| step type | requirements | statement |
0 | instantiation | 1, 2, 3, 4 | , ⊢ |
| : , : , : , : |
1 | theorem | | ⊢ |
| proveit.linear_algebra.scalar_multiplication.scalar_mult_closure |
2 | instantiation | 5, 19, 10, 11, 12 | ⊢ |
| : , : , : |
3 | instantiation | 6, 7, 8 | , ⊢ |
| : , : |
4 | instantiation | 9, 19, 10, 11, 12, 13, 14, 15 | , ⊢ |
| : , : , : , : |
5 | theorem | | ⊢ |
| proveit.linear_algebra.tensors.tensor_prod_of_vec_spaces_is_vec_space |
6 | theorem | | ⊢ |
| proveit.numbers.exponentiation.exp_complex_closure |
7 | instantiation | 77, 52, 16 | ⊢ |
| : , : , : |
8 | instantiation | 29, 17, 18 | , ⊢ |
| : , : , : |
9 | theorem | | ⊢ |
| proveit.linear_algebra.tensors.tensor_prod_is_in_tensor_prod_space |
10 | instantiation | 48 | ⊢ |
| : , : |
11 | instantiation | 20, 19 | ⊢ |
| : |
12 | instantiation | 20, 21 | ⊢ |
| : |
13 | instantiation | 48 | ⊢ |
| : , : |
14 | theorem | | ⊢ |
| proveit.physics.quantum.algebra.ket_one_in_qubit_space |
15 | instantiation | 22, 76, 62 | , ⊢ |
| : , : |
16 | instantiation | 77, 57, 23 | ⊢ |
| : , : , : |
17 | instantiation | 45, 32, 24 | , ⊢ |
| : , : |
18 | instantiation | 25, 26, 27 | , ⊢ |
| : , : , : |
19 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.posnat2 |
20 | theorem | | ⊢ |
| proveit.linear_algebra.complex_vec_set_is_vec_space |
21 | instantiation | 28, 74, 71 | ⊢ |
| : , : |
22 | theorem | | ⊢ |
| proveit.physics.quantum.algebra.num_ket_in_register_space |
23 | theorem | | ⊢ |
| proveit.numbers.number_sets.real_numbers.e_is_real_pos |
24 | instantiation | 29, 30, 31 | , ⊢ |
| : , : , : |
25 | axiom | | ⊢ |
| proveit.logic.equality.equals_transitivity |
26 | instantiation | 37, 79, 33, 38, 35, 39, 32, 46, 47, 41 | , ⊢ |
| : , : , : , : , : , : |
27 | instantiation | 37, 38, 74, 33, 39, 34, 35, 42, 43, 46, 47, 41 | , ⊢ |
| : , : , : , : , : , : |
28 | theorem | | ⊢ |
| proveit.numbers.exponentiation.exp_natpos_closure |
29 | theorem | | ⊢ |
| proveit.logic.equality.sub_right_side_into |
30 | instantiation | 45, 36, 41 | , ⊢ |
| : , : |
31 | instantiation | 37, 38, 74, 79, 39, 40, 46, 47, 41 | , ⊢ |
| : , : , : , : , : , : |
32 | instantiation | 45, 42, 43 | ⊢ |
| : , : |
33 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.nat3 |
34 | instantiation | 48 | ⊢ |
| : , : |
35 | instantiation | 44 | ⊢ |
| : , : , : |
36 | instantiation | 45, 46, 47 | ⊢ |
| : , : |
37 | theorem | | ⊢ |
| proveit.numbers.multiplication.disassociation |
38 | axiom | | ⊢ |
| proveit.numbers.number_sets.natural_numbers.zero_in_nats |
39 | theorem | | ⊢ |
| proveit.core_expr_types.tuples.tuple_len_0_typical_eq |
40 | instantiation | 48 | ⊢ |
| : , : |
41 | instantiation | 77, 52, 49 | , ⊢ |
| : , : , : |
42 | instantiation | 77, 52, 50 | ⊢ |
| : , : , : |
43 | instantiation | 77, 52, 51 | ⊢ |
| : , : , : |
44 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.tuple_len_3_typical_eq |
45 | theorem | | ⊢ |
| proveit.numbers.multiplication.mult_complex_closure_bin |
46 | theorem | | ⊢ |
| proveit.numbers.number_sets.complex_numbers.i_is_complex |
47 | instantiation | 77, 52, 53 | ⊢ |
| : , : , : |
48 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.tuple_len_2_typical_eq |
49 | instantiation | 77, 55, 54 | , ⊢ |
| : , : , : |
50 | instantiation | 77, 55, 56 | ⊢ |
| : , : , : |
51 | instantiation | 77, 57, 58 | ⊢ |
| : , : , : |
52 | theorem | | ⊢ |
| proveit.numbers.number_sets.complex_numbers.real_within_complex |
53 | theorem | | ⊢ |
| proveit.physics.quantum.QPE._phase_is_real |
54 | instantiation | 77, 60, 59 | , ⊢ |
| : , : , : |
55 | theorem | | ⊢ |
| proveit.numbers.number_sets.real_numbers.rational_within_real |
56 | instantiation | 77, 60, 70 | ⊢ |
| : , : , : |
57 | theorem | | ⊢ |
| proveit.numbers.number_sets.real_numbers.real_pos_within_real |
58 | theorem | | ⊢ |
| proveit.numbers.number_sets.real_numbers.pi_is_real_pos |
59 | instantiation | 77, 61, 62 | , ⊢ |
| : , : , : |
60 | theorem | | ⊢ |
| proveit.numbers.number_sets.rational_numbers.int_within_rational |
61 | instantiation | 63, 64, 65 | ⊢ |
| : , : |
62 | assumption | | ⊢ |
63 | theorem | | ⊢ |
| proveit.numbers.number_sets.integers.int_interval_within_int |
64 | theorem | | ⊢ |
| proveit.numbers.number_sets.integers.zero_is_int |
65 | instantiation | 66, 67, 68 | ⊢ |
| : , : |
66 | theorem | | ⊢ |
| proveit.numbers.addition.add_int_closure_bin |
67 | instantiation | 69, 70, 71 | ⊢ |
| : , : |
68 | instantiation | 72, 73 | ⊢ |
| : |
69 | theorem | | ⊢ |
| proveit.numbers.exponentiation.exp_int_closure |
70 | instantiation | 77, 78, 74 | ⊢ |
| : , : , : |
71 | instantiation | 77, 75, 76 | ⊢ |
| : , : , : |
72 | theorem | | ⊢ |
| proveit.numbers.negation.int_closure |
73 | instantiation | 77, 78, 79 | ⊢ |
| : , : , : |
74 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.nat2 |
75 | theorem | | ⊢ |
| proveit.numbers.number_sets.natural_numbers.nat_pos_within_nat |
76 | assumption | | ⊢ |
77 | theorem | | ⊢ |
| proveit.logic.sets.inclusion.superset_membership_from_proper_subset |
78 | theorem | | ⊢ |
| proveit.numbers.number_sets.integers.nat_within_int |
79 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.nat1 |