| step type | requirements | statement |
0 | instantiation | 1, 2 | ⊢ |
| : , : |
1 | reference | 53 | ⊢ |
2 | instantiation | 3, 4 | ⊢ |
| : , : |
3 | theorem | | ⊢ |
| proveit.physics.quantum.circuits.prob_eq_via_equiv |
4 | modus ponens | 5, 6 | ⊢ |
5 | instantiation | 7, 95, 134, 131, 97, 8 | ⊢ |
| : , : , : , : , : , : , : , : |
6 | instantiation | 9, 10, 11, 93, 52, 12, 13, 14, 15, 16, 17, 18, 19, 20, 48, 95, 21, 22, 23, 45* | ⊢ |
| : , : , : , : , : , : |
7 | theorem | | ⊢ |
| proveit.physics.quantum.circuits.circuit_equiv_temporal_sub |
8 | instantiation | 108 | ⊢ |
| : , : |
9 | theorem | | ⊢ |
| proveit.physics.quantum.circuits.input_consolidation |
10 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.posnat2 |
11 | instantiation | 108 | ⊢ |
| : , : |
12 | instantiation | 108 | ⊢ |
| : , : |
13 | instantiation | 24, 25 | ⊢ |
| : , : |
14 | axiom | | ⊢ |
| proveit.physics.quantum.QPE._u_ket_register |
15 | instantiation | 31, 26, 27, 28 | ⊢ |
| : , : , : , : |
16 | instantiation | 53, 29 | ⊢ |
| : , : |
17 | instantiation | 108 | ⊢ |
| : , : |
18 | instantiation | 53, 30 | ⊢ |
| : , : |
19 | instantiation | 31, 32, 33, 34 | ⊢ |
| : , : , : , : |
20 | instantiation | 61, 90, 121, 45 | ⊢ |
| : , : , : |
21 | instantiation | 132, 79, 93 | ⊢ |
| : , : , : |
22 | instantiation | 132, 79, 35 | ⊢ |
| : , : , : |
23 | instantiation | 36, 86, 37, 38, 39, 40 | ⊢ |
| : , : |
24 | theorem | | ⊢ |
| proveit.logic.booleans.conjunction.left_from_and |
25 | instantiation | 41, 93 | ⊢ |
| : |
26 | instantiation | 42 | ⊢ |
| : , : , : |
27 | instantiation | 55 | ⊢ |
| : |
28 | instantiation | 53, 43 | ⊢ |
| : , : |
29 | instantiation | 44, 47, 45 | ⊢ |
| : , : , : |
30 | instantiation | 46, 47, 48 | ⊢ |
| : , : , : |
31 | theorem | | ⊢ |
| proveit.logic.equality.four_chain_transitivity |
32 | instantiation | 49 | ⊢ |
| : , : |
33 | instantiation | 55 | ⊢ |
| : |
34 | instantiation | 53, 50 | ⊢ |
| : , : |
35 | instantiation | 51, 93, 52 | ⊢ |
| : , : |
36 | theorem | | ⊢ |
| proveit.logic.booleans.conjunction.and_if_all |
37 | instantiation | 103 | ⊢ |
| : , : , : |
38 | instantiation | 55 | ⊢ |
| : |
39 | instantiation | 53, 54 | ⊢ |
| : , : |
40 | instantiation | 55 | ⊢ |
| : |
41 | theorem | | ⊢ |
| proveit.physics.quantum.QPE._psi_t_ket_is_normalized_vec |
42 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.tuple_len_3 |
43 | instantiation | 62, 56, 57 | ⊢ |
| : , : , : |
44 | theorem | | ⊢ |
| proveit.core_expr_types.tuples.partition_front |
45 | instantiation | 65, 121 | ⊢ |
| : |
46 | theorem | | ⊢ |
| proveit.core_expr_types.tuples.partition_back |
47 | instantiation | 58, 59, 60 | ⊢ |
| : |
48 | instantiation | 61, 121, 119, 106 | ⊢ |
| : , : , : |
49 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.tuple_len_2 |
50 | instantiation | 62, 63, 64 | ⊢ |
| : , : , : |
51 | theorem | | ⊢ |
| proveit.numbers.addition.add_nat_pos_closure_bin |
52 | axiom | | ⊢ |
| proveit.physics.quantum.QPE._s_in_nat_pos |
53 | theorem | | ⊢ |
| proveit.logic.equality.equals_reversal |
54 | instantiation | 65, 66 | ⊢ |
| : |
55 | axiom | | ⊢ |
| proveit.logic.equality.equals_reflexivity |
56 | instantiation | 74, 67 | ⊢ |
| : , : , : |
57 | instantiation | 104, 68, 69 | ⊢ |
| : , : , : |
58 | theorem | | ⊢ |
| proveit.numbers.number_sets.integers.nonneg_int_is_natural |
59 | instantiation | 70, 128, 71 | ⊢ |
| : , : |
60 | instantiation | 72, 73 | ⊢ |
| : , : |
61 | theorem | | ⊢ |
| proveit.numbers.addition.subtraction.subtract_from_add |
62 | theorem | | ⊢ |
| proveit.logic.equality.sub_right_side_into |
63 | instantiation | 74, 75 | ⊢ |
| : , : , : |
64 | instantiation | 104, 76, 77 | ⊢ |
| : , : , : |
65 | theorem | | ⊢ |
| proveit.numbers.addition.elim_zero_left |
66 | instantiation | 132, 123, 78 | ⊢ |
| : , : , : |
67 | instantiation | 132, 79, 80 | ⊢ |
| : , : , : |
68 | instantiation | 113, 118 | ⊢ |
| : , : , : |
69 | instantiation | 88, 95, 131, 134, 97, 81, 119, 90, 121, 82* | ⊢ |
| : , : , : , : , : , : |
70 | theorem | | ⊢ |
| proveit.numbers.addition.add_int_closure_bin |
71 | instantiation | 109, 83, 111 | ⊢ |
| : , : , : |
72 | theorem | | ⊢ |
| proveit.numbers.addition.subtraction.nonneg_difference |
73 | instantiation | 84, 131 | ⊢ |
| : |
74 | theorem | | ⊢ |
| proveit.core_expr_types.tuples.range_len |
75 | instantiation | 85, 86, 87, 134, 98 | ⊢ |
| : , : |
76 | instantiation | 113, 118 | ⊢ |
| : , : , : |
77 | instantiation | 88, 95, 131, 134, 97, 89, 121, 90, 91* | ⊢ |
| : , : , : , : , : , : |
78 | instantiation | 109, 92, 93 | ⊢ |
| : , : , : |
79 | theorem | | ⊢ |
| proveit.numbers.number_sets.natural_numbers.nat_pos_within_nat |
80 | instantiation | 94, 131, 95, 96, 97, 98, 134, 99 | ⊢ |
| : , : , : , : , : |
81 | instantiation | 108 | ⊢ |
| : , : |
82 | instantiation | 104, 100, 101 | ⊢ |
| : , : , : |
83 | instantiation | 115, 102 | ⊢ |
| : , : |
84 | theorem | | ⊢ |
| proveit.numbers.number_sets.natural_numbers.natural_lower_bound |
85 | theorem | | ⊢ |
| proveit.numbers.addition.add_nat_closure |
86 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.nat3 |
87 | instantiation | 103 | ⊢ |
| : , : , : |
88 | theorem | | ⊢ |
| proveit.numbers.addition.association |
89 | instantiation | 108 | ⊢ |
| : , : |
90 | theorem | | ⊢ |
| proveit.numbers.number_sets.complex_numbers.zero_is_complex |
91 | instantiation | 104, 105, 106 | ⊢ |
| : , : , : |
92 | instantiation | 115, 107 | ⊢ |
| : , : |
93 | axiom | | ⊢ |
| proveit.physics.quantum.QPE._t_in_natural_pos |
94 | theorem | | ⊢ |
| proveit.numbers.addition.add_nat_pos_from_nonneg |
95 | axiom | | ⊢ |
| proveit.numbers.number_sets.natural_numbers.zero_in_nats |
96 | instantiation | 108 | ⊢ |
| : , : |
97 | theorem | | ⊢ |
| proveit.core_expr_types.tuples.tuple_len_0_typical_eq |
98 | instantiation | 109, 110, 111 | ⊢ |
| : , : , : |
99 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.less_0_1 |
100 | instantiation | 113, 112 | ⊢ |
| : , : , : |
101 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.add_2_1 |
102 | theorem | | ⊢ |
| proveit.numbers.number_sets.integers.zero_set_within_int |
103 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.tuple_len_3_typical_eq |
104 | axiom | | ⊢ |
| proveit.logic.equality.equals_transitivity |
105 | instantiation | 113, 114 | ⊢ |
| : , : , : |
106 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.add_1_1 |
107 | theorem | | ⊢ |
| proveit.numbers.number_sets.real_numbers.nat_pos_within_real |
108 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.tuple_len_2_typical_eq |
109 | theorem | | ⊢ |
| proveit.logic.sets.inclusion.unfold_subset_eq |
110 | instantiation | 115, 116 | ⊢ |
| : , : |
111 | instantiation | 117, 118 | ⊢ |
| : , : |
112 | instantiation | 120, 119 | ⊢ |
| : |
113 | axiom | | ⊢ |
| proveit.logic.equality.substitution |
114 | instantiation | 120, 121 | ⊢ |
| : |
115 | theorem | | ⊢ |
| proveit.logic.sets.inclusion.relax_proper_subset |
116 | theorem | | ⊢ |
| proveit.numbers.number_sets.natural_numbers.zero_set_within_nat |
117 | theorem | | ⊢ |
| proveit.logic.sets.enumeration.fold_singleton |
118 | theorem | | ⊢ |
| proveit.numbers.negation.negated_zero |
119 | instantiation | 132, 123, 122 | ⊢ |
| : , : , : |
120 | theorem | | ⊢ |
| proveit.numbers.addition.elim_zero_right |
121 | instantiation | 132, 123, 124 | ⊢ |
| : , : , : |
122 | instantiation | 132, 126, 125 | ⊢ |
| : , : , : |
123 | theorem | | ⊢ |
| proveit.numbers.number_sets.complex_numbers.real_within_complex |
124 | instantiation | 132, 126, 127 | ⊢ |
| : , : , : |
125 | instantiation | 132, 129, 128 | ⊢ |
| : , : , : |
126 | theorem | | ⊢ |
| proveit.numbers.number_sets.real_numbers.rational_within_real |
127 | instantiation | 132, 129, 130 | ⊢ |
| : , : , : |
128 | instantiation | 132, 133, 131 | ⊢ |
| : , : , : |
129 | theorem | | ⊢ |
| proveit.numbers.number_sets.rational_numbers.int_within_rational |
130 | instantiation | 132, 133, 134 | ⊢ |
| : , : , : |
131 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.nat2 |
132 | theorem | | ⊢ |
| proveit.logic.sets.inclusion.superset_membership_from_proper_subset |
133 | theorem | | ⊢ |
| proveit.numbers.number_sets.integers.nat_within_int |
134 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.nat1 |
*equality replacement requirements |