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