| 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 |