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