| step type | requirements | statement |
0 | instantiation | 1, 2, 3, 4 | , ⊢ |
| : , : , : , : |
1 | reference | 15 | ⊢ |
2 | reference | 16 | ⊢ |
3 | instantiation | 5, 6, 7, 8 | ⊢ |
| : , : |
4 | instantiation | 9, 16, 10, 11 | , ⊢ |
| : , : , : , : |
5 | theorem | | ⊢ |
| proveit.numbers.division.div_complex_closure |
6 | instantiation | 94, 74, 65 | ⊢ |
| : , : , : |
7 | instantiation | 12, 61 | ⊢ |
| : |
8 | instantiation | 13, 21, 14 | ⊢ |
| : , : |
9 | theorem | | ⊢ |
| proveit.linear_algebra.addition.binary_closure |
10 | theorem | | ⊢ |
| proveit.physics.quantum.algebra.ket_zero_in_qubit_space |
11 | instantiation | 15, 16, 17, 18 | , ⊢ |
| : , : , : , : |
12 | theorem | | ⊢ |
| proveit.numbers.exponentiation.sqrt_complex_closure |
13 | theorem | | ⊢ |
| proveit.numbers.exponentiation.exp_rational_non_zero__not_zero |
14 | instantiation | 19, 20, 21 | ⊢ |
| : , : |
15 | theorem | | ⊢ |
| proveit.linear_algebra.scalar_multiplication.scalar_mult_closure |
16 | instantiation | 22, 33 | ⊢ |
| : |
17 | instantiation | 60, 23, 24 | , ⊢ |
| : , : |
18 | theorem | | ⊢ |
| proveit.physics.quantum.algebra.ket_one_in_qubit_space |
19 | theorem | | ⊢ |
| proveit.numbers.division.div_rational_nonzero_closure |
20 | instantiation | 94, 26, 25 | ⊢ |
| : , : , : |
21 | instantiation | 94, 26, 27 | ⊢ |
| : , : , : |
22 | theorem | | ⊢ |
| proveit.linear_algebra.complex_vec_set_is_vec_space |
23 | instantiation | 94, 74, 28 | ⊢ |
| : , : , : |
24 | instantiation | 39, 29, 30 | , ⊢ |
| : , : , : |
25 | instantiation | 94, 32, 31 | ⊢ |
| : , : , : |
26 | theorem | | ⊢ |
| proveit.numbers.number_sets.rational_numbers.nonzero_int_within_rational_nonzero |
27 | instantiation | 94, 32, 33 | ⊢ |
| : , : , : |
28 | instantiation | 94, 67, 34 | ⊢ |
| : , : , : |
29 | instantiation | 54, 42, 35 | , ⊢ |
| : , : |
30 | instantiation | 36, 37, 38 | , ⊢ |
| : , : , : |
31 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.posnat1 |
32 | theorem | | ⊢ |
| proveit.numbers.number_sets.integers.nat_pos_within_nonzero_int |
33 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.posnat2 |
34 | theorem | | ⊢ |
| proveit.numbers.number_sets.real_numbers.e_is_real_pos |
35 | instantiation | 39, 40, 41 | , ⊢ |
| : , : , : |
36 | axiom | | ⊢ |
| proveit.logic.equality.equals_transitivity |
37 | instantiation | 47, 93, 43, 48, 45, 49, 42, 55, 56, 51 | , ⊢ |
| : , : , : , : , : , : |
38 | instantiation | 47, 48, 79, 43, 49, 44, 45, 61, 52, 55, 56, 51 | , ⊢ |
| : , : , : , : , : , : |
39 | theorem | | ⊢ |
| proveit.logic.equality.sub_right_side_into |
40 | instantiation | 54, 46, 51 | , ⊢ |
| : , : |
41 | instantiation | 47, 48, 79, 93, 49, 50, 55, 56, 51 | , ⊢ |
| : , : , : , : , : , : |
42 | instantiation | 54, 61, 52 | ⊢ |
| : , : |
43 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.nat3 |
44 | instantiation | 57 | ⊢ |
| : , : |
45 | instantiation | 53 | ⊢ |
| : , : , : |
46 | instantiation | 54, 55, 56 | , ⊢ |
| : , : |
47 | theorem | | ⊢ |
| proveit.numbers.multiplication.disassociation |
48 | axiom | | ⊢ |
| proveit.numbers.number_sets.natural_numbers.zero_in_nats |
49 | theorem | | ⊢ |
| proveit.core_expr_types.tuples.tuple_len_0_typical_eq |
50 | instantiation | 57 | ⊢ |
| : , : |
51 | instantiation | 94, 74, 58 | ⊢ |
| : , : , : |
52 | instantiation | 94, 74, 59 | ⊢ |
| : , : , : |
53 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.tuple_len_3_typical_eq |
54 | theorem | | ⊢ |
| proveit.numbers.multiplication.mult_complex_closure_bin |
55 | theorem | | ⊢ |
| proveit.numbers.number_sets.complex_numbers.i_is_complex |
56 | instantiation | 60, 61, 62 | , ⊢ |
| : , : |
57 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.tuple_len_2_typical_eq |
58 | instantiation | 63, 64, 65, 66 | ⊢ |
| : , : , : |
59 | instantiation | 94, 67, 68 | ⊢ |
| : , : , : |
60 | theorem | | ⊢ |
| proveit.numbers.exponentiation.exp_complex_closure |
61 | instantiation | 94, 74, 69 | ⊢ |
| : , : , : |
62 | instantiation | 70, 71 | , ⊢ |
| : |
63 | theorem | | ⊢ |
| proveit.numbers.number_sets.real_numbers.all_in_interval_co__is__real |
64 | theorem | | ⊢ |
| proveit.numbers.number_sets.real_numbers.zero_is_real |
65 | instantiation | 94, 77, 72 | ⊢ |
| : , : , : |
66 | axiom | | ⊢ |
| proveit.physics.quantum.QPE._phase_in_interval |
67 | theorem | | ⊢ |
| proveit.numbers.number_sets.real_numbers.real_pos_within_real |
68 | theorem | | ⊢ |
| proveit.numbers.number_sets.real_numbers.pi_is_real_pos |
69 | instantiation | 94, 77, 73 | ⊢ |
| : , : , : |
70 | theorem | | ⊢ |
| proveit.numbers.negation.complex_closure |
71 | instantiation | 94, 74, 75 | , ⊢ |
| : , : , : |
72 | instantiation | 94, 80, 89 | ⊢ |
| : , : , : |
73 | instantiation | 94, 80, 76 | ⊢ |
| : , : , : |
74 | theorem | | ⊢ |
| proveit.numbers.number_sets.complex_numbers.real_within_complex |
75 | instantiation | 94, 77, 78 | , ⊢ |
| : , : , : |
76 | instantiation | 94, 92, 79 | ⊢ |
| : , : , : |
77 | theorem | | ⊢ |
| proveit.numbers.number_sets.real_numbers.rational_within_real |
78 | instantiation | 94, 80, 81 | , ⊢ |
| : , : , : |
79 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.nat2 |
80 | theorem | | ⊢ |
| proveit.numbers.number_sets.rational_numbers.int_within_rational |
81 | instantiation | 94, 82, 83 | , ⊢ |
| : , : , : |
82 | instantiation | 84, 85, 86 | ⊢ |
| : , : |
83 | assumption | | ⊢ |
84 | theorem | | ⊢ |
| proveit.numbers.number_sets.integers.int_interval_within_int |
85 | instantiation | 87, 88, 89 | ⊢ |
| : , : |
86 | theorem | | ⊢ |
| proveit.numbers.number_sets.integers.zero_is_int |
87 | theorem | | ⊢ |
| proveit.numbers.addition.add_int_closure_bin |
88 | instantiation | 90, 91 | ⊢ |
| : |
89 | instantiation | 94, 92, 93 | ⊢ |
| : , : , : |
90 | theorem | | ⊢ |
| proveit.numbers.negation.int_closure |
91 | instantiation | 94, 95, 96 | ⊢ |
| : , : , : |
92 | theorem | | ⊢ |
| proveit.numbers.number_sets.integers.nat_within_int |
93 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.nat1 |
94 | theorem | | ⊢ |
| proveit.logic.sets.inclusion.superset_membership_from_proper_subset |
95 | theorem | | ⊢ |
| proveit.numbers.number_sets.integers.nat_pos_within_int |
96 | assumption | | ⊢ |