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