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