| step type | requirements | statement |
0 | instantiation | 1, 2, 3 | ⊢ |
| : , : , : |
1 | reference | 54 | ⊢ |
2 | instantiation | 24, 4, 5 | ⊢ |
| : , : , : |
3 | instantiation | 64, 6 | ⊢ |
| : , : , : |
4 | instantiation | 24, 7, 8 | ⊢ |
| : , : , : |
5 | instantiation | 24, 9, 23 | ⊢ |
| : , : , : |
6 | instantiation | 64, 10 | ⊢ |
| : , : , : |
7 | instantiation | 64, 11 | ⊢ |
| : , : , : |
8 | instantiation | 12, 102, 13, 14, 74, 32, 15, 16* | ⊢ |
| : , : , : , : , : , : |
9 | axiom | | ⊢ |
| proveit.physics.quantum.QPE._best_floor_def |
10 | instantiation | 17, 18 | ⊢ |
| : , : |
11 | instantiation | 19, 75 | ⊢ |
| : |
12 | theorem | | ⊢ |
| proveit.numbers.multiplication.distribute_through_subtract |
13 | axiom | | ⊢ |
| proveit.numbers.number_sets.natural_numbers.zero_in_nats |
14 | theorem | | ⊢ |
| proveit.core_expr_types.tuples.tuple_len_0_typical_eq |
15 | instantiation | 20, 48, 74, 42 | ⊢ |
| : , : |
16 | instantiation | 24, 21, 22 | ⊢ |
| : , : , : |
17 | theorem | | ⊢ |
| proveit.logic.equality.equals_reversal |
18 | instantiation | 64, 23 | ⊢ |
| : , : , : |
19 | axiom | | ⊢ |
| proveit.physics.quantum.QPE._delta_b_def |
20 | theorem | | ⊢ |
| proveit.numbers.division.div_complex_closure |
21 | instantiation | 24, 25, 26 | ⊢ |
| : , : , : |
22 | instantiation | 27, 28, 29, 30 | ⊢ |
| : , : , : , : |
23 | instantiation | 31, 74, 32 | ⊢ |
| : , : |
24 | theorem | | ⊢ |
| proveit.logic.equality.sub_right_side_into |
25 | instantiation | 33, 47, 48, 34, 35 | ⊢ |
| : , : , : , : , : |
26 | instantiation | 54, 36, 37 | ⊢ |
| : , : , : |
27 | theorem | | ⊢ |
| proveit.logic.equality.four_chain_transitivity |
28 | instantiation | 64, 38 | ⊢ |
| : , : , : |
29 | instantiation | 64, 39 | ⊢ |
| : , : , : |
30 | instantiation | 73, 48 | ⊢ |
| : |
31 | theorem | | ⊢ |
| proveit.numbers.multiplication.commutation |
32 | instantiation | 100, 76, 40 | ⊢ |
| : , : , : |
33 | theorem | | ⊢ |
| proveit.numbers.division.mult_frac_cancel_numer_left |
34 | instantiation | 41, 74, 42 | ⊢ |
| : |
35 | instantiation | 100, 43, 44 | ⊢ |
| : , : , : |
36 | instantiation | 64, 45 | ⊢ |
| : , : , : |
37 | instantiation | 64, 46 | ⊢ |
| : , : , : |
38 | instantiation | 66, 47 | ⊢ |
| : |
39 | instantiation | 66, 48 | ⊢ |
| : |
40 | theorem | | ⊢ |
| proveit.physics.quantum.QPE._phase_is_real |
41 | theorem | | ⊢ |
| proveit.numbers.number_sets.complex_numbers.nonzero_complex_is_complex_nonzero |
42 | instantiation | 49, 50, 51 | ⊢ |
| : , : |
43 | theorem | | ⊢ |
| proveit.numbers.number_sets.complex_numbers.real_nonzero_within_complex_nonzero |
44 | instantiation | 100, 52, 53 | ⊢ |
| : , : , : |
45 | instantiation | 54, 55, 56 | ⊢ |
| : , : , : |
46 | instantiation | 64, 57 | ⊢ |
| : , : , : |
47 | instantiation | 100, 76, 58 | ⊢ |
| : , : , : |
48 | instantiation | 100, 76, 59 | ⊢ |
| : , : , : |
49 | theorem | | ⊢ |
| proveit.numbers.exponentiation.exp_rational_non_zero__not_zero |
50 | instantiation | 100, 62, 60 | ⊢ |
| : , : , : |
51 | instantiation | 100, 62, 61 | ⊢ |
| : , : , : |
52 | theorem | | ⊢ |
| proveit.numbers.number_sets.real_numbers.rational_nonzero_within_real_nonzero |
53 | instantiation | 100, 62, 63 | ⊢ |
| : , : , : |
54 | axiom | | ⊢ |
| proveit.logic.equality.equals_transitivity |
55 | instantiation | 64, 65 | ⊢ |
| : , : , : |
56 | instantiation | 66, 74 | ⊢ |
| : |
57 | instantiation | 67, 74 | ⊢ |
| : |
58 | instantiation | 100, 81, 68 | ⊢ |
| : , : , : |
59 | instantiation | 100, 81, 69 | ⊢ |
| : , : , : |
60 | instantiation | 100, 71, 70 | ⊢ |
| : , : , : |
61 | instantiation | 100, 71, 99 | ⊢ |
| : , : , : |
62 | theorem | | ⊢ |
| proveit.numbers.number_sets.rational_numbers.nonzero_int_within_rational_nonzero |
63 | instantiation | 100, 71, 72 | ⊢ |
| : , : , : |
64 | axiom | | ⊢ |
| proveit.logic.equality.substitution |
65 | instantiation | 73, 74 | ⊢ |
| : |
66 | theorem | | ⊢ |
| proveit.numbers.division.frac_one_denom |
67 | theorem | | ⊢ |
| proveit.numbers.multiplication.elim_one_right |
68 | instantiation | 100, 85, 96 | ⊢ |
| : , : , : |
69 | instantiation | 100, 85, 75 | ⊢ |
| : , : , : |
70 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.posnat2 |
71 | theorem | | ⊢ |
| proveit.numbers.number_sets.integers.nat_pos_within_nonzero_int |
72 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.posnat1 |
73 | theorem | | ⊢ |
| proveit.numbers.multiplication.elim_one_left |
74 | instantiation | 100, 76, 77 | ⊢ |
| : , : , : |
75 | instantiation | 78, 79, 80 | ⊢ |
| : , : , : |
76 | theorem | | ⊢ |
| proveit.numbers.number_sets.complex_numbers.real_within_complex |
77 | instantiation | 100, 81, 82 | ⊢ |
| : , : , : |
78 | theorem | | ⊢ |
| proveit.logic.sets.inclusion.unfold_subset_eq |
79 | instantiation | 83, 84 | ⊢ |
| : , : |
80 | theorem | | ⊢ |
| proveit.physics.quantum.QPE._best_floor_is_in_m_domain |
81 | theorem | | ⊢ |
| proveit.numbers.number_sets.real_numbers.rational_within_real |
82 | instantiation | 100, 85, 90 | ⊢ |
| : , : , : |
83 | theorem | | ⊢ |
| proveit.logic.sets.inclusion.relax_proper_subset |
84 | instantiation | 86, 87, 88 | ⊢ |
| : , : |
85 | theorem | | ⊢ |
| proveit.numbers.number_sets.rational_numbers.int_within_rational |
86 | theorem | | ⊢ |
| proveit.numbers.number_sets.integers.int_interval_within_int |
87 | theorem | | ⊢ |
| proveit.numbers.number_sets.integers.zero_is_int |
88 | instantiation | 89, 90, 91 | ⊢ |
| : , : |
89 | theorem | | ⊢ |
| proveit.numbers.addition.add_int_closure_bin |
90 | instantiation | 92, 93, 94 | ⊢ |
| : , : |
91 | instantiation | 95, 96 | ⊢ |
| : |
92 | theorem | | ⊢ |
| proveit.numbers.exponentiation.exp_int_closure |
93 | instantiation | 100, 101, 97 | ⊢ |
| : , : , : |
94 | instantiation | 100, 98, 99 | ⊢ |
| : , : , : |
95 | theorem | | ⊢ |
| proveit.numbers.negation.int_closure |
96 | instantiation | 100, 101, 102 | ⊢ |
| : , : , : |
97 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.nat2 |
98 | theorem | | ⊢ |
| proveit.numbers.number_sets.natural_numbers.nat_pos_within_nat |
99 | axiom | | ⊢ |
| proveit.physics.quantum.QPE._t_in_natural_pos |
100 | theorem | | ⊢ |
| proveit.logic.sets.inclusion.superset_membership_from_proper_subset |
101 | theorem | | ⊢ |
| proveit.numbers.number_sets.integers.nat_within_int |
102 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.nat1 |
*equality replacement requirements |