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