
| | :  , : , : |
| 46 | theorem | | ⊢  |
| | proveit.physics.quantum.algebra.qmult_op_ket_in_QmultCodomain |
| 47 | theorem | | ⊢  |
| | proveit.numbers.exponentiation.exp_complex_closure |
| 48 | instantiation | 136, 107, 53 | ⊢  |
| | :  , : , : |
| 49 | instantiation | 69, 54, 55 | ⊢  |
| | : , :  , : |
| 50 | theorem | | ⊢  |
| | proveit.logic.equality.sub_left_side_into |
| 51 | instantiation | 56, 89, 90, 57, 58 | , ⊢  |
| | : , : , : , : |
| 52 | instantiation | 59, 60, 61 | ⊢  |
| | : , : , : |
| 53 | instantiation | 136, 112, 62 | ⊢  |
| | :  , : , : |
| 54 | instantiation | 94, 72, 63 | ⊢  |
| | :  , :  |
| 55 | instantiation | 64, 65, 66 | ⊢  |
| | : , :  , : |
| 56 | theorem | | ⊢  |
| | proveit.physics.quantum.algebra.qmult_op_ket_is_ket |
| 57 | instantiation | 88, 89, 90, 67 | ⊢  |
| | : , : , : |
| 58 | instantiation | 68, 135, 121 | ⊢  |
| | :  ,  : |
| 59 | axiom | | ⊢  |
| | proveit.physics.quantum.algebra.multi_qmult_def |
| 60 | theorem | | ⊢  |
| | proveit.numbers.numerals.decimals.posnat2 |
| 61 | instantiation | 97 | ⊢  |
| | : , : |
| 62 | theorem | | ⊢  |
| | proveit.numbers.number_sets.real_numbers.e_is_real_pos |
| 63 | instantiation | 69, 70, 71 | ⊢  |
| | : , :  , : |
| 64 | axiom | | ⊢  |
| | proveit.logic.equality.equals_transitivity |
| 65 | instantiation | 80, 138, 73, 81, 75, 82, 72, 95, 96, 84 | ⊢  |
| | : , : , : , :  , :  , : |
| 66 | instantiation | 80, 81, 133, 73, 82, 74, 75, 85, 86, 95, 96, 84 | ⊢  |
| | : , : , : , : , :  , : |
| 67 | instantiation | 76, 89, 90, 77, 78 | ⊢  |
| | : , : ,  : , : , : |
| 68 | theorem | | ⊢  |
| | proveit.physics.quantum.algebra.num_ket_in_register_space |
| 69 | theorem | | ⊢  |
| | proveit.logic.equality.sub_right_side_into |
| 70 | instantiation | 94, 79, 84 | ⊢  |
| | :  , : |
| 71 | instantiation | 80, 81, 133, 138, 82, 83, 95, 96, 84 | ⊢  |
| | : , : , : , : , :  , : |
| 72 | instantiation | 94, 85, 86 | ⊢  |
| | : , :  |
| 73 | theorem | | ⊢  |
| | proveit.numbers.numerals.decimals.nat3 |
| 74 | instantiation | 97 | ⊢  |
| | : , : |
| 75 | instantiation | 87 | ⊢  |
| | :  , :  , : |
| 76 | theorem | | ⊢  |
| | proveit.physics.quantum.algebra.qmult_op_op_is_op |
| 77 | instantiation | 88, 89, 90, 91 | ⊢  |
| | : , : , : |
| 78 | instantiation | 92, 115, 93 | ⊢  |
| | : , : ,  : |
| 79 | instantiation | 94, 95, 96 | ⊢  |
| | : , : |
| 80 | theorem | | ⊢  |
| | proveit.numbers.multiplication.disassociation |
| 81 | axiom | | ⊢  |
| | proveit.numbers.number_sets.natural_numbers.zero_in_nats |
| 82 | theorem | | ⊢  |
| | proveit.core_expr_types.tuples.tuple_len_0_typical_eq |
| 83 | instantiation | 97 | ⊢  |
| | : , : |
| 84 | instantiation | 136, 107, 98 | ⊢  |
| | : , : , : |
| 85 | instantiation | 136, 107, 99 | ⊢  |
| | : , : , : |
| 86 | instantiation | 136, 107, 100 | ⊢  |
| | : , : , : |
| 87 | theorem | | ⊢  |
| | proveit.numbers.numerals.decimals.tuple_len_3_typical_eq |
| 88 | theorem | | ⊢  |
| | proveit.physics.quantum.algebra.qmult_op_is_linmap |
| 89 | instantiation | 101, 115 | ⊢  |
| | : |
| 90 | theorem | | ⊢  |
| | proveit.linear_algebra.inner_products.complex_set_is_hilbert_space |
| 91 | instantiation | 102, 135, 103 | ⊢  |
| | : , : |
| 92 | theorem | | ⊢  |
| | proveit.physics.quantum.algebra.qmult_matrix_is_linmap |
| 93 | instantiation | 104, 105, 106 | ⊢  |
| | :  , :  , : |
| 94 | theorem | | ⊢  |
| | proveit.numbers.multiplication.mult_complex_closure_bin |
| 95 | theorem | | ⊢  |
| | proveit.numbers.number_sets.complex_numbers.i_is_complex |
| 96 | instantiation | 136, 107, 108 | ⊢  |
| | : , : , : |
| 97 | theorem | | ⊢  |
| | proveit.numbers.numerals.decimals.tuple_len_2_typical_eq |
| 98 | instantiation | 136, 110, 109 | ⊢  |
| | :  , : , : |
| 99 | instantiation | 136, 110, 111 | ⊢  |
| | : , : , : |
| 100 | instantiation | 136, 112, 113 | ⊢  |
| | : , : , : |
| 101 | theorem | | ⊢  |
| | proveit.linear_algebra.inner_products.complex_vec_set_is_hilbert_space |
| 102 | theorem | | ⊢  |
| | proveit.physics.quantum.algebra.num_bra_is_lin_map |
| 103 | assumption | | ⊢ |
| 104 | theorem | | ⊢  |
| | proveit.logic.sets.inclusion.unfold_subset_eq |
| 105 | instantiation | 114, 115 | ⊢  |
| | : |
| 106 | instantiation | 116, 135 | ⊢  |
| | : |
| 107 | theorem | | ⊢  |
| | proveit.numbers.number_sets.complex_numbers.real_within_complex |
| 108 | theorem | | ⊢  |
| | proveit.physics.quantum.QPE._phase_is_real |
| 109 | instantiation | 136, 118, 117 | ⊢  |
| | :  , : , : |
| 110 | theorem | | ⊢  |
| | proveit.numbers.number_sets.real_numbers.rational_within_real |
| 111 | instantiation | 136, 118, 129 | ⊢  |
| | : , : , : |
| 112 | theorem | | ⊢  |
| | proveit.numbers.number_sets.real_numbers.real_pos_within_real |
| 113 | theorem | | ⊢  |
| | proveit.numbers.number_sets.real_numbers.pi_is_real_pos |
| 114 | theorem | | ⊢  |
| | proveit.linear_algebra.matrices.unitaries_are_matrices |
| 115 | instantiation | 119, 133, 130 | ⊢  |
| | : , : |
| 116 | theorem | | ⊢  |
| | proveit.physics.quantum.QFT.invFT_is_unitary |
| 117 | instantiation | 136, 120, 121 | ⊢  |
| | :  , : , : |
| 118 | theorem | | ⊢  |
| | proveit.numbers.number_sets.rational_numbers.int_within_rational |
| 119 | theorem | | ⊢  |
| | proveit.numbers.exponentiation.exp_natpos_closure |
| 120 | instantiation | 122, 123, 124 | ⊢  |
| | : , :  |
| 121 | assumption | | ⊢ |
| 122 | theorem | | ⊢  |
| | proveit.numbers.number_sets.integers.int_interval_within_int |
| 123 | theorem | | ⊢  |
| | proveit.numbers.number_sets.integers.zero_is_int |
| 124 | instantiation | 125, 126, 127 | ⊢  |
| | : , :  |
| 125 | theorem | | ⊢  |
| | proveit.numbers.addition.add_int_closure_bin |
| 126 | instantiation | 128, 129, 130 | ⊢  |
| | : , : |
| 127 | instantiation | 131, 132 | ⊢  |
| | : |
| 128 | theorem | | ⊢  |
| | proveit.numbers.exponentiation.exp_int_closure |
| 129 | instantiation | 136, 137, 133 | ⊢  |
| | :  , : , : |
| 130 | instantiation | 136, 134, 135 | ⊢  |
| | :  , : , : |
| 131 | theorem | | ⊢  |
| | proveit.numbers.negation.int_closure |
| 132 | instantiation | 136, 137, 138 | ⊢  |
| | : , : , : |
| 133 | theorem | | ⊢  |
| | proveit.numbers.numerals.decimals.nat2 |
| 134 | theorem | | ⊢  |
| | proveit.numbers.number_sets.natural_numbers.nat_pos_within_nat |
| 135 | axiom | | ⊢  |
| | proveit.physics.quantum.QPE._t_in_natural_pos |
| 136 | theorem | | ⊢  |
| | proveit.logic.sets.inclusion.superset_membership_from_proper_subset |
| 137 | theorem | | ⊢  |
| | proveit.numbers.number_sets.integers.nat_within_int |
| 138 | theorem | | ⊢  |
| | proveit.numbers.numerals.decimals.nat1 |
| *equality replacement requirements |
