| step type | requirements | statement |
0 | instantiation | 1, 2, 3, 4, 5, 6, 7, 8, 9, 10 | ⊢ |
| : , : , : , : |
1 | theorem | | ⊢ |
| proveit.physics.quantum.circuits.qcircuit_neq |
2 | reference | 46 | ⊢ |
3 | reference | 64 | ⊢ |
4 | instantiation | 78, 11, 13, 14 | ⊢ |
| : , : , : , : |
5 | instantiation | 78, 12, 13, 14 | ⊢ |
| : , : , : , : |
6 | instantiation | 78, 15, 20, 21 | ⊢ |
| : , : , : , : |
7 | instantiation | 78, 16, 20, 21 | ⊢ |
| : , : , : , : |
8 | instantiation | 78, 17, 20, 21 | ⊢ |
| : , : , : , : |
9 | instantiation | 78, 18, 20, 21 | ⊢ |
| : , : , : , : |
10 | instantiation | 78, 19, 20, 21 | ⊢ |
| : , : , : , : |
11 | instantiation | 37, 23, 22, 25, 26, 40, 41, 34, 27* | ⊢ |
| : , : , : , : |
12 | instantiation | 37, 23, 24, 25, 26, 40, 41, 34, 27* | ⊢ |
| : , : , : , : |
13 | instantiation | 94, 28 | ⊢ |
| : , : |
14 | instantiation | 94, 29 | ⊢ |
| : , : |
15 | instantiation | 37, 38, 30, 112, 101, 40, 41, 57*, 104* | ⊢ |
| : , : , : , : |
16 | instantiation | 37, 38, 31, 32, 33, 40, 34, 57*, 58* | ⊢ |
| : , : , : , : |
17 | instantiation | 37, 38, 35, 112, 101, 40, 41, 57*, 104* | ⊢ |
| : , : , : , : |
18 | instantiation | 37, 38, 36, 112, 101, 40, 41, 57*, 104* | ⊢ |
| : , : , : , : |
19 | instantiation | 37, 38, 39, 112, 101, 40, 41, 57*, 104* | ⊢ |
| : , : , : , : |
20 | instantiation | 131 | ⊢ |
| : |
21 | instantiation | 94, 42 | ⊢ |
| : , : |
22 | instantiation | 65 | ⊢ |
| : , : , : , : , : , : , : , : |
23 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.posnat8 |
24 | instantiation | 65 | ⊢ |
| : , : , : , : , : , : , : , : |
25 | instantiation | 65 | ⊢ |
| : , : , : , : , : , : , : , : |
26 | instantiation | 65 | ⊢ |
| : , : , : , : , : , : , : , : |
27 | instantiation | 150, 43, 44 | ⊢ |
| : , : , : |
28 | instantiation | 109, 171, 168, 136, 101, 137, 93, 129, 125 | ⊢ |
| : , : , : , : , : , : |
29 | instantiation | 45, 46, 47, 52 | ⊢ |
| : , : , : |
30 | instantiation | 146 | ⊢ |
| : , : |
31 | instantiation | 146 | ⊢ |
| : , : |
32 | instantiation | 146 | ⊢ |
| : , : |
33 | instantiation | 146 | ⊢ |
| : , : |
34 | instantiation | 49, 50, 58 | ⊢ |
| : , : , : |
35 | instantiation | 146 | ⊢ |
| : , : |
36 | instantiation | 146 | ⊢ |
| : , : |
37 | theorem | | ⊢ |
| proveit.core_expr_types.tuples.general_len |
38 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.posnat2 |
39 | instantiation | 146 | ⊢ |
| : , : |
40 | instantiation | 49, 48, 57 | ⊢ |
| : , : , : |
41 | instantiation | 49, 50, 104 | ⊢ |
| : , : , : |
42 | instantiation | 51, 52 | ⊢ |
| : , : |
43 | instantiation | 53, 54, 55, 56, 57, 104, 58 | ⊢ |
| : , : , : , : |
44 | instantiation | 78, 59, 60, 61 | ⊢ |
| : , : , : , : |
45 | theorem | | ⊢ |
| proveit.core_expr_types.tuples.len_of_ranges_with_repeated_indices_from_1 |
46 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.posnat4 |
47 | instantiation | 62, 144 | ⊢ |
| : , : |
48 | instantiation | 169, 63, 155 | ⊢ |
| : , : , : |
49 | theorem | | ⊢ |
| proveit.logic.equality.sub_left_side_into |
50 | instantiation | 169, 63, 145 | ⊢ |
| : , : , : |
51 | theorem | | ⊢ |
| proveit.core_expr_types.tuples.range_from1_len |
52 | instantiation | 169, 63, 64 | ⊢ |
| : , : , : |
53 | axiom | | ⊢ |
| proveit.core_expr_types.operations.operands_substitution |
54 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.nat8 |
55 | instantiation | 65 | ⊢ |
| : , : , : , : , : , : , : , : |
56 | instantiation | 65 | ⊢ |
| : , : , : , : , : , : , : , : |
57 | instantiation | 120, 140, 129, 121 | ⊢ |
| : , : , : |
58 | instantiation | 150, 66, 67 | ⊢ |
| : , : , : |
59 | instantiation | 78, 68, 69, 70 | ⊢ |
| : , : , : , : |
60 | instantiation | 135, 136, 144, 137, 71, 73, 129, 125, 72* | ⊢ |
| : , : , : , : , : , : |
61 | instantiation | 135, 171, 144, 136, 73, 137, 74, 125, 75* | ⊢ |
| : , : , : , : , : , : |
62 | theorem | | ⊢ |
| proveit.core_expr_types.tuples.range_from1_len_typical_eq |
63 | theorem | | ⊢ |
| proveit.numbers.number_sets.natural_numbers.nat_pos_within_nat |
64 | instantiation | 76, 155, 145 | ⊢ |
| : , : |
65 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.tuple_len_8_typical_eq |
66 | instantiation | 160, 77 | ⊢ |
| : , : , : |
67 | instantiation | 78, 79, 80, 81 | ⊢ |
| : , : , : , : |
68 | instantiation | 87, 171, 82, 83, 129, 125 | ⊢ |
| : , : , : , : , : , : , : |
69 | instantiation | 87, 168, 88, 84, 85, 86, 129, 125 | ⊢ |
| : , : , : , : , : , : , : |
70 | instantiation | 87, 88, 171, 89, 90, 129, 125 | ⊢ |
| : , : , : , : , : , : , : |
71 | instantiation | 123 | ⊢ |
| : , : , : , : |
72 | instantiation | 94, 91, 96* | ⊢ |
| : , : |
73 | instantiation | 123 | ⊢ |
| : , : , : , : |
74 | instantiation | 92, 93, 129 | ⊢ |
| : , : |
75 | instantiation | 94, 95, 96* | ⊢ |
| : , : |
76 | theorem | | ⊢ |
| proveit.numbers.addition.add_nat_pos_closure_bin |
77 | instantiation | 97, 129, 140 | ⊢ |
| : , : |
78 | theorem | | ⊢ |
| proveit.logic.equality.four_chain_transitivity |
79 | instantiation | 100, 136, 168, 137, 101, 98, 129, 125, 99, 140 | ⊢ |
| : , : , : , : , : , : |
80 | instantiation | 100, 168, 171, 101, 102, 129, 125, 115, 118, 140 | ⊢ |
| : , : , : , : , : , : |
81 | instantiation | 150, 103, 104 | ⊢ |
| : , : , : |
82 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.nat5 |
83 | instantiation | 105 | ⊢ |
| : , : , : , : , : |
84 | instantiation | 146 | ⊢ |
| : , : |
85 | instantiation | 146 | ⊢ |
| : , : |
86 | instantiation | 106 | ⊢ |
| : , : , : |
87 | theorem | | ⊢ |
| proveit.numbers.addition.leftward_commutation |
88 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.nat3 |
89 | instantiation | 106 | ⊢ |
| : , : , : |
90 | instantiation | 106 | ⊢ |
| : , : , : |
91 | instantiation | 109, 136, 144, 171, 137, 110, 140, 129, 107* | ⊢ |
| : , : , : , : , : , : |
92 | theorem | | ⊢ |
| proveit.numbers.multiplication.mult_complex_closure_bin |
93 | instantiation | 169, 148, 108 | ⊢ |
| : , : , : |
94 | theorem | | ⊢ |
| proveit.logic.equality.equals_reversal |
95 | instantiation | 109, 136, 144, 171, 137, 110, 140, 125, 111* | ⊢ |
| : , : , : , : , : , : |
96 | instantiation | 135, 136, 168, 137, 112, 140, 113* | ⊢ |
| : , : , : , : , : , : |
97 | theorem | | ⊢ |
| proveit.numbers.negation.distribute_neg_through_binary_sum |
98 | instantiation | 146 | ⊢ |
| : , : |
99 | instantiation | 114, 115, 118 | ⊢ |
| : , : |
100 | theorem | | ⊢ |
| proveit.numbers.addition.disassociation |
101 | instantiation | 146 | ⊢ |
| : , : |
102 | instantiation | 146 | ⊢ |
| : , : |
103 | instantiation | 116, 136, 171, 168, 137, 117, 129, 125, 118, 140, 119 | ⊢ |
| : , : , : , : , : , : , : , : |
104 | instantiation | 120, 140, 125, 121 | ⊢ |
| : , : , : |
105 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.tuple_len_5_typical_eq |
106 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.tuple_len_3_typical_eq |
107 | instantiation | 124, 129 | ⊢ |
| : |
108 | instantiation | 169, 158, 122 | ⊢ |
| : , : , : |
109 | theorem | | ⊢ |
| proveit.numbers.multiplication.distribute_through_sum |
110 | instantiation | 123 | ⊢ |
| : , : , : , : |
111 | instantiation | 124, 125 | ⊢ |
| : |
112 | instantiation | 146 | ⊢ |
| : , : |
113 | instantiation | 150, 126, 127 | ⊢ |
| : , : , : |
114 | theorem | | ⊢ |
| proveit.numbers.addition.add_complex_closure_bin |
115 | instantiation | 128, 129 | ⊢ |
| : |
116 | theorem | | ⊢ |
| proveit.numbers.addition.subtraction.add_cancel_general |
117 | instantiation | 146 | ⊢ |
| : , : |
118 | instantiation | 169, 148, 130 | ⊢ |
| : , : , : |
119 | instantiation | 131 | ⊢ |
| : |
120 | theorem | | ⊢ |
| proveit.numbers.addition.subtraction.add_cancel_triple_32 |
121 | instantiation | 131 | ⊢ |
| : |
122 | instantiation | 169, 166, 132 | ⊢ |
| : , : , : |
123 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.tuple_len_4_typical_eq |
124 | theorem | | ⊢ |
| proveit.numbers.multiplication.elim_one_left |
125 | instantiation | 169, 148, 133 | ⊢ |
| : , : , : |
126 | instantiation | 160, 134 | ⊢ |
| : , : , : |
127 | instantiation | 135, 136, 168, 171, 137, 138, 139, 140, 141* | ⊢ |
| : , : , : , : , : , : |
128 | theorem | | ⊢ |
| proveit.numbers.negation.complex_closure |
129 | instantiation | 169, 148, 142 | ⊢ |
| : , : , : |
130 | instantiation | 169, 158, 143 | ⊢ |
| : , : , : |
131 | axiom | | ⊢ |
| proveit.logic.equality.equals_reflexivity |
132 | instantiation | 169, 170, 144 | ⊢ |
| : , : , : |
133 | instantiation | 153, 154, 145 | ⊢ |
| : , : , : |
134 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.add_1_1 |
135 | theorem | | ⊢ |
| proveit.numbers.addition.association |
136 | axiom | | ⊢ |
| proveit.numbers.number_sets.natural_numbers.zero_in_nats |
137 | theorem | | ⊢ |
| proveit.core_expr_types.tuples.tuple_len_0_typical_eq |
138 | instantiation | 146 | ⊢ |
| : , : |
139 | instantiation | 169, 148, 147 | ⊢ |
| : , : , : |
140 | instantiation | 169, 148, 149 | ⊢ |
| : , : , : |
141 | instantiation | 150, 151, 152 | ⊢ |
| : , : , : |
142 | instantiation | 153, 154, 155 | ⊢ |
| : , : , : |
143 | instantiation | 169, 166, 156 | ⊢ |
| : , : , : |
144 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.nat4 |
145 | axiom | | ⊢ |
| proveit.physics.quantum.QPE._s_in_nat_pos |
146 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.tuple_len_2_typical_eq |
147 | instantiation | 169, 158, 157 | ⊢ |
| : , : , : |
148 | theorem | | ⊢ |
| proveit.numbers.number_sets.complex_numbers.real_within_complex |
149 | instantiation | 169, 158, 159 | ⊢ |
| : , : , : |
150 | axiom | | ⊢ |
| proveit.logic.equality.equals_transitivity |
151 | instantiation | 160, 161 | ⊢ |
| : , : , : |
152 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.add_3_1 |
153 | theorem | | ⊢ |
| proveit.logic.sets.inclusion.unfold_subset_eq |
154 | instantiation | 162, 163 | ⊢ |
| : , : |
155 | axiom | | ⊢ |
| proveit.physics.quantum.QPE._t_in_natural_pos |
156 | instantiation | 164, 167 | ⊢ |
| : |
157 | instantiation | 169, 166, 165 | ⊢ |
| : , : , : |
158 | theorem | | ⊢ |
| proveit.numbers.number_sets.real_numbers.rational_within_real |
159 | instantiation | 169, 166, 167 | ⊢ |
| : , : , : |
160 | axiom | | ⊢ |
| proveit.logic.equality.substitution |
161 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.add_2_1 |
162 | theorem | | ⊢ |
| proveit.logic.sets.inclusion.relax_proper_subset |
163 | theorem | | ⊢ |
| proveit.numbers.number_sets.real_numbers.nat_pos_within_real |
164 | theorem | | ⊢ |
| proveit.numbers.negation.int_closure |
165 | instantiation | 169, 170, 168 | ⊢ |
| : , : , : |
166 | theorem | | ⊢ |
| proveit.numbers.number_sets.rational_numbers.int_within_rational |
167 | instantiation | 169, 170, 171 | ⊢ |
| : , : , : |
168 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.nat2 |
169 | theorem | | ⊢ |
| proveit.logic.sets.inclusion.superset_membership_from_proper_subset |
170 | theorem | | ⊢ |
| proveit.numbers.number_sets.integers.nat_within_int |
171 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.nat1 |
*equality replacement requirements |