| step type | requirements | statement |
0 | instantiation | 1, 2, 3 | , ⊢ |
| : , : , : |
1 | theorem | | ⊢ |
| proveit.logic.equality.sub_left_side_into |
2 | instantiation | 4, 5 | , ⊢ |
| : , : , : |
3 | instantiation | 6, 7, 8, 9 | , ⊢ |
| : , : , : |
4 | axiom | | ⊢ |
| proveit.logic.equality.substitution |
5 | instantiation | 10, 11, 77, 39, 12, 13, 40, 43, 44, 48, 49, 36, 42 | , ⊢ |
| : , : , : , : , : , : |
6 | theorem | | ⊢ |
| proveit.numbers.exponentiation.product_of_complex_powers |
7 | theorem | | ⊢ |
| proveit.numbers.number_sets.real_numbers.e_is_real_pos |
8 | instantiation | 29, 14, 15 | , ⊢ |
| : , : , : |
9 | instantiation | 29, 16, 17 | ⊢ |
| : , : , : |
10 | theorem | | ⊢ |
| proveit.numbers.multiplication.distribute_through_sum |
11 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.nat4 |
12 | instantiation | 18 | ⊢ |
| : , : , : , : |
13 | instantiation | 50 | ⊢ |
| : , : |
14 | instantiation | 47, 32, 19 | , ⊢ |
| : , : |
15 | instantiation | 23, 20, 21 | , ⊢ |
| : , : , : |
16 | instantiation | 47, 32, 22 | ⊢ |
| : , : |
17 | instantiation | 23, 24, 25 | ⊢ |
| : , : , : |
18 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.tuple_len_4_typical_eq |
19 | instantiation | 29, 26, 27 | , ⊢ |
| : , : , : |
20 | instantiation | 38, 82, 33, 39, 28, 40, 32, 48, 49, 36 | , ⊢ |
| : , : , : , : , : , : |
21 | instantiation | 38, 39, 77, 33, 40, 34, 28, 43, 44, 48, 49, 36 | , ⊢ |
| : , : , : , : , : , : |
22 | instantiation | 29, 30, 31 | ⊢ |
| : , : , : |
23 | axiom | | ⊢ |
| proveit.logic.equality.equals_transitivity |
24 | instantiation | 38, 82, 33, 39, 35, 40, 32, 48, 49, 42 | ⊢ |
| : , : , : , : , : , : |
25 | instantiation | 38, 39, 77, 33, 40, 34, 35, 43, 44, 48, 49, 42 | ⊢ |
| : , : , : , : , : , : |
26 | instantiation | 47, 37, 36 | , ⊢ |
| : , : |
27 | instantiation | 38, 39, 77, 82, 40, 41, 48, 49, 36 | , ⊢ |
| : , : , : , : , : , : |
28 | instantiation | 45 | ⊢ |
| : , : , : |
29 | theorem | | ⊢ |
| proveit.logic.equality.sub_right_side_into |
30 | instantiation | 47, 37, 42 | ⊢ |
| : , : |
31 | instantiation | 38, 39, 77, 82, 40, 41, 48, 49, 42 | ⊢ |
| : , : , : , : , : , : |
32 | instantiation | 47, 43, 44 | ⊢ |
| : , : |
33 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.nat3 |
34 | instantiation | 50 | ⊢ |
| : , : |
35 | instantiation | 45 | ⊢ |
| : , : , : |
36 | instantiation | 80, 55, 46 | , ⊢ |
| : , : , : |
37 | instantiation | 47, 48, 49 | ⊢ |
| : , : |
38 | theorem | | ⊢ |
| proveit.numbers.multiplication.disassociation |
39 | axiom | | ⊢ |
| proveit.numbers.number_sets.natural_numbers.zero_in_nats |
40 | theorem | | ⊢ |
| proveit.core_expr_types.tuples.tuple_len_0_typical_eq |
41 | instantiation | 50 | ⊢ |
| : , : |
42 | instantiation | 80, 55, 51 | ⊢ |
| : , : , : |
43 | instantiation | 80, 55, 52 | ⊢ |
| : , : , : |
44 | instantiation | 80, 55, 53 | ⊢ |
| : , : , : |
45 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.tuple_len_3_typical_eq |
46 | instantiation | 80, 58, 54 | , ⊢ |
| : , : , : |
47 | theorem | | ⊢ |
| proveit.numbers.multiplication.mult_complex_closure_bin |
48 | theorem | | ⊢ |
| proveit.numbers.number_sets.complex_numbers.i_is_complex |
49 | instantiation | 80, 55, 56 | ⊢ |
| : , : , : |
50 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.tuple_len_2_typical_eq |
51 | instantiation | 80, 58, 57 | ⊢ |
| : , : , : |
52 | instantiation | 80, 58, 59 | ⊢ |
| : , : , : |
53 | instantiation | 80, 60, 61 | ⊢ |
| : , : , : |
54 | instantiation | 80, 63, 62 | , ⊢ |
| : , : , : |
55 | theorem | | ⊢ |
| proveit.numbers.number_sets.complex_numbers.real_within_complex |
56 | theorem | | ⊢ |
| proveit.physics.quantum.QPE._phase_is_real |
57 | instantiation | 80, 63, 70 | ⊢ |
| : , : , : |
58 | theorem | | ⊢ |
| proveit.numbers.number_sets.real_numbers.rational_within_real |
59 | instantiation | 80, 63, 73 | ⊢ |
| : , : , : |
60 | theorem | | ⊢ |
| proveit.numbers.number_sets.real_numbers.real_pos_within_real |
61 | theorem | | ⊢ |
| proveit.numbers.number_sets.real_numbers.pi_is_real_pos |
62 | instantiation | 80, 64, 65 | , ⊢ |
| : , : , : |
63 | theorem | | ⊢ |
| proveit.numbers.number_sets.rational_numbers.int_within_rational |
64 | instantiation | 66, 67, 68 | ⊢ |
| : , : |
65 | assumption | | ⊢ |
66 | theorem | | ⊢ |
| proveit.numbers.number_sets.integers.int_interval_within_int |
67 | theorem | | ⊢ |
| proveit.numbers.number_sets.integers.zero_is_int |
68 | instantiation | 69, 70, 71 | ⊢ |
| : , : |
69 | theorem | | ⊢ |
| proveit.numbers.addition.add_int_closure_bin |
70 | instantiation | 72, 73, 74 | ⊢ |
| : , : |
71 | instantiation | 75, 76 | ⊢ |
| : |
72 | theorem | | ⊢ |
| proveit.numbers.exponentiation.exp_int_closure |
73 | instantiation | 80, 81, 77 | ⊢ |
| : , : , : |
74 | instantiation | 80, 78, 79 | ⊢ |
| : , : , : |
75 | theorem | | ⊢ |
| proveit.numbers.negation.int_closure |
76 | instantiation | 80, 81, 82 | ⊢ |
| : , : , : |
77 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.nat2 |
78 | theorem | | ⊢ |
| proveit.numbers.number_sets.natural_numbers.nat_pos_within_nat |
79 | assumption | | ⊢ |
80 | theorem | | ⊢ |
| proveit.logic.sets.inclusion.superset_membership_from_proper_subset |
81 | theorem | | ⊢ |
| proveit.numbers.number_sets.integers.nat_within_int |
82 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.nat1 |