| step type | requirements | statement |
0 | generalization | 1 | ⊢ |
1 | instantiation | 2, 3 | ⊢ |
| : , : , : |
2 | axiom | | ⊢ |
| proveit.core_expr_types.conditionals.conditional_substitution |
3 | deduction | 4 | ⊢ |
4 | instantiation | 5, 6, 7 | , ⊢ |
| : , : |
5 | theorem | | ⊢ |
| proveit.numbers.multiplication.commutation |
6 | instantiation | 9, 10, 8 | ⊢ |
| : , : |
7 | instantiation | 9, 10, 11 | , ⊢ |
| : , : |
8 | instantiation | 42, 12, 13 | ⊢ |
| : , : , : |
9 | theorem | | ⊢ |
| proveit.numbers.exponentiation.exp_complex_closure |
10 | instantiation | 94, 66, 14 | ⊢ |
| : , : , : |
11 | instantiation | 15, 16 | , ⊢ |
| : |
12 | instantiation | 59, 45, 17 | ⊢ |
| : , : |
13 | instantiation | 36, 18, 19 | ⊢ |
| : , : , : |
14 | instantiation | 94, 70, 20 | ⊢ |
| : , : , : |
15 | theorem | | ⊢ |
| proveit.numbers.negation.complex_closure |
16 | instantiation | 21, 22, 23, 24 | , ⊢ |
| : , : |
17 | instantiation | 42, 25, 26 | ⊢ |
| : , : , : |
18 | instantiation | 51, 96, 46, 52, 27, 53, 45, 60, 41, 61 | ⊢ |
| : , : , : , : , : , : |
19 | instantiation | 51, 52, 91, 46, 53, 47, 27, 56, 57, 60, 41, 61 | ⊢ |
| : , : , : , : , : , : |
20 | theorem | | ⊢ |
| proveit.numbers.number_sets.real_numbers.e_is_real_pos |
21 | theorem | | ⊢ |
| proveit.numbers.division.div_complex_closure |
22 | instantiation | 42, 28, 29 | , ⊢ |
| : , : , : |
23 | instantiation | 94, 66, 30 | ⊢ |
| : , : , : |
24 | instantiation | 31, 32 | ⊢ |
| : |
25 | instantiation | 59, 33, 61 | ⊢ |
| : , : |
26 | instantiation | 51, 52, 91, 96, 53, 34, 60, 41, 61 | ⊢ |
| : , : , : , : , : , : |
27 | instantiation | 58 | ⊢ |
| : , : , : |
28 | instantiation | 59, 45, 35 | , ⊢ |
| : , : |
29 | instantiation | 36, 37, 38 | , ⊢ |
| : , : , : |
30 | instantiation | 94, 72, 39 | ⊢ |
| : , : , : |
31 | theorem | | ⊢ |
| proveit.numbers.number_sets.natural_numbers.nonzero_if_is_nat_pos |
32 | instantiation | 40, 91, 88 | ⊢ |
| : , : |
33 | instantiation | 59, 60, 41 | ⊢ |
| : , : |
34 | instantiation | 62 | ⊢ |
| : , : |
35 | instantiation | 42, 43, 44 | , ⊢ |
| : , : , : |
36 | axiom | | ⊢ |
| proveit.logic.equality.equals_transitivity |
37 | instantiation | 51, 96, 46, 52, 48, 53, 45, 60, 61, 55 | , ⊢ |
| : , : , : , : , : , : |
38 | instantiation | 51, 52, 91, 46, 53, 47, 48, 56, 57, 60, 61, 55 | , ⊢ |
| : , : , : , : , : , : |
39 | instantiation | 94, 75, 84 | ⊢ |
| : , : , : |
40 | theorem | | ⊢ |
| proveit.numbers.exponentiation.exp_natpos_closure |
41 | instantiation | 94, 66, 49 | ⊢ |
| : , : , : |
42 | theorem | | ⊢ |
| proveit.logic.equality.sub_right_side_into |
43 | instantiation | 59, 50, 55 | , ⊢ |
| : , : |
44 | instantiation | 51, 52, 91, 96, 53, 54, 60, 61, 55 | , ⊢ |
| : , : , : , : , : , : |
45 | instantiation | 59, 56, 57 | ⊢ |
| : , : |
46 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.nat3 |
47 | instantiation | 62 | ⊢ |
| : , : |
48 | instantiation | 58 | ⊢ |
| : , : , : |
49 | theorem | | ⊢ |
| proveit.physics.quantum.QPE._phase_is_real |
50 | instantiation | 59, 60, 61 | ⊢ |
| : , : |
51 | theorem | | ⊢ |
| proveit.numbers.multiplication.disassociation |
52 | axiom | | ⊢ |
| proveit.numbers.number_sets.natural_numbers.zero_in_nats |
53 | theorem | | ⊢ |
| proveit.core_expr_types.tuples.tuple_len_0_typical_eq |
54 | instantiation | 62 | ⊢ |
| : , : |
55 | instantiation | 94, 66, 63 | ⊢ |
| : , : , : |
56 | instantiation | 94, 66, 64 | ⊢ |
| : , : , : |
57 | instantiation | 94, 66, 65 | ⊢ |
| : , : , : |
58 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.tuple_len_3_typical_eq |
59 | theorem | | ⊢ |
| proveit.numbers.multiplication.mult_complex_closure_bin |
60 | theorem | | ⊢ |
| proveit.numbers.number_sets.complex_numbers.i_is_complex |
61 | instantiation | 94, 66, 67 | ⊢ |
| : , : , : |
62 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.tuple_len_2_typical_eq |
63 | instantiation | 94, 72, 68 | ⊢ |
| : , : , : |
64 | instantiation | 94, 72, 69 | ⊢ |
| : , : , : |
65 | instantiation | 94, 70, 71 | ⊢ |
| : , : , : |
66 | theorem | | ⊢ |
| proveit.numbers.number_sets.complex_numbers.real_within_complex |
67 | instantiation | 94, 72, 73 | ⊢ |
| : , : , : |
68 | instantiation | 94, 75, 74 | ⊢ |
| : , : , : |
69 | instantiation | 94, 75, 87 | ⊢ |
| : , : , : |
70 | theorem | | ⊢ |
| proveit.numbers.number_sets.real_numbers.real_pos_within_real |
71 | theorem | | ⊢ |
| proveit.numbers.number_sets.real_numbers.pi_is_real_pos |
72 | theorem | | ⊢ |
| proveit.numbers.number_sets.real_numbers.rational_within_real |
73 | instantiation | 94, 75, 76 | ⊢ |
| : , : , : |
74 | instantiation | 94, 78, 77 | ⊢ |
| : , : , : |
75 | theorem | | ⊢ |
| proveit.numbers.number_sets.rational_numbers.int_within_rational |
76 | instantiation | 94, 78, 79 | ⊢ |
| : , : , : |
77 | assumption | | ⊢ |
78 | instantiation | 80, 81, 82 | ⊢ |
| : , : |
79 | assumption | | ⊢ |
80 | theorem | | ⊢ |
| proveit.numbers.number_sets.integers.int_interval_within_int |
81 | theorem | | ⊢ |
| proveit.numbers.number_sets.integers.zero_is_int |
82 | instantiation | 83, 84, 85 | ⊢ |
| : , : |
83 | theorem | | ⊢ |
| proveit.numbers.addition.add_int_closure_bin |
84 | instantiation | 86, 87, 88 | ⊢ |
| : , : |
85 | instantiation | 89, 90 | ⊢ |
| : |
86 | theorem | | ⊢ |
| proveit.numbers.exponentiation.exp_int_closure |
87 | instantiation | 94, 95, 91 | ⊢ |
| : , : , : |
88 | instantiation | 94, 92, 93 | ⊢ |
| : , : , : |
89 | theorem | | ⊢ |
| proveit.numbers.negation.int_closure |
90 | instantiation | 94, 95, 96 | ⊢ |
| : , : , : |
91 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.nat2 |
92 | theorem | | ⊢ |
| proveit.numbers.number_sets.natural_numbers.nat_pos_within_nat |
93 | axiom | | ⊢ |
| proveit.physics.quantum.QPE._t_in_natural_pos |
94 | theorem | | ⊢ |
| proveit.logic.sets.inclusion.superset_membership_from_proper_subset |
95 | theorem | | ⊢ |
| proveit.numbers.number_sets.integers.nat_within_int |
96 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.nat1 |