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