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