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