| step type | requirements | statement |
0 | instantiation | 1, 2, 3, 4, 5* | ⊢ |
| : , : , : |
1 | theorem | | ⊢ |
| proveit.numbers.exponentiation.complex_power_of_complex_power |
2 | theorem | | ⊢ |
| proveit.numbers.number_sets.real_numbers.e_is_real_pos |
3 | instantiation | 6, 7, 8 | ⊢ |
| : , : , : |
4 | reference | 45 | ⊢ |
5 | instantiation | 18, 19, 9, 72, 20, 10, 23, 24, 25, 26, 45 | ⊢ |
| : , : , : , : , : , : |
6 | theorem | | ⊢ |
| proveit.logic.equality.sub_right_side_into |
7 | instantiation | 16, 17, 11 | ⊢ |
| : , : |
8 | instantiation | 12, 13, 14 | ⊢ |
| : , : , : |
9 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.nat4 |
10 | instantiation | 15 | ⊢ |
| : , : , : , : |
11 | instantiation | 16, 25, 26 | ⊢ |
| : , : |
12 | axiom | | ⊢ |
| proveit.logic.equality.equals_transitivity |
13 | instantiation | 18, 72, 52, 19, 22, 20, 17, 25, 26 | ⊢ |
| : , : , : , : , : , : |
14 | instantiation | 18, 19, 52, 20, 21, 22, 23, 24, 25, 26 | ⊢ |
| : , : , : , : , : , : |
15 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.tuple_len_4_typical_eq |
16 | theorem | | ⊢ |
| proveit.numbers.multiplication.mult_complex_closure_bin |
17 | instantiation | 73, 49, 27 | ⊢ |
| : , : , : |
18 | theorem | | ⊢ |
| proveit.numbers.multiplication.disassociation |
19 | axiom | | ⊢ |
| proveit.numbers.number_sets.natural_numbers.zero_in_nats |
20 | theorem | | ⊢ |
| proveit.core_expr_types.tuples.tuple_len_0_typical_eq |
21 | instantiation | 28 | ⊢ |
| : , : |
22 | instantiation | 28 | ⊢ |
| : , : |
23 | instantiation | 73, 49, 33 | ⊢ |
| : , : , : |
24 | instantiation | 73, 49, 34 | ⊢ |
| : , : , : |
25 | theorem | | ⊢ |
| proveit.numbers.number_sets.complex_numbers.i_is_complex |
26 | instantiation | 29, 30, 31 | ⊢ |
| : , : |
27 | instantiation | 32, 33, 34 | ⊢ |
| : , : |
28 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.tuple_len_2_typical_eq |
29 | theorem | | ⊢ |
| proveit.numbers.addition.add_complex_closure_bin |
30 | instantiation | 73, 49, 35 | ⊢ |
| : , : , : |
31 | instantiation | 36, 37 | ⊢ |
| : |
32 | theorem | | ⊢ |
| proveit.numbers.multiplication.mult_real_closure_bin |
33 | instantiation | 73, 53, 38 | ⊢ |
| : , : , : |
34 | instantiation | 73, 39, 40 | ⊢ |
| : , : , : |
35 | instantiation | 41, 42 | ⊢ |
| : |
36 | theorem | | ⊢ |
| proveit.numbers.negation.complex_closure |
37 | instantiation | 43, 44, 45, 46 | ⊢ |
| : , : |
38 | instantiation | 73, 58, 47 | ⊢ |
| : , : , : |
39 | theorem | | ⊢ |
| proveit.numbers.number_sets.real_numbers.real_pos_within_real |
40 | theorem | | ⊢ |
| proveit.numbers.number_sets.real_numbers.pi_is_real_pos |
41 | theorem | | ⊢ |
| proveit.physics.quantum.QPE._delta_b_is_real |
42 | theorem | | ⊢ |
| proveit.physics.quantum.QPE._best_floor_is_int |
43 | theorem | | ⊢ |
| proveit.numbers.division.div_complex_closure |
44 | instantiation | 73, 49, 48 | ⊢ |
| : , : , : |
45 | instantiation | 73, 49, 50 | ⊢ |
| : , : , : |
46 | instantiation | 51, 57 | ⊢ |
| : |
47 | instantiation | 73, 71, 52 | ⊢ |
| : , : , : |
48 | instantiation | 73, 53, 54 | ⊢ |
| : , : , : |
49 | theorem | | ⊢ |
| proveit.numbers.number_sets.complex_numbers.real_within_complex |
50 | instantiation | 55, 56, 57 | ⊢ |
| : , : , : |
51 | theorem | | ⊢ |
| proveit.numbers.number_sets.natural_numbers.nonzero_if_is_nat_pos |
52 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.nat2 |
53 | theorem | | ⊢ |
| proveit.numbers.number_sets.real_numbers.rational_within_real |
54 | instantiation | 73, 58, 59 | ⊢ |
| : , : , : |
55 | theorem | | ⊢ |
| proveit.logic.sets.inclusion.unfold_subset_eq |
56 | instantiation | 60, 61 | ⊢ |
| : , : |
57 | theorem | | ⊢ |
| proveit.physics.quantum.QPE._two_pow_t_is_nat_pos |
58 | theorem | | ⊢ |
| proveit.numbers.number_sets.rational_numbers.int_within_rational |
59 | instantiation | 73, 62, 63 | ⊢ |
| : , : , : |
60 | theorem | | ⊢ |
| proveit.logic.sets.inclusion.relax_proper_subset |
61 | theorem | | ⊢ |
| proveit.numbers.number_sets.real_numbers.nat_pos_within_real |
62 | instantiation | 64, 65, 70 | ⊢ |
| : , : |
63 | assumption | | ⊢ |
64 | theorem | | ⊢ |
| proveit.numbers.number_sets.integers.int_interval_within_int |
65 | instantiation | 66, 67, 68 | ⊢ |
| : , : |
66 | theorem | | ⊢ |
| proveit.numbers.addition.add_int_closure_bin |
67 | instantiation | 69, 70 | ⊢ |
| : |
68 | instantiation | 73, 71, 72 | ⊢ |
| : , : , : |
69 | theorem | | ⊢ |
| proveit.numbers.negation.int_closure |
70 | instantiation | 73, 74, 75 | ⊢ |
| : , : , : |
71 | theorem | | ⊢ |
| proveit.numbers.number_sets.integers.nat_within_int |
72 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.nat1 |
73 | theorem | | ⊢ |
| proveit.logic.sets.inclusion.superset_membership_from_proper_subset |
74 | theorem | | ⊢ |
| proveit.numbers.number_sets.integers.nat_pos_within_int |
75 | theorem | | ⊢ |
| proveit.physics.quantum.QPE._two_pow_t_minus_one_is_nat_pos |
*equality replacement requirements |