| step type | requirements | statement |
0 | modus ponens | 1, 2 | ⊢ |
1 | instantiation | 3 | ⊢ |
| : , : , : |
2 | generalization | 4 | ⊢ |
3 | theorem | | ⊢ |
| proveit.numbers.summation.summation_real_closure |
4 | instantiation | 5, 6, 7, 8 | , ⊢ |
| : , : |
5 | theorem | | ⊢ |
| proveit.numbers.division.div_real_closure |
6 | instantiation | 108, 46, 9 | ⊢ |
| : , : , : |
7 | instantiation | 54, 10, 11 | , ⊢ |
| : , : |
8 | instantiation | 12, 110, 13, 14, 15 | , ⊢ |
| : , : |
9 | instantiation | 108, 53, 97 | ⊢ |
| : , : , : |
10 | instantiation | 108, 46, 16 | ⊢ |
| : , : , : |
11 | instantiation | 17, 35, 110 | , ⊢ |
| : , : |
12 | theorem | | ⊢ |
| proveit.numbers.multiplication.mult_not_eq_zero |
13 | instantiation | 18 | ⊢ |
| : , : |
14 | instantiation | 108, 19, 20 | ⊢ |
| : , : , : |
15 | instantiation | 21, 22, 23 | , ⊢ |
| : , : |
16 | instantiation | 108, 53, 24 | ⊢ |
| : , : , : |
17 | theorem | | ⊢ |
| proveit.numbers.exponentiation.exp_real_closure_nat_power |
18 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.tuple_len_2_typical_eq |
19 | theorem | | ⊢ |
| proveit.numbers.number_sets.complex_numbers.real_nonzero_within_complex_nonzero |
20 | instantiation | 108, 25, 26 | ⊢ |
| : , : , : |
21 | theorem | | ⊢ |
| proveit.numbers.exponentiation.exp_complex_nonzero_closure |
22 | instantiation | 27, 28, 29 | , ⊢ |
| : |
23 | instantiation | 108, 34, 30 | ⊢ |
| : , : , : |
24 | instantiation | 108, 109, 31 | ⊢ |
| : , : , : |
25 | theorem | | ⊢ |
| proveit.numbers.number_sets.real_numbers.rational_nonzero_within_real_nonzero |
26 | instantiation | 108, 32, 33 | ⊢ |
| : , : , : |
27 | theorem | | ⊢ |
| proveit.numbers.number_sets.complex_numbers.nonzero_complex_is_complex_nonzero |
28 | instantiation | 108, 34, 35 | , ⊢ |
| : , : , : |
29 | instantiation | 36, 37 | , ⊢ |
| : , : |
30 | instantiation | 108, 46, 38 | ⊢ |
| : , : , : |
31 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.nat4 |
32 | theorem | | ⊢ |
| proveit.numbers.number_sets.rational_numbers.nonzero_int_within_rational_nonzero |
33 | instantiation | 108, 39, 40 | ⊢ |
| : , : , : |
34 | theorem | | ⊢ |
| proveit.numbers.number_sets.complex_numbers.real_within_complex |
35 | instantiation | 41, 42, 43 | , ⊢ |
| : , : |
36 | theorem | | ⊢ |
| proveit.numbers.addition.subtraction.nonzero_difference_if_different |
37 | instantiation | 44, 45 | , ⊢ |
| : , : |
38 | instantiation | 108, 53, 107 | ⊢ |
| : , : , : |
39 | theorem | | ⊢ |
| proveit.numbers.number_sets.integers.nat_pos_within_nonzero_int |
40 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.posnat4 |
41 | theorem | | ⊢ |
| proveit.numbers.addition.add_real_closure_bin |
42 | instantiation | 108, 46, 47 | , ⊢ |
| : , : , : |
43 | instantiation | 48, 49 | ⊢ |
| : |
44 | theorem | | ⊢ |
| proveit.logic.equality.not_equals_symmetry |
45 | instantiation | 50, 51, 61, 52 | , ⊢ |
| : , : |
46 | theorem | | ⊢ |
| proveit.numbers.number_sets.real_numbers.rational_within_real |
47 | instantiation | 108, 53, 61 | , ⊢ |
| : , : , : |
48 | theorem | | ⊢ |
| proveit.numbers.negation.real_closure |
49 | instantiation | 54, 55, 56 | ⊢ |
| : , : |
50 | theorem | | ⊢ |
| proveit.physics.quantum.QPE._scaled_delta_b_not_eq_nonzeroInt |
51 | instantiation | 57, 58, 100, 59 | ⊢ |
| : , : , : , : , : |
52 | instantiation | 60, 61, 62, 63 | , ⊢ |
| : , : |
53 | theorem | | ⊢ |
| proveit.numbers.number_sets.rational_numbers.int_within_rational |
54 | theorem | | ⊢ |
| proveit.numbers.multiplication.mult_real_closure_bin |
55 | instantiation | 64, 65, 66 | ⊢ |
| : , : , : |
56 | instantiation | 67, 68 | ⊢ |
| : |
57 | theorem | | ⊢ |
| proveit.logic.sets.enumeration.in_enumerated_set |
58 | axiom | | ⊢ |
| proveit.numbers.number_sets.natural_numbers.zero_in_nats |
59 | theorem | | ⊢ |
| proveit.core_expr_types.tuples.tuple_len_0_typical_eq |
60 | theorem | | ⊢ |
| proveit.numbers.ordering.less_is_not_eq_int |
61 | instantiation | 108, 69, 78 | , ⊢ |
| : , : , : |
62 | theorem | | ⊢ |
| proveit.numbers.number_sets.integers.zero_is_int |
63 | instantiation | 70, 71, 72 | , ⊢ |
| : , : , : |
64 | theorem | | ⊢ |
| proveit.logic.sets.inclusion.unfold_subset_eq |
65 | instantiation | 73, 74 | ⊢ |
| : , : |
66 | theorem | | ⊢ |
| proveit.physics.quantum.QPE._two_pow_t_is_nat_pos |
67 | theorem | | ⊢ |
| proveit.physics.quantum.QPE._delta_b_is_real |
68 | theorem | | ⊢ |
| proveit.physics.quantum.QPE._best_floor_is_int |
69 | instantiation | 95, 76, 77 | ⊢ |
| : , : |
70 | theorem | | ⊢ |
| proveit.numbers.ordering.transitivity_less_eq_less |
71 | instantiation | 75, 76, 77, 78 | , ⊢ |
| : , : , : |
72 | instantiation | 79, 80 | ⊢ |
| : |
73 | theorem | | ⊢ |
| proveit.logic.sets.inclusion.relax_proper_subset |
74 | theorem | | ⊢ |
| proveit.numbers.number_sets.real_numbers.nat_pos_within_real |
75 | theorem | | ⊢ |
| proveit.numbers.number_sets.integers.interval_upper_bound |
76 | instantiation | 101, 81, 97 | ⊢ |
| : , : |
77 | instantiation | 106, 82 | ⊢ |
| : |
78 | assumption | | ⊢ |
79 | theorem | | ⊢ |
| proveit.numbers.number_sets.integers.negative_if_in_neg_int |
80 | instantiation | 83, 84 | ⊢ |
| : |
81 | instantiation | 106, 102 | ⊢ |
| : |
82 | instantiation | 101, 89, 97 | ⊢ |
| : , : |
83 | theorem | | ⊢ |
| proveit.numbers.negation.int_neg_closure |
84 | instantiation | 85, 86, 87 | ⊢ |
| : , : |
85 | theorem | | ⊢ |
| proveit.numbers.addition.add_nat_pos_closure_bin |
86 | instantiation | 88, 89, 90 | ⊢ |
| : |
87 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.posnat1 |
88 | theorem | | ⊢ |
| proveit.numbers.number_sets.integers.pos_int_is_natural_pos |
89 | instantiation | 108, 91, 99 | ⊢ |
| : , : , : |
90 | instantiation | 92, 93, 94 | ⊢ |
| : , : , : |
91 | instantiation | 95, 97, 98 | ⊢ |
| : , : |
92 | theorem | | ⊢ |
| proveit.numbers.ordering.transitivity_less_less_eq |
93 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.less_0_1 |
94 | instantiation | 96, 97, 98, 99 | ⊢ |
| : , : , : |
95 | theorem | | ⊢ |
| proveit.numbers.number_sets.integers.int_interval_within_int |
96 | theorem | | ⊢ |
| proveit.numbers.number_sets.integers.interval_lower_bound |
97 | instantiation | 108, 109, 100 | ⊢ |
| : , : , : |
98 | instantiation | 101, 102, 103 | ⊢ |
| : , : |
99 | assumption | | ⊢ |
100 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.nat1 |
101 | theorem | | ⊢ |
| proveit.numbers.addition.add_int_closure_bin |
102 | instantiation | 108, 104, 105 | ⊢ |
| : , : , : |
103 | instantiation | 106, 107 | ⊢ |
| : |
104 | theorem | | ⊢ |
| proveit.numbers.number_sets.integers.nat_pos_within_int |
105 | theorem | | ⊢ |
| proveit.physics.quantum.QPE._two_pow_t_minus_one_is_nat_pos |
106 | theorem | | ⊢ |
| proveit.numbers.negation.int_closure |
107 | instantiation | 108, 109, 110 | ⊢ |
| : , : , : |
108 | theorem | | ⊢ |
| proveit.logic.sets.inclusion.superset_membership_from_proper_subset |
109 | theorem | | ⊢ |
| proveit.numbers.number_sets.integers.nat_within_int |
110 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.nat2 |