| step type | requirements | statement |
0 | instantiation | 1, 2 | ⊢ |
| : , : , : |
1 | axiom | | ⊢ |
| proveit.core_expr_types.conditionals.conditional_substitution |
2 | deduction | 3 | ⊢ |
3 | instantiation | 4, 5, 6 | , ⊢ |
| : , : |
4 | theorem | | ⊢ |
| proveit.numbers.multiplication.commutation |
5 | instantiation | 8, 9, 7 | ⊢ |
| : , : |
6 | instantiation | 8, 9, 10 | , ⊢ |
| : , : |
7 | instantiation | 41, 11, 12 | ⊢ |
| : , : , : |
8 | theorem | | ⊢ |
| proveit.numbers.exponentiation.exp_complex_closure |
9 | instantiation | 93, 65, 13 | ⊢ |
| : , : , : |
10 | instantiation | 14, 15 | , ⊢ |
| : |
11 | instantiation | 58, 44, 16 | ⊢ |
| : , : |
12 | instantiation | 35, 17, 18 | ⊢ |
| : , : , : |
13 | instantiation | 93, 69, 19 | ⊢ |
| : , : , : |
14 | theorem | | ⊢ |
| proveit.numbers.negation.complex_closure |
15 | instantiation | 20, 21, 22, 23 | , ⊢ |
| : , : |
16 | instantiation | 41, 24, 25 | ⊢ |
| : , : , : |
17 | instantiation | 50, 95, 45, 51, 26, 52, 44, 59, 40, 60 | ⊢ |
| : , : , : , : , : , : |
18 | instantiation | 50, 51, 90, 45, 52, 46, 26, 55, 56, 59, 40, 60 | ⊢ |
| : , : , : , : , : , : |
19 | theorem | | ⊢ |
| proveit.numbers.number_sets.real_numbers.e_is_real_pos |
20 | theorem | | ⊢ |
| proveit.numbers.division.div_complex_closure |
21 | instantiation | 41, 27, 28 | , ⊢ |
| : , : , : |
22 | instantiation | 93, 65, 29 | ⊢ |
| : , : , : |
23 | instantiation | 30, 31 | ⊢ |
| : |
24 | instantiation | 58, 32, 60 | ⊢ |
| : , : |
25 | instantiation | 50, 51, 90, 95, 52, 33, 59, 40, 60 | ⊢ |
| : , : , : , : , : , : |
26 | instantiation | 57 | ⊢ |
| : , : , : |
27 | instantiation | 58, 44, 34 | , ⊢ |
| : , : |
28 | instantiation | 35, 36, 37 | , ⊢ |
| : , : , : |
29 | instantiation | 93, 71, 38 | ⊢ |
| : , : , : |
30 | theorem | | ⊢ |
| proveit.numbers.number_sets.natural_numbers.nonzero_if_is_nat_pos |
31 | instantiation | 39, 90, 87 | ⊢ |
| : , : |
32 | instantiation | 58, 59, 40 | ⊢ |
| : , : |
33 | instantiation | 61 | ⊢ |
| : , : |
34 | instantiation | 41, 42, 43 | , ⊢ |
| : , : , : |
35 | axiom | | ⊢ |
| proveit.logic.equality.equals_transitivity |
36 | instantiation | 50, 95, 45, 51, 47, 52, 44, 59, 60, 54 | , ⊢ |
| : , : , : , : , : , : |
37 | instantiation | 50, 51, 90, 45, 52, 46, 47, 55, 56, 59, 60, 54 | , ⊢ |
| : , : , : , : , : , : |
38 | instantiation | 93, 74, 83 | ⊢ |
| : , : , : |
39 | theorem | | ⊢ |
| proveit.numbers.exponentiation.exp_natpos_closure |
40 | instantiation | 93, 65, 48 | ⊢ |
| : , : , : |
41 | theorem | | ⊢ |
| proveit.logic.equality.sub_right_side_into |
42 | instantiation | 58, 49, 54 | , ⊢ |
| : , : |
43 | instantiation | 50, 51, 90, 95, 52, 53, 59, 60, 54 | , ⊢ |
| : , : , : , : , : , : |
44 | instantiation | 58, 55, 56 | ⊢ |
| : , : |
45 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.nat3 |
46 | instantiation | 61 | ⊢ |
| : , : |
47 | instantiation | 57 | ⊢ |
| : , : , : |
48 | theorem | | ⊢ |
| proveit.physics.quantum.QPE._phase_is_real |
49 | instantiation | 58, 59, 60 | ⊢ |
| : , : |
50 | theorem | | ⊢ |
| proveit.numbers.multiplication.disassociation |
51 | axiom | | ⊢ |
| proveit.numbers.number_sets.natural_numbers.zero_in_nats |
52 | theorem | | ⊢ |
| proveit.core_expr_types.tuples.tuple_len_0_typical_eq |
53 | instantiation | 61 | ⊢ |
| : , : |
54 | instantiation | 93, 65, 62 | ⊢ |
| : , : , : |
55 | instantiation | 93, 65, 63 | ⊢ |
| : , : , : |
56 | instantiation | 93, 65, 64 | ⊢ |
| : , : , : |
57 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.tuple_len_3_typical_eq |
58 | theorem | | ⊢ |
| proveit.numbers.multiplication.mult_complex_closure_bin |
59 | theorem | | ⊢ |
| proveit.numbers.number_sets.complex_numbers.i_is_complex |
60 | instantiation | 93, 65, 66 | ⊢ |
| : , : , : |
61 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.tuple_len_2_typical_eq |
62 | instantiation | 93, 71, 67 | ⊢ |
| : , : , : |
63 | instantiation | 93, 71, 68 | ⊢ |
| : , : , : |
64 | instantiation | 93, 69, 70 | ⊢ |
| : , : , : |
65 | theorem | | ⊢ |
| proveit.numbers.number_sets.complex_numbers.real_within_complex |
66 | instantiation | 93, 71, 72 | ⊢ |
| : , : , : |
67 | instantiation | 93, 74, 73 | ⊢ |
| : , : , : |
68 | instantiation | 93, 74, 86 | ⊢ |
| : , : , : |
69 | theorem | | ⊢ |
| proveit.numbers.number_sets.real_numbers.real_pos_within_real |
70 | theorem | | ⊢ |
| proveit.numbers.number_sets.real_numbers.pi_is_real_pos |
71 | theorem | | ⊢ |
| proveit.numbers.number_sets.real_numbers.rational_within_real |
72 | instantiation | 93, 74, 75 | ⊢ |
| : , : , : |
73 | instantiation | 93, 77, 76 | ⊢ |
| : , : , : |
74 | theorem | | ⊢ |
| proveit.numbers.number_sets.rational_numbers.int_within_rational |
75 | instantiation | 93, 77, 78 | ⊢ |
| : , : , : |
76 | assumption | | ⊢ |
77 | instantiation | 79, 80, 81 | ⊢ |
| : , : |
78 | assumption | | ⊢ |
79 | theorem | | ⊢ |
| proveit.numbers.number_sets.integers.int_interval_within_int |
80 | theorem | | ⊢ |
| proveit.numbers.number_sets.integers.zero_is_int |
81 | instantiation | 82, 83, 84 | ⊢ |
| : , : |
82 | theorem | | ⊢ |
| proveit.numbers.addition.add_int_closure_bin |
83 | instantiation | 85, 86, 87 | ⊢ |
| : , : |
84 | instantiation | 88, 89 | ⊢ |
| : |
85 | theorem | | ⊢ |
| proveit.numbers.exponentiation.exp_int_closure |
86 | instantiation | 93, 94, 90 | ⊢ |
| : , : , : |
87 | instantiation | 93, 91, 92 | ⊢ |
| : , : , : |
88 | theorem | | ⊢ |
| proveit.numbers.negation.int_closure |
89 | instantiation | 93, 94, 95 | ⊢ |
| : , : , : |
90 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.nat2 |
91 | theorem | | ⊢ |
| proveit.numbers.number_sets.natural_numbers.nat_pos_within_nat |
92 | axiom | | ⊢ |
| proveit.physics.quantum.QPE._t_in_natural_pos |
93 | theorem | | ⊢ |
| proveit.logic.sets.inclusion.superset_membership_from_proper_subset |
94 | theorem | | ⊢ |
| proveit.numbers.number_sets.integers.nat_within_int |
95 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.nat1 |