| step type | requirements | statement |
0 | instantiation | 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12 | ⊢ |
| : , : , : , : , : , : , : , : , : , : |
1 | theorem | | ⊢ |
| proveit.linear_algebra.tensors.tensor_prod_disassociation |
2 | reference | 141 | ⊢ |
3 | reference | 31 | ⊢ |
4 | reference | 188 | ⊢ |
5 | reference | 142 | ⊢ |
6 | reference | 24 | ⊢ |
7 | instantiation | 56, 13, 117, 17 | ⊢ |
| : , : , : , : |
8 | instantiation | 14, 180, 181, 85, 27 | ⊢ |
| : , : , : |
9 | instantiation | 98, 15 | ⊢ |
| : |
10 | instantiation | 56, 16, 117, 17 | ⊢ |
| : , : , : , : |
11 | modus ponens | 18, 19 | ⊢ |
12 | axiom | | ⊢ |
| proveit.physics.quantum.QPE._u_ket_register |
13 | instantiation | 129, 20, 24 | ⊢ |
| : , : , : |
14 | theorem | | ⊢ |
| proveit.logic.booleans.conjunction.redundant_conjunction_general |
15 | instantiation | 21, 174, 22 | ⊢ |
| : , : |
16 | instantiation | 129, 23, 24 | ⊢ |
| : , : , : |
17 | instantiation | 79, 25 | ⊢ |
| : , : |
18 | instantiation | 26, 180, 181, 27 | ⊢ |
| : , : , : , : |
19 | generalization | 28 | ⊢ |
20 | instantiation | 30, 31 | ⊢ |
| : , : , : |
21 | theorem | | ⊢ |
| proveit.numbers.exponentiation.exp_natpos_closure |
22 | instantiation | 189, 50, 29 | ⊢ |
| : , : , : |
23 | instantiation | 30, 31 | ⊢ |
| : , : , : |
24 | instantiation | 123, 32, 33 | ⊢ |
| : , : , : |
25 | instantiation | 34, 35 | ⊢ |
| : , : |
26 | theorem | | ⊢ |
| proveit.logic.booleans.conjunction.conjunction_from_quantification |
27 | instantiation | 101, 36, 159, 127, 37, 38*, 39* | ⊢ |
| : , : , : |
28 | instantiation | 84, 85, 40, 41 | , ⊢ |
| : , : , : , : |
29 | axiom | | ⊢ |
| proveit.physics.quantum.QPE._s_in_nat_pos |
30 | theorem | | ⊢ |
| proveit.core_expr_types.tuples.range_len |
31 | instantiation | 42, 133, 43, 141, 44, 188 | ⊢ |
| : , : |
32 | instantiation | 45, 46 | ⊢ |
| : , : , : |
33 | instantiation | 56, 47, 48, 49 | ⊢ |
| : , : , : , : |
34 | theorem | | ⊢ |
| proveit.core_expr_types.tuples.range_from1_len |
35 | instantiation | 189, 50, 191 | ⊢ |
| : , : , : |
36 | instantiation | 189, 172, 51 | ⊢ |
| : , : , : |
37 | instantiation | 52, 53 | ⊢ |
| : , : |
38 | instantiation | 123, 54, 55 | ⊢ |
| : , : , : |
39 | instantiation | 56, 57, 73, 58 | ⊢ |
| : , : , : , : |
40 | instantiation | 59, 113, 60, 61 | ⊢ |
| : , : |
41 | instantiation | 62, 85, 63, 64 | , ⊢ |
| : , : , : , : |
42 | theorem | | ⊢ |
| proveit.numbers.addition.add_nat_closure |
43 | instantiation | 146 | ⊢ |
| : , : , : |
44 | instantiation | 65, 66 | ⊢ |
| : |
45 | axiom | | ⊢ |
| proveit.logic.equality.substitution |
46 | instantiation | 67, 114, 113, 68* | ⊢ |
| : , : |
47 | instantiation | 91, 188, 174, 69, 75, 116, 71, 113 | ⊢ |
| : , : , : , : , : , : |
48 | instantiation | 76, 141, 133, 142, 70, 116, 71, 113 | ⊢ |
| : , : , : , : |
49 | instantiation | 72, 113, 116, 73 | ⊢ |
| : , : , : |
50 | theorem | | ⊢ |
| proveit.numbers.number_sets.natural_numbers.nat_pos_within_nat |
51 | instantiation | 189, 175, 180 | ⊢ |
| : , : , : |
52 | theorem | | ⊢ |
| proveit.numbers.ordering.relax_less |
53 | instantiation | 74, 191 | ⊢ |
| : |
54 | instantiation | 91, 188, 174, 141, 92, 142, 75, 114, 113 | ⊢ |
| : , : , : , : , : , : |
55 | instantiation | 76, 141, 174, 142, 92, 114, 113 | ⊢ |
| : , : , : , : |
56 | theorem | | ⊢ |
| proveit.logic.equality.four_chain_transitivity |
57 | instantiation | 123, 77, 78 | ⊢ |
| : , : , : |
58 | instantiation | 79, 80 | ⊢ |
| : , : |
59 | theorem | | ⊢ |
| proveit.numbers.division.div_complex_closure |
60 | instantiation | 81, 156 | ⊢ |
| : |
61 | instantiation | 82, 97, 83 | ⊢ |
| : , : |
62 | theorem | | ⊢ |
| proveit.linear_algebra.addition.binary_closure |
63 | theorem | | ⊢ |
| proveit.physics.quantum.algebra.ket_zero_in_qubit_space |
64 | instantiation | 84, 85, 86, 87 | , ⊢ |
| : , : , : , : |
65 | theorem | | ⊢ |
| proveit.numbers.negation.nat_closure |
66 | instantiation | 88, 180, 89 | ⊢ |
| : |
67 | theorem | | ⊢ |
| proveit.numbers.negation.distribute_neg_through_binary_sum |
68 | instantiation | 90, 116 | ⊢ |
| : |
69 | instantiation | 152 | ⊢ |
| : , : |
70 | instantiation | 146 | ⊢ |
| : , : , : |
71 | instantiation | 165, 113 | ⊢ |
| : |
72 | theorem | | ⊢ |
| proveit.numbers.addition.subtraction.add_cancel_triple_32 |
73 | instantiation | 128 | ⊢ |
| : |
74 | theorem | | ⊢ |
| proveit.numbers.number_sets.natural_numbers.natural_pos_is_pos |
75 | theorem | | ⊢ |
| proveit.numbers.number_sets.complex_numbers.zero_is_complex |
76 | theorem | | ⊢ |
| proveit.numbers.addition.elim_zero_any |
77 | instantiation | 91, 188, 174, 141, 92, 142, 116, 114, 113 | ⊢ |
| : , : , : , : , : , : |
78 | instantiation | 93, 116, 113, 117 | ⊢ |
| : , : , : |
79 | theorem | | ⊢ |
| proveit.logic.equality.equals_reversal |
80 | instantiation | 94, 113 | ⊢ |
| : |
81 | theorem | | ⊢ |
| proveit.numbers.exponentiation.sqrt_complex_closure |
82 | theorem | | ⊢ |
| proveit.numbers.exponentiation.exp_rational_non_zero__not_zero |
83 | instantiation | 95, 96, 97 | ⊢ |
| : , : |
84 | theorem | | ⊢ |
| proveit.linear_algebra.scalar_multiplication.scalar_mult_closure |
85 | instantiation | 98, 120 | ⊢ |
| : |
86 | instantiation | 155, 99, 100 | , ⊢ |
| : , : |
87 | theorem | | ⊢ |
| proveit.physics.quantum.algebra.ket_one_in_qubit_space |
88 | theorem | | ⊢ |
| proveit.numbers.number_sets.integers.nonpos_int_is_int_nonpos |
89 | instantiation | 101, 126, 160, 127, 102, 103*, 104* | ⊢ |
| : , : , : |
90 | theorem | | ⊢ |
| proveit.numbers.negation.double_negation |
91 | theorem | | ⊢ |
| proveit.numbers.addition.disassociation |
92 | instantiation | 152 | ⊢ |
| : , : |
93 | theorem | | ⊢ |
| proveit.numbers.addition.subtraction.add_cancel_triple_12 |
94 | theorem | | ⊢ |
| proveit.numbers.addition.elim_zero_left |
95 | theorem | | ⊢ |
| proveit.numbers.division.div_rational_nonzero_closure |
96 | instantiation | 189, 106, 105 | ⊢ |
| : , : , : |
97 | instantiation | 189, 106, 107 | ⊢ |
| : , : , : |
98 | theorem | | ⊢ |
| proveit.linear_algebra.complex_vec_set_is_vec_space |
99 | instantiation | 189, 169, 108 | ⊢ |
| : , : , : |
100 | instantiation | 129, 109, 110 | , ⊢ |
| : , : , : |
101 | theorem | | ⊢ |
| proveit.numbers.addition.weak_bound_via_left_term_bound |
102 | instantiation | 111, 191 | ⊢ |
| : |
103 | instantiation | 112, 113, 114 | ⊢ |
| : , : |
104 | instantiation | 115, 116, 117 | ⊢ |
| : , : |
105 | instantiation | 189, 119, 118 | ⊢ |
| : , : , : |
106 | theorem | | ⊢ |
| proveit.numbers.number_sets.rational_numbers.nonzero_int_within_rational_nonzero |
107 | instantiation | 189, 119, 120 | ⊢ |
| : , : , : |
108 | instantiation | 189, 162, 121 | ⊢ |
| : , : , : |
109 | instantiation | 149, 132, 122 | , ⊢ |
| : , : |
110 | instantiation | 123, 124, 125 | , ⊢ |
| : , : , : |
111 | theorem | | ⊢ |
| proveit.numbers.number_sets.natural_numbers.natural_pos_lower_bound |
112 | theorem | | ⊢ |
| proveit.numbers.addition.commutation |
113 | instantiation | 189, 169, 160 | ⊢ |
| : , : , : |
114 | instantiation | 189, 169, 126 | ⊢ |
| : , : , : |
115 | theorem | | ⊢ |
| proveit.numbers.addition.subtraction.add_cancel_basic |
116 | instantiation | 189, 169, 127 | ⊢ |
| : , : , : |
117 | instantiation | 128 | ⊢ |
| : |
118 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.posnat1 |
119 | theorem | | ⊢ |
| proveit.numbers.number_sets.integers.nat_pos_within_nonzero_int |
120 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.posnat2 |
121 | theorem | | ⊢ |
| proveit.numbers.number_sets.real_numbers.e_is_real_pos |
122 | instantiation | 129, 130, 131 | , ⊢ |
| : , : , : |
123 | axiom | | ⊢ |
| proveit.logic.equality.equals_transitivity |
124 | instantiation | 140, 188, 133, 141, 135, 142, 132, 150, 151, 144 | , ⊢ |
| : , : , : , : , : , : |
125 | instantiation | 140, 141, 174, 133, 142, 134, 135, 156, 145, 150, 151, 144 | , ⊢ |
| : , : , : , : , : , : |
126 | instantiation | 189, 172, 136 | ⊢ |
| : , : , : |
127 | instantiation | 137, 138, 191 | ⊢ |
| : , : , : |
128 | axiom | | ⊢ |
| proveit.logic.equality.equals_reflexivity |
129 | theorem | | ⊢ |
| proveit.logic.equality.sub_right_side_into |
130 | instantiation | 149, 139, 144 | , ⊢ |
| : , : |
131 | instantiation | 140, 141, 174, 188, 142, 143, 150, 151, 144 | , ⊢ |
| : , : , : , : , : , : |
132 | instantiation | 149, 156, 145 | ⊢ |
| : , : |
133 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.nat3 |
134 | instantiation | 152 | ⊢ |
| : , : |
135 | instantiation | 146 | ⊢ |
| : , : , : |
136 | instantiation | 189, 175, 183 | ⊢ |
| : , : , : |
137 | theorem | | ⊢ |
| proveit.logic.sets.inclusion.unfold_subset_eq |
138 | instantiation | 147, 148 | ⊢ |
| : , : |
139 | instantiation | 149, 150, 151 | , ⊢ |
| : , : |
140 | theorem | | ⊢ |
| proveit.numbers.multiplication.disassociation |
141 | axiom | | ⊢ |
| proveit.numbers.number_sets.natural_numbers.zero_in_nats |
142 | theorem | | ⊢ |
| proveit.core_expr_types.tuples.tuple_len_0_typical_eq |
143 | instantiation | 152 | ⊢ |
| : , : |
144 | instantiation | 189, 169, 153 | ⊢ |
| : , : , : |
145 | instantiation | 189, 169, 154 | ⊢ |
| : , : , : |
146 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.tuple_len_3_typical_eq |
147 | theorem | | ⊢ |
| proveit.logic.sets.inclusion.relax_proper_subset |
148 | theorem | | ⊢ |
| proveit.numbers.number_sets.real_numbers.nat_pos_within_real |
149 | theorem | | ⊢ |
| proveit.numbers.multiplication.mult_complex_closure_bin |
150 | theorem | | ⊢ |
| proveit.numbers.number_sets.complex_numbers.i_is_complex |
151 | instantiation | 155, 156, 157 | , ⊢ |
| : , : |
152 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.tuple_len_2_typical_eq |
153 | instantiation | 158, 159, 160, 161 | ⊢ |
| : , : , : |
154 | instantiation | 189, 162, 163 | ⊢ |
| : , : , : |
155 | theorem | | ⊢ |
| proveit.numbers.exponentiation.exp_complex_closure |
156 | instantiation | 189, 169, 164 | ⊢ |
| : , : , : |
157 | instantiation | 165, 166 | , ⊢ |
| : |
158 | theorem | | ⊢ |
| proveit.numbers.number_sets.real_numbers.all_in_interval_co__is__real |
159 | theorem | | ⊢ |
| proveit.numbers.number_sets.real_numbers.zero_is_real |
160 | instantiation | 189, 172, 167 | ⊢ |
| : , : , : |
161 | axiom | | ⊢ |
| proveit.physics.quantum.QPE._phase_in_interval |
162 | theorem | | ⊢ |
| proveit.numbers.number_sets.real_numbers.real_pos_within_real |
163 | theorem | | ⊢ |
| proveit.numbers.number_sets.real_numbers.pi_is_real_pos |
164 | instantiation | 189, 172, 168 | ⊢ |
| : , : , : |
165 | theorem | | ⊢ |
| proveit.numbers.negation.complex_closure |
166 | instantiation | 189, 169, 170 | , ⊢ |
| : , : , : |
167 | instantiation | 189, 175, 184 | ⊢ |
| : , : , : |
168 | instantiation | 189, 175, 171 | ⊢ |
| : , : , : |
169 | theorem | | ⊢ |
| proveit.numbers.number_sets.complex_numbers.real_within_complex |
170 | instantiation | 189, 172, 173 | , ⊢ |
| : , : , : |
171 | instantiation | 189, 187, 174 | ⊢ |
| : , : , : |
172 | theorem | | ⊢ |
| proveit.numbers.number_sets.real_numbers.rational_within_real |
173 | instantiation | 189, 175, 176 | , ⊢ |
| : , : , : |
174 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.nat2 |
175 | theorem | | ⊢ |
| proveit.numbers.number_sets.rational_numbers.int_within_rational |
176 | instantiation | 189, 177, 178 | , ⊢ |
| : , : , : |
177 | instantiation | 179, 180, 181 | ⊢ |
| : , : |
178 | assumption | | ⊢ |
179 | theorem | | ⊢ |
| proveit.numbers.number_sets.integers.int_interval_within_int |
180 | instantiation | 182, 183, 184 | ⊢ |
| : , : |
181 | theorem | | ⊢ |
| proveit.numbers.number_sets.integers.zero_is_int |
182 | theorem | | ⊢ |
| proveit.numbers.addition.add_int_closure_bin |
183 | instantiation | 185, 186 | ⊢ |
| : |
184 | instantiation | 189, 187, 188 | ⊢ |
| : , : , : |
185 | theorem | | ⊢ |
| proveit.numbers.negation.int_closure |
186 | instantiation | 189, 190, 191 | ⊢ |
| : , : , : |
187 | theorem | | ⊢ |
| proveit.numbers.number_sets.integers.nat_within_int |
188 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.nat1 |
189 | theorem | | ⊢ |
| proveit.logic.sets.inclusion.superset_membership_from_proper_subset |
190 | theorem | | ⊢ |
| proveit.numbers.number_sets.integers.nat_pos_within_int |
191 | assumption | | ⊢ |
*equality replacement requirements |