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