| step type | requirements | statement |
0 | instantiation | 1, 2, 3 | ⊢ |
| : , : , : |
1 | reference | 6 | ⊢ |
2 | instantiation | 4, 5 | ⊢ |
| : , : , : |
3 | instantiation | 6, 7, 8 | ⊢ |
| : , : , : |
4 | axiom | | ⊢ |
| proveit.logic.equality.substitution |
5 | instantiation | 9, 37, 30, 10, 11, 12, 13* | ⊢ |
| : , : , : |
6 | axiom | | ⊢ |
| proveit.logic.equality.equals_transitivity |
7 | instantiation | 14, 73, 83, 16, 18, 17, 41, 19, 20 | ⊢ |
| : , : , : , : , : , : |
8 | instantiation | 15, 16, 83, 17, 18, 19, 20 | ⊢ |
| : , : , : , : |
9 | theorem | | ⊢ |
| proveit.numbers.exponentiation.real_power_of_product |
10 | instantiation | 21, 52 | ⊢ |
| : |
11 | instantiation | 22, 66 | ⊢ |
| : |
12 | instantiation | 22, 23 | ⊢ |
| : |
13 | instantiation | 24, 25, 64, 26* | ⊢ |
| : , : |
14 | theorem | | ⊢ |
| proveit.numbers.multiplication.disassociation |
15 | theorem | | ⊢ |
| proveit.numbers.multiplication.elim_one_any |
16 | axiom | | ⊢ |
| proveit.numbers.number_sets.natural_numbers.zero_in_nats |
17 | theorem | | ⊢ |
| proveit.core_expr_types.tuples.tuple_len_0_typical_eq |
18 | instantiation | 27 | ⊢ |
| : , : |
19 | instantiation | 81, 51, 28 | ⊢ |
| : , : , : |
20 | instantiation | 29, 30, 31 | ⊢ |
| : , : |
21 | theorem | | ⊢ |
| proveit.numbers.negation.real_closure |
22 | theorem | | ⊢ |
| proveit.numbers.number_sets.natural_numbers.nonzero_if_is_nat_pos |
23 | instantiation | 32, 60, 33 | ⊢ |
| : |
24 | theorem | | ⊢ |
| proveit.numbers.exponentiation.neg_power_as_div |
25 | instantiation | 81, 34, 35 | ⊢ |
| : , : , : |
26 | instantiation | 36, 37 | ⊢ |
| : |
27 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.tuple_len_2_typical_eq |
28 | instantiation | 81, 61, 38 | ⊢ |
| : , : , : |
29 | theorem | | ⊢ |
| proveit.numbers.exponentiation.exp_complex_closure |
30 | instantiation | 81, 51, 39 | ⊢ |
| : , : , : |
31 | instantiation | 40, 41 | ⊢ |
| : |
32 | theorem | | ⊢ |
| proveit.numbers.number_sets.integers.pos_int_is_natural_pos |
33 | instantiation | 42, 43, 44 | ⊢ |
| : , : , : |
34 | theorem | | ⊢ |
| proveit.numbers.number_sets.complex_numbers.real_nonzero_within_complex_nonzero |
35 | instantiation | 81, 45, 46 | ⊢ |
| : , : , : |
36 | theorem | | ⊢ |
| proveit.numbers.exponentiation.complex_x_to_first_power_is_x |
37 | instantiation | 81, 51, 47 | ⊢ |
| : , : , : |
38 | instantiation | 81, 48, 49 | ⊢ |
| : , : , : |
39 | instantiation | 81, 61, 50 | ⊢ |
| : , : , : |
40 | theorem | | ⊢ |
| proveit.numbers.negation.complex_closure |
41 | instantiation | 81, 51, 52 | ⊢ |
| : , : , : |
42 | theorem | | ⊢ |
| proveit.numbers.ordering.transitivity_less_less_eq |
43 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.less_0_1 |
44 | instantiation | 53, 71, 72, 68 | ⊢ |
| : , : , : |
45 | theorem | | ⊢ |
| proveit.numbers.number_sets.real_numbers.rational_nonzero_within_real_nonzero |
46 | instantiation | 81, 54, 55 | ⊢ |
| : , : , : |
47 | instantiation | 81, 61, 56 | ⊢ |
| : , : , : |
48 | theorem | | ⊢ |
| proveit.numbers.number_sets.rational_numbers.rational_pos_within_rational |
49 | instantiation | 57, 58, 59 | ⊢ |
| : , : |
50 | instantiation | 81, 69, 60 | ⊢ |
| : , : , : |
51 | theorem | | ⊢ |
| proveit.numbers.number_sets.complex_numbers.real_within_complex |
52 | instantiation | 81, 61, 62 | ⊢ |
| : , : , : |
53 | theorem | | ⊢ |
| proveit.numbers.number_sets.integers.interval_lower_bound |
54 | theorem | | ⊢ |
| proveit.numbers.number_sets.rational_numbers.nonzero_int_within_rational_nonzero |
55 | instantiation | 81, 63, 66 | ⊢ |
| : , : , : |
56 | instantiation | 81, 69, 80 | ⊢ |
| : , : , : |
57 | theorem | | ⊢ |
| proveit.numbers.division.div_rational_pos_closure |
58 | instantiation | 81, 65, 64 | ⊢ |
| : , : , : |
59 | instantiation | 81, 65, 66 | ⊢ |
| : , : , : |
60 | instantiation | 81, 67, 68 | ⊢ |
| : , : , : |
61 | theorem | | ⊢ |
| proveit.numbers.number_sets.real_numbers.rational_within_real |
62 | instantiation | 81, 69, 71 | ⊢ |
| : , : , : |
63 | theorem | | ⊢ |
| proveit.numbers.number_sets.integers.nat_pos_within_nonzero_int |
64 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.posnat1 |
65 | theorem | | ⊢ |
| proveit.numbers.number_sets.rational_numbers.nat_pos_within_rational_pos |
66 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.posnat2 |
67 | instantiation | 70, 71, 72 | ⊢ |
| : , : |
68 | assumption | | ⊢ |
69 | theorem | | ⊢ |
| proveit.numbers.number_sets.rational_numbers.int_within_rational |
70 | theorem | | ⊢ |
| proveit.numbers.number_sets.integers.int_interval_within_int |
71 | instantiation | 81, 82, 73 | ⊢ |
| : , : , : |
72 | instantiation | 74, 75, 76 | ⊢ |
| : , : |
73 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.nat1 |
74 | theorem | | ⊢ |
| proveit.numbers.addition.add_int_closure_bin |
75 | instantiation | 81, 77, 78 | ⊢ |
| : , : , : |
76 | instantiation | 79, 80 | ⊢ |
| : |
77 | theorem | | ⊢ |
| proveit.numbers.number_sets.integers.nat_pos_within_int |
78 | theorem | | ⊢ |
| proveit.physics.quantum.QPE._two_pow_t_minus_one_is_nat_pos |
79 | theorem | | ⊢ |
| proveit.numbers.negation.int_closure |
80 | instantiation | 81, 82, 83 | ⊢ |
| : , : , : |
81 | theorem | | ⊢ |
| proveit.logic.sets.inclusion.superset_membership_from_proper_subset |
82 | theorem | | ⊢ |
| proveit.numbers.number_sets.integers.nat_within_int |
83 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.nat2 |
*equality replacement requirements |