| step type | requirements | statement |
0 | instantiation | 1, 2 | ⊢ |
| : , : , : |
1 | axiom | | ⊢ |
| proveit.logic.equality.substitution |
2 | modus ponens | 3, 4 | ⊢ |
3 | instantiation | 5, 76 | ⊢ |
| : , : , : , : , : , : , : |
4 | generalization | 6 | ⊢ |
5 | theorem | | ⊢ |
| proveit.core_expr_types.lambda_maps.general_lambda_substitution |
6 | instantiation | 7, 8 | , ⊢ |
| : , : |
7 | theorem | | ⊢ |
| proveit.logic.equality.equals_reversal |
8 | instantiation | 9, 19, 10, 11, 12* | , ⊢ |
| : , : , : , : |
9 | theorem | | ⊢ |
| proveit.numbers.division.prod_of_fracs |
10 | instantiation | 97, 13, 14 | ⊢ |
| : , : , : |
11 | instantiation | 15, 16, 17 | , ⊢ |
| : , : |
12 | instantiation | 18, 19 | ⊢ |
| : |
13 | theorem | | ⊢ |
| proveit.numbers.number_sets.complex_numbers.real_nonzero_within_complex_nonzero |
14 | instantiation | 97, 20, 21 | ⊢ |
| : , : , : |
15 | theorem | | ⊢ |
| proveit.numbers.exponentiation.exp_complex_nonzero_closure |
16 | instantiation | 22, 23, 24 | , ⊢ |
| : |
17 | instantiation | 97, 29, 25 | ⊢ |
| : , : , : |
18 | theorem | | ⊢ |
| proveit.numbers.multiplication.elim_one_left |
19 | instantiation | 97, 29, 26 | ⊢ |
| : , : , : |
20 | theorem | | ⊢ |
| proveit.numbers.number_sets.real_numbers.rational_nonzero_within_real_nonzero |
21 | instantiation | 97, 27, 28 | ⊢ |
| : , : , : |
22 | theorem | | ⊢ |
| proveit.numbers.number_sets.complex_numbers.nonzero_complex_is_complex_nonzero |
23 | instantiation | 97, 29, 30 | , ⊢ |
| : , : , : |
24 | instantiation | 31, 32 | , ⊢ |
| : , : |
25 | instantiation | 97, 42, 33 | ⊢ |
| : , : , : |
26 | instantiation | 97, 42, 34 | ⊢ |
| : , : , : |
27 | theorem | | ⊢ |
| proveit.numbers.number_sets.rational_numbers.nonzero_int_within_rational_nonzero |
28 | instantiation | 97, 35, 36 | ⊢ |
| : , : , : |
29 | theorem | | ⊢ |
| proveit.numbers.number_sets.complex_numbers.real_within_complex |
30 | instantiation | 37, 38, 39 | , ⊢ |
| : , : |
31 | theorem | | ⊢ |
| proveit.numbers.addition.subtraction.nonzero_difference_if_different |
32 | instantiation | 40, 41 | , ⊢ |
| : , : |
33 | instantiation | 97, 49, 96 | ⊢ |
| : , : , : |
34 | instantiation | 97, 49, 86 | ⊢ |
| : , : , : |
35 | theorem | | ⊢ |
| proveit.numbers.number_sets.integers.nat_pos_within_nonzero_int |
36 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.posnat4 |
37 | theorem | | ⊢ |
| proveit.numbers.addition.add_real_closure_bin |
38 | instantiation | 97, 42, 43 | , ⊢ |
| : , : , : |
39 | instantiation | 44, 45 | ⊢ |
| : |
40 | theorem | | ⊢ |
| proveit.logic.equality.not_equals_symmetry |
41 | instantiation | 46, 47, 63, 48 | , ⊢ |
| : , : |
42 | theorem | | ⊢ |
| proveit.numbers.number_sets.real_numbers.rational_within_real |
43 | instantiation | 97, 49, 63 | , ⊢ |
| : , : , : |
44 | theorem | | ⊢ |
| proveit.numbers.negation.real_closure |
45 | instantiation | 50, 51, 52 | ⊢ |
| : , : |
46 | theorem | | ⊢ |
| proveit.physics.quantum.QPE._scaled_delta_b_not_eq_nonzeroInt |
47 | instantiation | 53, 54, 89, 55 | ⊢ |
| : , : , : , : , : |
48 | instantiation | 56, 57 | , ⊢ |
| : |
49 | theorem | | ⊢ |
| proveit.numbers.number_sets.rational_numbers.int_within_rational |
50 | theorem | | ⊢ |
| proveit.numbers.multiplication.mult_real_closure_bin |
51 | instantiation | 58, 59, 60 | ⊢ |
| : , : , : |
52 | instantiation | 61, 62 | ⊢ |
| : |
53 | theorem | | ⊢ |
| proveit.logic.sets.enumeration.in_enumerated_set |
54 | axiom | | ⊢ |
| proveit.numbers.number_sets.natural_numbers.zero_in_nats |
55 | theorem | | ⊢ |
| proveit.core_expr_types.tuples.tuple_len_0_typical_eq |
56 | theorem | | ⊢ |
| proveit.numbers.number_sets.natural_numbers.nonzero_if_is_nat_pos |
57 | instantiation | 77, 63, 64 | , ⊢ |
| : |
58 | theorem | | ⊢ |
| proveit.logic.sets.inclusion.unfold_subset_eq |
59 | instantiation | 65, 66 | ⊢ |
| : , : |
60 | theorem | | ⊢ |
| proveit.physics.quantum.QPE._two_pow_t_is_nat_pos |
61 | theorem | | ⊢ |
| proveit.physics.quantum.QPE._delta_b_is_real |
62 | theorem | | ⊢ |
| proveit.physics.quantum.QPE._best_floor_is_int |
63 | instantiation | 97, 67, 73 | , ⊢ |
| : , : , : |
64 | instantiation | 81, 68, 69 | , ⊢ |
| : , : , : |
65 | theorem | | ⊢ |
| proveit.logic.sets.inclusion.relax_proper_subset |
66 | theorem | | ⊢ |
| proveit.numbers.number_sets.real_numbers.nat_pos_within_real |
67 | instantiation | 84, 72, 91 | ⊢ |
| : , : |
68 | instantiation | 70, 71 | ⊢ |
| : |
69 | instantiation | 85, 72, 91, 73 | , ⊢ |
| : , : , : |
70 | theorem | | ⊢ |
| proveit.numbers.number_sets.natural_numbers.natural_pos_is_pos |
71 | instantiation | 74, 75, 76 | ⊢ |
| : , : |
72 | instantiation | 90, 78, 86 | ⊢ |
| : , : |
73 | assumption | | ⊢ |
74 | theorem | | ⊢ |
| proveit.numbers.addition.add_nat_pos_closure_bin |
75 | instantiation | 77, 78, 79 | ⊢ |
| : |
76 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.posnat1 |
77 | theorem | | ⊢ |
| proveit.numbers.number_sets.integers.pos_int_is_natural_pos |
78 | instantiation | 97, 80, 88 | ⊢ |
| : , : , : |
79 | instantiation | 81, 82, 83 | ⊢ |
| : , : , : |
80 | instantiation | 84, 86, 87 | ⊢ |
| : , : |
81 | theorem | | ⊢ |
| proveit.numbers.ordering.transitivity_less_less_eq |
82 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.less_0_1 |
83 | instantiation | 85, 86, 87, 88 | ⊢ |
| : , : , : |
84 | theorem | | ⊢ |
| proveit.numbers.number_sets.integers.int_interval_within_int |
85 | theorem | | ⊢ |
| proveit.numbers.number_sets.integers.interval_lower_bound |
86 | instantiation | 97, 98, 89 | ⊢ |
| : , : , : |
87 | instantiation | 90, 91, 92 | ⊢ |
| : , : |
88 | assumption | | ⊢ |
89 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.nat1 |
90 | theorem | | ⊢ |
| proveit.numbers.addition.add_int_closure_bin |
91 | instantiation | 97, 93, 94 | ⊢ |
| : , : , : |
92 | instantiation | 95, 96 | ⊢ |
| : |
93 | theorem | | ⊢ |
| proveit.numbers.number_sets.integers.nat_pos_within_int |
94 | theorem | | ⊢ |
| proveit.physics.quantum.QPE._two_pow_t_minus_one_is_nat_pos |
95 | theorem | | ⊢ |
| proveit.numbers.negation.int_closure |
96 | instantiation | 97, 98, 99 | ⊢ |
| : , : , : |
97 | theorem | | ⊢ |
| proveit.logic.sets.inclusion.superset_membership_from_proper_subset |
98 | theorem | | ⊢ |
| proveit.numbers.number_sets.integers.nat_within_int |
99 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.nat2 |
*equality replacement requirements |