| step type | requirements | statement |
0 | instantiation | 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20* | ⊢ |
| : , : , : , : , : , : |
1 | theorem | | ⊢ |
| proveit.physics.quantum.circuits.output_consolidation |
2 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.posnat2 |
3 | instantiation | 92 | ⊢ |
| : , : |
4 | reference | 85 | ⊢ |
5 | reference | 50 | ⊢ |
6 | instantiation | 92 | ⊢ |
| : , : |
7 | instantiation | 21, 22 | ⊢ |
| : , : |
8 | axiom | | ⊢ |
| proveit.physics.quantum.QPE._u_ket_register |
9 | instantiation | 28, 23, 24, 25 | ⊢ |
| : , : , : , : |
10 | instantiation | 51, 26 | ⊢ |
| : , : |
11 | instantiation | 92 | ⊢ |
| : , : |
12 | instantiation | 51, 27 | ⊢ |
| : , : |
13 | instantiation | 28, 29, 30, 31 | ⊢ |
| : , : , : , : |
14 | instantiation | 57, 82, 106, 43 | ⊢ |
| : , : , : |
15 | reference | 46 | ⊢ |
16 | reference | 79 | ⊢ |
17 | reference | 32 | ⊢ |
18 | instantiation | 56, 32, 33 | ⊢ |
| : , : |
19 | instantiation | 34, 75, 35, 36, 37, 38 | ⊢ |
| : , : |
20 | reference | 43 | ⊢ |
21 | theorem | | ⊢ |
| proveit.logic.booleans.conjunction.left_from_and |
22 | instantiation | 39, 85 | ⊢ |
| : |
23 | instantiation | 40 | ⊢ |
| : , : , : |
24 | instantiation | 53 | ⊢ |
| : |
25 | instantiation | 51, 41 | ⊢ |
| : , : |
26 | instantiation | 42, 45, 43 | ⊢ |
| : , : , : |
27 | instantiation | 44, 45, 46 | ⊢ |
| : , : , : |
28 | theorem | | ⊢ |
| proveit.logic.equality.four_chain_transitivity |
29 | instantiation | 47 | ⊢ |
| : , : |
30 | instantiation | 53 | ⊢ |
| : |
31 | instantiation | 51, 48 | ⊢ |
| : , : |
32 | instantiation | 117, 49, 85 | ⊢ |
| : , : , : |
33 | instantiation | 117, 49, 50 | ⊢ |
| : , : , : |
34 | theorem | | ⊢ |
| proveit.logic.booleans.conjunction.and_if_all |
35 | instantiation | 88 | ⊢ |
| : , : , : |
36 | instantiation | 53 | ⊢ |
| : |
37 | instantiation | 51, 52 | ⊢ |
| : , : |
38 | instantiation | 53 | ⊢ |
| : |
39 | theorem | | ⊢ |
| proveit.physics.quantum.QPE._psi_t_ket_is_normalized_vec |
40 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.tuple_len_3 |
41 | instantiation | 58, 54, 55 | ⊢ |
| : , : , : |
42 | theorem | | ⊢ |
| proveit.core_expr_types.tuples.partition_front |
43 | instantiation | 61, 106 | ⊢ |
| : |
44 | theorem | | ⊢ |
| proveit.core_expr_types.tuples.partition_back |
45 | instantiation | 56, 116, 77 | ⊢ |
| : , : |
46 | instantiation | 57, 106, 104, 95 | ⊢ |
| : , : , : |
47 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.tuple_len_2 |
48 | instantiation | 58, 59, 60 | ⊢ |
| : , : , : |
49 | theorem | | ⊢ |
| proveit.numbers.number_sets.natural_numbers.nat_pos_within_nat |
50 | axiom | | ⊢ |
| proveit.physics.quantum.QPE._s_in_nat_pos |
51 | theorem | | ⊢ |
| proveit.logic.equality.equals_reversal |
52 | instantiation | 61, 62 | ⊢ |
| : |
53 | axiom | | ⊢ |
| proveit.logic.equality.equals_reflexivity |
54 | instantiation | 66, 63 | ⊢ |
| : , : , : |
55 | instantiation | 93, 64, 65 | ⊢ |
| : , : , : |
56 | theorem | | ⊢ |
| proveit.numbers.addition.add_nat_closure_bin |
57 | theorem | | ⊢ |
| proveit.numbers.addition.subtraction.subtract_from_add |
58 | theorem | | ⊢ |
| proveit.logic.equality.sub_right_side_into |
59 | instantiation | 66, 67 | ⊢ |
| : , : , : |
60 | instantiation | 93, 68, 69 | ⊢ |
| : , : , : |
61 | theorem | | ⊢ |
| proveit.numbers.addition.elim_zero_left |
62 | instantiation | 117, 108, 70 | ⊢ |
| : , : , : |
63 | instantiation | 74, 75, 71, 116, 77, 119 | ⊢ |
| : , : |
64 | instantiation | 102, 101 | ⊢ |
| : , : , : |
65 | instantiation | 78, 79, 116, 119, 80, 72, 104, 82, 106, 73* | ⊢ |
| : , : , : , : , : , : |
66 | theorem | | ⊢ |
| proveit.core_expr_types.tuples.range_len |
67 | instantiation | 74, 75, 76, 119, 77 | ⊢ |
| : , : |
68 | instantiation | 102, 101 | ⊢ |
| : , : , : |
69 | instantiation | 78, 79, 116, 119, 80, 81, 106, 82, 83* | ⊢ |
| : , : , : , : , : , : |
70 | instantiation | 89, 84, 85 | ⊢ |
| : , : , : |
71 | instantiation | 88 | ⊢ |
| : , : , : |
72 | instantiation | 92 | ⊢ |
| : , : |
73 | instantiation | 93, 86, 87 | ⊢ |
| : , : , : |
74 | theorem | | ⊢ |
| proveit.numbers.addition.add_nat_closure |
75 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.nat3 |
76 | instantiation | 88 | ⊢ |
| : , : , : |
77 | instantiation | 89, 90, 91 | ⊢ |
| : , : , : |
78 | theorem | | ⊢ |
| proveit.numbers.addition.association |
79 | axiom | | ⊢ |
| proveit.numbers.number_sets.natural_numbers.zero_in_nats |
80 | theorem | | ⊢ |
| proveit.core_expr_types.tuples.tuple_len_0_typical_eq |
81 | instantiation | 92 | ⊢ |
| : , : |
82 | theorem | | ⊢ |
| proveit.numbers.number_sets.complex_numbers.zero_is_complex |
83 | instantiation | 93, 94, 95 | ⊢ |
| : , : , : |
84 | instantiation | 98, 96 | ⊢ |
| : , : |
85 | assumption | | ⊢ |
86 | instantiation | 102, 97 | ⊢ |
| : , : , : |
87 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.add_2_1 |
88 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.tuple_len_3_typical_eq |
89 | theorem | | ⊢ |
| proveit.logic.sets.inclusion.unfold_subset_eq |
90 | instantiation | 98, 99 | ⊢ |
| : , : |
91 | instantiation | 100, 101 | ⊢ |
| : , : |
92 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.tuple_len_2_typical_eq |
93 | axiom | | ⊢ |
| proveit.logic.equality.equals_transitivity |
94 | instantiation | 102, 103 | ⊢ |
| : , : , : |
95 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.add_1_1 |
96 | theorem | | ⊢ |
| proveit.numbers.number_sets.real_numbers.nat_pos_within_real |
97 | instantiation | 105, 104 | ⊢ |
| : |
98 | theorem | | ⊢ |
| proveit.logic.sets.inclusion.relax_proper_subset |
99 | theorem | | ⊢ |
| proveit.numbers.number_sets.natural_numbers.zero_set_within_nat |
100 | theorem | | ⊢ |
| proveit.logic.sets.enumeration.fold_singleton |
101 | theorem | | ⊢ |
| proveit.numbers.negation.negated_zero |
102 | axiom | | ⊢ |
| proveit.logic.equality.substitution |
103 | instantiation | 105, 106 | ⊢ |
| : |
104 | instantiation | 117, 108, 107 | ⊢ |
| : , : , : |
105 | theorem | | ⊢ |
| proveit.numbers.addition.elim_zero_right |
106 | instantiation | 117, 108, 109 | ⊢ |
| : , : , : |
107 | instantiation | 117, 111, 110 | ⊢ |
| : , : , : |
108 | theorem | | ⊢ |
| proveit.numbers.number_sets.complex_numbers.real_within_complex |
109 | instantiation | 117, 111, 112 | ⊢ |
| : , : , : |
110 | instantiation | 117, 114, 113 | ⊢ |
| : , : , : |
111 | theorem | | ⊢ |
| proveit.numbers.number_sets.real_numbers.rational_within_real |
112 | instantiation | 117, 114, 115 | ⊢ |
| : , : , : |
113 | instantiation | 117, 118, 116 | ⊢ |
| : , : , : |
114 | theorem | | ⊢ |
| proveit.numbers.number_sets.rational_numbers.int_within_rational |
115 | instantiation | 117, 118, 119 | ⊢ |
| : , : , : |
116 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.nat2 |
117 | theorem | | ⊢ |
| proveit.logic.sets.inclusion.superset_membership_from_proper_subset |
118 | theorem | | ⊢ |
| proveit.numbers.number_sets.integers.nat_within_int |
119 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.nat1 |
*equality replacement requirements |