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