| step type | requirements | statement |
0 | generalization | 1 | ⊢ |
1 | instantiation | 2, 3, 4 | , ⊢ |
| : , : , : |
2 | theorem | | ⊢ |
| proveit.logic.equality.sub_left_side_into |
3 | instantiation | 5, 6, 9, 7 | , ⊢ |
| : , : , : , : |
4 | instantiation | 8, 9, 84, 43, 44, 13, 14, 16, 17 | , ⊢ |
| : , : , : , : , : , : , : , : , : , : |
5 | theorem | | ⊢ |
| proveit.linear_algebra.scalar_multiplication.scalar_mult_closure |
6 | instantiation | 10, 21, 12, 13, 14 | ⊢ |
| : , : , : |
7 | instantiation | 11, 21, 12, 13, 14, 15, 16, 17 | , ⊢ |
| : , : , : , : |
8 | theorem | | ⊢ |
| proveit.linear_algebra.tensors.factor_scalar_from_tensor_prod |
9 | instantiation | 18, 19, 20 | , ⊢ |
| : , : |
10 | theorem | | ⊢ |
| proveit.linear_algebra.tensors.tensor_prod_of_vec_spaces_is_vec_space |
11 | theorem | | ⊢ |
| proveit.linear_algebra.tensors.tensor_prod_is_in_tensor_prod_space |
12 | instantiation | 53 | ⊢ |
| : , : |
13 | instantiation | 22, 21 | ⊢ |
| : |
14 | instantiation | 22, 23 | ⊢ |
| : |
15 | instantiation | 53 | ⊢ |
| : , : |
16 | theorem | | ⊢ |
| proveit.physics.quantum.algebra.ket_one_in_qubit_space |
17 | instantiation | 24, 81, 67 | , ⊢ |
| : , : |
18 | theorem | | ⊢ |
| proveit.numbers.exponentiation.exp_complex_closure |
19 | instantiation | 82, 57, 25 | ⊢ |
| : , : , : |
20 | instantiation | 34, 26, 27 | , ⊢ |
| : , : , : |
21 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.posnat2 |
22 | theorem | | ⊢ |
| proveit.linear_algebra.complex_vec_set_is_vec_space |
23 | instantiation | 28, 79, 76 | ⊢ |
| : , : |
24 | theorem | | ⊢ |
| proveit.physics.quantum.algebra.num_ket_in_register_space |
25 | instantiation | 82, 62, 29 | ⊢ |
| : , : , : |
26 | instantiation | 50, 37, 30 | , ⊢ |
| : , : |
27 | instantiation | 31, 32, 33 | , ⊢ |
| : , : , : |
28 | theorem | | ⊢ |
| proveit.numbers.exponentiation.exp_natpos_closure |
29 | theorem | | ⊢ |
| proveit.numbers.number_sets.real_numbers.e_is_real_pos |
30 | instantiation | 34, 35, 36 | , ⊢ |
| : , : , : |
31 | axiom | | ⊢ |
| proveit.logic.equality.equals_transitivity |
32 | instantiation | 42, 84, 38, 43, 40, 44, 37, 51, 52, 46 | , ⊢ |
| : , : , : , : , : , : |
33 | instantiation | 42, 43, 79, 38, 44, 39, 40, 47, 48, 51, 52, 46 | , ⊢ |
| : , : , : , : , : , : |
34 | theorem | | ⊢ |
| proveit.logic.equality.sub_right_side_into |
35 | instantiation | 50, 41, 46 | , ⊢ |
| : , : |
36 | instantiation | 42, 43, 79, 84, 44, 45, 51, 52, 46 | , ⊢ |
| : , : , : , : , : , : |
37 | instantiation | 50, 47, 48 | ⊢ |
| : , : |
38 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.nat3 |
39 | instantiation | 53 | ⊢ |
| : , : |
40 | instantiation | 49 | ⊢ |
| : , : , : |
41 | instantiation | 50, 51, 52 | ⊢ |
| : , : |
42 | theorem | | ⊢ |
| proveit.numbers.multiplication.disassociation |
43 | axiom | | ⊢ |
| proveit.numbers.number_sets.natural_numbers.zero_in_nats |
44 | theorem | | ⊢ |
| proveit.core_expr_types.tuples.tuple_len_0_typical_eq |
45 | instantiation | 53 | ⊢ |
| : , : |
46 | instantiation | 82, 57, 54 | , ⊢ |
| : , : , : |
47 | instantiation | 82, 57, 55 | ⊢ |
| : , : , : |
48 | instantiation | 82, 57, 56 | ⊢ |
| : , : , : |
49 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.tuple_len_3_typical_eq |
50 | theorem | | ⊢ |
| proveit.numbers.multiplication.mult_complex_closure_bin |
51 | theorem | | ⊢ |
| proveit.numbers.number_sets.complex_numbers.i_is_complex |
52 | instantiation | 82, 57, 58 | ⊢ |
| : , : , : |
53 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.tuple_len_2_typical_eq |
54 | instantiation | 82, 60, 59 | , ⊢ |
| : , : , : |
55 | instantiation | 82, 60, 61 | ⊢ |
| : , : , : |
56 | instantiation | 82, 62, 63 | ⊢ |
| : , : , : |
57 | theorem | | ⊢ |
| proveit.numbers.number_sets.complex_numbers.real_within_complex |
58 | theorem | | ⊢ |
| proveit.physics.quantum.QPE._phase_is_real |
59 | instantiation | 82, 65, 64 | , ⊢ |
| : , : , : |
60 | theorem | | ⊢ |
| proveit.numbers.number_sets.real_numbers.rational_within_real |
61 | instantiation | 82, 65, 75 | ⊢ |
| : , : , : |
62 | theorem | | ⊢ |
| proveit.numbers.number_sets.real_numbers.real_pos_within_real |
63 | theorem | | ⊢ |
| proveit.numbers.number_sets.real_numbers.pi_is_real_pos |
64 | instantiation | 82, 66, 67 | , ⊢ |
| : , : , : |
65 | theorem | | ⊢ |
| proveit.numbers.number_sets.rational_numbers.int_within_rational |
66 | instantiation | 68, 69, 70 | ⊢ |
| : , : |
67 | assumption | | ⊢ |
68 | theorem | | ⊢ |
| proveit.numbers.number_sets.integers.int_interval_within_int |
69 | theorem | | ⊢ |
| proveit.numbers.number_sets.integers.zero_is_int |
70 | instantiation | 71, 72, 73 | ⊢ |
| : , : |
71 | theorem | | ⊢ |
| proveit.numbers.addition.add_int_closure_bin |
72 | instantiation | 74, 75, 76 | ⊢ |
| : , : |
73 | instantiation | 77, 78 | ⊢ |
| : |
74 | theorem | | ⊢ |
| proveit.numbers.exponentiation.exp_int_closure |
75 | instantiation | 82, 83, 79 | ⊢ |
| : , : , : |
76 | instantiation | 82, 80, 81 | ⊢ |
| : , : , : |
77 | theorem | | ⊢ |
| proveit.numbers.negation.int_closure |
78 | instantiation | 82, 83, 84 | ⊢ |
| : , : , : |
79 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.nat2 |
80 | theorem | | ⊢ |
| proveit.numbers.number_sets.natural_numbers.nat_pos_within_nat |
81 | assumption | | ⊢ |
82 | theorem | | ⊢ |
| proveit.logic.sets.inclusion.superset_membership_from_proper_subset |
83 | theorem | | ⊢ |
| proveit.numbers.number_sets.integers.nat_within_int |
84 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.nat1 |