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