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