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