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