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