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