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