| step type | requirements | statement |
0 | instantiation | 1, 2, 3, 4, 5, 6, 7, 8, 9 | ⊢ |
| : , : , : , : |
1 | theorem | | ⊢ |
| proveit.physics.quantum.circuits.qcircuit_eq |
2 | reference | 47 | ⊢ |
3 | reference | 68 | ⊢ |
4 | instantiation | 91, 10, 12, 13 | ⊢ |
| : , : , : , : |
5 | instantiation | 91, 11, 12, 13 | ⊢ |
| : , : , : , : |
6 | instantiation | 91, 14, 18, 19 | ⊢ |
| : , : , : , : |
7 | instantiation | 91, 15, 18, 19 | ⊢ |
| : , : , : , : |
8 | instantiation | 91, 16, 18, 19 | ⊢ |
| : , : , : , : |
9 | instantiation | 91, 17, 18, 19 | ⊢ |
| : , : , : , : |
10 | instantiation | 35, 20, 21, 22, 56, 23, 40, 34, 24* | ⊢ |
| : , : , : , : |
11 | instantiation | 35, 25, 26, 27, 28, 40, 41, 34, 29* | ⊢ |
| : , : , : , : |
12 | instantiation | 102, 30 | ⊢ |
| : , : |
13 | instantiation | 102, 31 | ⊢ |
| : , : |
14 | instantiation | 52, 53 | ⊢ |
| : , : |
15 | instantiation | 35, 36, 32, 119, 109, 40, 34, 64*, 112* | ⊢ |
| : , : , : , : |
16 | instantiation | 35, 36, 33, 119, 109, 40, 34, 64*, 112* | ⊢ |
| : , : , : , : |
17 | instantiation | 35, 36, 37, 38, 39, 40, 41, 64*, 65* | ⊢ |
| : , : , : , : |
18 | instantiation | 144 | ⊢ |
| : |
19 | instantiation | 102, 42 | ⊢ |
| : , : |
20 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.posnat5 |
21 | instantiation | 69 | ⊢ |
| : , : , : , : , : |
22 | instantiation | 69 | ⊢ |
| : , : , : , : , : |
23 | instantiation | 50, 53, 57 | ⊢ |
| : , : , : |
24 | instantiation | 137, 43, 44 | ⊢ |
| : , : , : |
25 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.posnat6 |
26 | instantiation | 77 | ⊢ |
| : , : , : , : , : , : |
27 | instantiation | 77 | ⊢ |
| : , : , : , : , : , : |
28 | instantiation | 77 | ⊢ |
| : , : , : , : , : , : |
29 | instantiation | 137, 45, 59 | ⊢ |
| : , : , : |
30 | instantiation | 115, 172, 125, 124, 109, 126, 101, 132, 136 | ⊢ |
| : , : , : , : , : , : |
31 | instantiation | 46, 47, 48, 53 | ⊢ |
| : , : , : |
32 | instantiation | 141 | ⊢ |
| : , : |
33 | instantiation | 141 | ⊢ |
| : , : |
34 | instantiation | 50, 51, 112 | ⊢ |
| : , : , : |
35 | theorem | | ⊢ |
| proveit.core_expr_types.tuples.general_len |
36 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.posnat2 |
37 | instantiation | 141 | ⊢ |
| : , : |
38 | instantiation | 141 | ⊢ |
| : , : |
39 | instantiation | 141 | ⊢ |
| : , : |
40 | instantiation | 50, 49, 64 | ⊢ |
| : , : , : |
41 | instantiation | 50, 51, 65 | ⊢ |
| : , : , : |
42 | instantiation | 52, 53 | ⊢ |
| : , : |
43 | instantiation | 60, 54, 55, 56, 57, 64, 112 | ⊢ |
| : , : , : , : |
44 | instantiation | 137, 58, 59 | ⊢ |
| : , : , : |
45 | instantiation | 60, 61, 62, 63, 64, 65, 112 | ⊢ |
| : , : , : , : |
46 | theorem | | ⊢ |
| proveit.core_expr_types.tuples.len_of_ranges_with_repeated_indices_from_1 |
47 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.posnat3 |
48 | instantiation | 66, 154 | ⊢ |
| : , : |
49 | instantiation | 170, 67, 169 | ⊢ |
| : , : , : |
50 | theorem | | ⊢ |
| proveit.logic.equality.sub_left_side_into |
51 | instantiation | 170, 67, 157 | ⊢ |
| : , : , : |
52 | theorem | | ⊢ |
| proveit.core_expr_types.tuples.range_from1_len |
53 | instantiation | 170, 67, 68 | ⊢ |
| : , : , : |
54 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.nat5 |
55 | instantiation | 69 | ⊢ |
| : , : , : , : , : |
56 | instantiation | 69 | ⊢ |
| : , : , : , : , : |
57 | instantiation | 137, 70, 71 | ⊢ |
| : , : , : |
58 | instantiation | 108, 124, 125, 72, 126, 109, 73, 132, 136 | ⊢ |
| : , : , : , : , : , : |
59 | instantiation | 91, 74, 75, 76 | ⊢ |
| : , : , : , : |
60 | axiom | | ⊢ |
| proveit.core_expr_types.operations.operands_substitution |
61 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.nat6 |
62 | instantiation | 77 | ⊢ |
| : , : , : , : , : , : |
63 | instantiation | 77 | ⊢ |
| : , : , : , : , : , : |
64 | instantiation | 130, 143, 132, 131 | ⊢ |
| : , : , : |
65 | instantiation | 137, 78, 79 | ⊢ |
| : , : , : |
66 | theorem | | ⊢ |
| proveit.core_expr_types.tuples.range_from1_len_typical_eq |
67 | theorem | | ⊢ |
| proveit.numbers.number_sets.natural_numbers.nat_pos_within_nat |
68 | instantiation | 80, 169, 157 | ⊢ |
| : , : |
69 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.tuple_len_5_typical_eq |
70 | instantiation | 108, 124, 125, 126, 109, 127, 132, 136, 128, 143 | ⊢ |
| : , : , : , : , : , : |
71 | instantiation | 81, 125, 124, 109, 126, 132, 136, 143 | ⊢ |
| : , : , : , : , : , : , : , : |
72 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.nat4 |
73 | instantiation | 82 | ⊢ |
| : , : , : , : |
74 | instantiation | 137, 83, 84 | ⊢ |
| : , : , : |
75 | instantiation | 118, 124, 154, 126, 85, 87, 132, 136, 86* | ⊢ |
| : , : , : , : , : , : |
76 | instantiation | 118, 172, 154, 124, 87, 126, 88, 136, 89* | ⊢ |
| : , : , : , : , : , : |
77 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.tuple_len_6_typical_eq |
78 | instantiation | 148, 90 | ⊢ |
| : , : , : |
79 | instantiation | 91, 92, 93, 94 | ⊢ |
| : , : , : , : |
80 | theorem | | ⊢ |
| proveit.numbers.addition.add_nat_pos_closure_bin |
81 | theorem | | ⊢ |
| proveit.numbers.addition.subtraction.add_cancel_general_rev |
82 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.tuple_len_4_typical_eq |
83 | instantiation | 96, 172, 154, 95, 132, 136 | ⊢ |
| : , : , : , : , : , : , : |
84 | instantiation | 96, 125, 172, 97, 98, 132, 136 | ⊢ |
| : , : , : , : , : , : , : |
85 | instantiation | 134 | ⊢ |
| : , : , : |
86 | instantiation | 102, 99, 104* | ⊢ |
| : , : |
87 | instantiation | 134 | ⊢ |
| : , : , : |
88 | instantiation | 100, 101, 132 | ⊢ |
| : , : |
89 | instantiation | 102, 103, 104* | ⊢ |
| : , : |
90 | instantiation | 105, 132, 143 | ⊢ |
| : , : |
91 | theorem | | ⊢ |
| proveit.logic.equality.four_chain_transitivity |
92 | instantiation | 108, 124, 125, 126, 109, 106, 132, 136, 107, 143 | ⊢ |
| : , : , : , : , : , : |
93 | instantiation | 108, 125, 172, 109, 110, 132, 136, 122, 128, 143 | ⊢ |
| : , : , : , : , : , : |
94 | instantiation | 137, 111, 112 | ⊢ |
| : , : , : |
95 | instantiation | 134 | ⊢ |
| : , : , : |
96 | theorem | | ⊢ |
| proveit.numbers.addition.leftward_commutation |
97 | instantiation | 141 | ⊢ |
| : , : |
98 | instantiation | 141 | ⊢ |
| : , : |
99 | instantiation | 115, 124, 154, 172, 126, 116, 143, 132, 113* | ⊢ |
| : , : , : , : , : , : |
100 | theorem | | ⊢ |
| proveit.numbers.multiplication.mult_complex_closure_bin |
101 | instantiation | 170, 152, 114 | ⊢ |
| : , : , : |
102 | theorem | | ⊢ |
| proveit.logic.equality.equals_reversal |
103 | instantiation | 115, 124, 154, 172, 126, 116, 143, 136, 117* | ⊢ |
| : , : , : , : , : , : |
104 | instantiation | 118, 124, 125, 172, 126, 119, 143, 120* | ⊢ |
| : , : , : , : , : , : |
105 | theorem | | ⊢ |
| proveit.numbers.negation.distribute_neg_through_binary_sum |
106 | instantiation | 141 | ⊢ |
| : , : |
107 | instantiation | 121, 122, 128 | ⊢ |
| : , : |
108 | theorem | | ⊢ |
| proveit.numbers.addition.disassociation |
109 | instantiation | 141 | ⊢ |
| : , : |
110 | instantiation | 141 | ⊢ |
| : , : |
111 | instantiation | 123, 124, 172, 125, 126, 127, 132, 136, 128, 143, 129 | ⊢ |
| : , : , : , : , : , : , : , : |
112 | instantiation | 130, 143, 136, 131 | ⊢ |
| : , : , : |
113 | instantiation | 135, 132 | ⊢ |
| : |
114 | instantiation | 170, 160, 133 | ⊢ |
| : , : , : |
115 | theorem | | ⊢ |
| proveit.numbers.multiplication.distribute_through_sum |
116 | instantiation | 134 | ⊢ |
| : , : , : |
117 | instantiation | 135, 136 | ⊢ |
| : |
118 | theorem | | ⊢ |
| proveit.numbers.addition.association |
119 | instantiation | 141 | ⊢ |
| : , : |
120 | instantiation | 137, 138, 139 | ⊢ |
| : , : , : |
121 | theorem | | ⊢ |
| proveit.numbers.addition.add_complex_closure_bin |
122 | instantiation | 170, 152, 140 | ⊢ |
| : , : , : |
123 | theorem | | ⊢ |
| proveit.numbers.addition.subtraction.add_cancel_general |
124 | axiom | | ⊢ |
| proveit.numbers.number_sets.natural_numbers.zero_in_nats |
125 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.nat2 |
126 | theorem | | ⊢ |
| proveit.core_expr_types.tuples.tuple_len_0_typical_eq |
127 | instantiation | 141 | ⊢ |
| : , : |
128 | instantiation | 142, 143 | ⊢ |
| : |
129 | instantiation | 144 | ⊢ |
| : |
130 | theorem | | ⊢ |
| proveit.numbers.addition.subtraction.add_cancel_triple_32 |
131 | instantiation | 144 | ⊢ |
| : |
132 | instantiation | 170, 152, 145 | ⊢ |
| : , : , : |
133 | instantiation | 170, 166, 146 | ⊢ |
| : , : , : |
134 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.tuple_len_3_typical_eq |
135 | theorem | | ⊢ |
| proveit.numbers.multiplication.elim_one_left |
136 | instantiation | 170, 152, 147 | ⊢ |
| : , : , : |
137 | axiom | | ⊢ |
| proveit.logic.equality.equals_transitivity |
138 | instantiation | 148, 149 | ⊢ |
| : , : , : |
139 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.add_2_1 |
140 | instantiation | 170, 150, 151 | ⊢ |
| : , : , : |
141 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.tuple_len_2_typical_eq |
142 | theorem | | ⊢ |
| proveit.numbers.negation.complex_closure |
143 | instantiation | 170, 152, 153 | ⊢ |
| : , : , : |
144 | axiom | | ⊢ |
| proveit.logic.equality.equals_reflexivity |
145 | instantiation | 155, 156, 169 | ⊢ |
| : , : , : |
146 | instantiation | 170, 171, 154 | ⊢ |
| : , : , : |
147 | instantiation | 155, 156, 157 | ⊢ |
| : , : , : |
148 | axiom | | ⊢ |
| proveit.logic.equality.substitution |
149 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.add_1_1 |
150 | theorem | | ⊢ |
| proveit.numbers.number_sets.real_numbers.real_neg_within_real |
151 | instantiation | 170, 158, 159 | ⊢ |
| : , : , : |
152 | theorem | | ⊢ |
| proveit.numbers.number_sets.complex_numbers.real_within_complex |
153 | instantiation | 170, 160, 161 | ⊢ |
| : , : , : |
154 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.nat3 |
155 | theorem | | ⊢ |
| proveit.logic.sets.inclusion.unfold_subset_eq |
156 | instantiation | 162, 163 | ⊢ |
| : , : |
157 | axiom | | ⊢ |
| proveit.physics.quantum.QPE._s_in_nat_pos |
158 | theorem | | ⊢ |
| proveit.numbers.number_sets.real_numbers.rational_neg_within_real_neg |
159 | instantiation | 170, 164, 165 | ⊢ |
| : , : , : |
160 | theorem | | ⊢ |
| proveit.numbers.number_sets.real_numbers.rational_within_real |
161 | instantiation | 170, 166, 167 | ⊢ |
| : , : , : |
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.number_sets.rational_numbers.neg_int_within_rational_neg |
165 | instantiation | 168, 169 | ⊢ |
| : |
166 | theorem | | ⊢ |
| proveit.numbers.number_sets.rational_numbers.int_within_rational |
167 | instantiation | 170, 171, 172 | ⊢ |
| : , : , : |
168 | theorem | | ⊢ |
| proveit.numbers.negation.int_neg_closure |
169 | axiom | | ⊢ |
| proveit.physics.quantum.QPE._t_in_natural_pos |
170 | theorem | | ⊢ |
| proveit.logic.sets.inclusion.superset_membership_from_proper_subset |
171 | theorem | | ⊢ |
| proveit.numbers.number_sets.integers.nat_within_int |
172 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.nat1 |
*equality replacement requirements |