| step type | requirements | statement |
0 | instantiation | 1, 2, 3, 4, 5, 6, 7, 8, 9 | ⊢ |
| : , : , : , : , : , : , : , : , : , : |
1 | theorem | | ⊢ |
| proveit.linear_algebra.tensors.factor_scalar_from_tensor_prod |
2 | instantiation | 29, 10, 11, 12 | ⊢ |
| : , : |
3 | reference | 155 | ⊢ |
4 | reference | 98 | ⊢ |
5 | reference | 99 | ⊢ |
6 | reference | 23 | ⊢ |
7 | reference | 35 | ⊢ |
8 | instantiation | 13, 23, 14, 15 | ⊢ |
| : , : , : , : |
9 | modus ponens | 16, 17 | ⊢ |
10 | instantiation | 153, 124, 18 | ⊢ |
| : , : , : |
11 | instantiation | 47, 102, 19 | ⊢ |
| : , : |
12 | instantiation | 20, 21, 22 | ⊢ |
| : , : , : |
13 | theorem | | ⊢ |
| proveit.linear_algebra.addition.binary_closure |
14 | theorem | | ⊢ |
| proveit.physics.quantum.algebra.ket_zero_in_qubit_space |
15 | instantiation | 34, 23, 24, 25 | ⊢ |
| : , : , : , : |
16 | instantiation | 26, 132, 35 | ⊢ |
| : , : , : , : , : , : |
17 | generalization | 27 | ⊢ |
18 | instantiation | 153, 127, 28 | ⊢ |
| : , : , : |
19 | instantiation | 29, 66, 102, 41 | ⊢ |
| : , : |
20 | theorem | | ⊢ |
| proveit.logic.equality.sub_left_side_into |
21 | instantiation | 30, 106, 31 | ⊢ |
| : , : |
22 | instantiation | 63, 32 | ⊢ |
| : , : , : |
23 | instantiation | 45, 134 | ⊢ |
| : |
24 | instantiation | 47, 48, 33 | ⊢ |
| : , : |
25 | theorem | | ⊢ |
| proveit.physics.quantum.algebra.ket_one_in_qubit_space |
26 | theorem | | ⊢ |
| proveit.linear_algebra.addition.summation_closure |
27 | instantiation | 34, 35, 36, 37 | , ⊢ |
| : , : , : , : |
28 | instantiation | 153, 136, 149 | ⊢ |
| : , : , : |
29 | theorem | | ⊢ |
| proveit.numbers.division.div_complex_closure |
30 | theorem | | ⊢ |
| proveit.numbers.exponentiation.exp_rational_non_zero__not_zero |
31 | instantiation | 153, 38, 39 | ⊢ |
| : , : , : |
32 | instantiation | 40, 66, 102, 41, 42* | ⊢ |
| : , : |
33 | instantiation | 82, 43, 44 | ⊢ |
| : , : , : |
34 | theorem | | ⊢ |
| proveit.linear_algebra.scalar_multiplication.scalar_mult_closure |
35 | instantiation | 45, 46 | ⊢ |
| : |
36 | instantiation | 47, 48, 49 | , ⊢ |
| : , : |
37 | instantiation | 50, 152, 138 | , ⊢ |
| : , : |
38 | theorem | | ⊢ |
| proveit.numbers.number_sets.rational_numbers.rational_pos_within_rational_nonzero |
39 | instantiation | 51, 110, 52 | ⊢ |
| : , : |
40 | theorem | | ⊢ |
| proveit.numbers.division.div_as_mult |
41 | instantiation | 53, 134 | ⊢ |
| : |
42 | instantiation | 73, 54, 55 | ⊢ |
| : , : , : |
43 | instantiation | 112, 85, 56 | ⊢ |
| : , : |
44 | instantiation | 73, 57, 58 | ⊢ |
| : , : , : |
45 | theorem | | ⊢ |
| proveit.linear_algebra.complex_vec_set_is_vec_space |
46 | instantiation | 59, 150, 147 | ⊢ |
| : , : |
47 | theorem | | ⊢ |
| proveit.numbers.exponentiation.exp_complex_closure |
48 | instantiation | 153, 124, 60 | ⊢ |
| : , : , : |
49 | instantiation | 82, 61, 62 | , ⊢ |
| : , : , : |
50 | theorem | | ⊢ |
| proveit.physics.quantum.algebra.num_ket_in_register_space |
51 | theorem | | ⊢ |
| proveit.numbers.multiplication.mult_rational_pos_closure_bin |
52 | instantiation | 153, 133, 152 | ⊢ |
| : , : , : |
53 | theorem | | ⊢ |
| proveit.numbers.number_sets.natural_numbers.nonzero_if_is_nat_pos |
54 | instantiation | 63, 64 | ⊢ |
| : , : , : |
55 | instantiation | 65, 66, 67 | ⊢ |
| : , : |
56 | instantiation | 82, 68, 69 | ⊢ |
| : , : , : |
57 | instantiation | 97, 155, 86, 98, 70, 99, 85, 113, 114, 81 | ⊢ |
| : , : , : , : , : , : |
58 | instantiation | 97, 98, 150, 86, 99, 87, 70, 102, 103, 113, 114, 81 | ⊢ |
| : , : , : , : , : , : |
59 | theorem | | ⊢ |
| proveit.numbers.exponentiation.exp_natpos_closure |
60 | instantiation | 153, 129, 71 | ⊢ |
| : , : , : |
61 | instantiation | 112, 85, 72 | , ⊢ |
| : , : |
62 | instantiation | 73, 74, 75 | , ⊢ |
| : , : , : |
63 | axiom | | ⊢ |
| proveit.logic.equality.substitution |
64 | instantiation | 76, 77, 132, 78* | ⊢ |
| : , : |
65 | theorem | | ⊢ |
| proveit.numbers.multiplication.commutation |
66 | instantiation | 153, 124, 79 | ⊢ |
| : , : , : |
67 | instantiation | 153, 124, 80 | ⊢ |
| : , : , : |
68 | instantiation | 112, 96, 81 | ⊢ |
| : , : |
69 | instantiation | 97, 98, 150, 155, 99, 100, 113, 114, 81 | ⊢ |
| : , : , : , : , : , : |
70 | instantiation | 104 | ⊢ |
| : , : , : |
71 | theorem | | ⊢ |
| proveit.numbers.number_sets.real_numbers.e_is_real_pos |
72 | instantiation | 82, 83, 84 | , ⊢ |
| : , : , : |
73 | axiom | | ⊢ |
| proveit.logic.equality.equals_transitivity |
74 | instantiation | 97, 155, 86, 98, 88, 99, 85, 113, 114, 101 | , ⊢ |
| : , : , : , : , : , : |
75 | instantiation | 97, 98, 150, 86, 99, 87, 88, 102, 103, 113, 114, 101 | , ⊢ |
| : , : , : , : , : , : |
76 | theorem | | ⊢ |
| proveit.numbers.exponentiation.neg_power_as_div |
77 | instantiation | 153, 89, 90 | ⊢ |
| : , : , : |
78 | instantiation | 91, 102 | ⊢ |
| : |
79 | instantiation | 92, 93, 152 | ⊢ |
| : , : , : |
80 | instantiation | 153, 127, 94 | ⊢ |
| : , : , : |
81 | instantiation | 153, 124, 95 | ⊢ |
| : , : , : |
82 | theorem | | ⊢ |
| proveit.logic.equality.sub_right_side_into |
83 | instantiation | 112, 96, 101 | , ⊢ |
| : , : |
84 | instantiation | 97, 98, 150, 155, 99, 100, 113, 114, 101 | , ⊢ |
| : , : , : , : , : , : |
85 | instantiation | 112, 102, 103 | ⊢ |
| : , : |
86 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.nat3 |
87 | instantiation | 115 | ⊢ |
| : , : |
88 | instantiation | 104 | ⊢ |
| : , : , : |
89 | theorem | | ⊢ |
| proveit.numbers.number_sets.complex_numbers.real_nonzero_within_complex_nonzero |
90 | instantiation | 153, 105, 106 | ⊢ |
| : , : , : |
91 | theorem | | ⊢ |
| proveit.numbers.exponentiation.complex_x_to_first_power_is_x |
92 | theorem | | ⊢ |
| proveit.logic.sets.inclusion.unfold_subset_eq |
93 | instantiation | 107, 108 | ⊢ |
| : , : |
94 | instantiation | 153, 109, 110 | ⊢ |
| : , : , : |
95 | instantiation | 153, 127, 111 | ⊢ |
| : , : , : |
96 | instantiation | 112, 113, 114 | ⊢ |
| : , : |
97 | theorem | | ⊢ |
| proveit.numbers.multiplication.disassociation |
98 | axiom | | ⊢ |
| proveit.numbers.number_sets.natural_numbers.zero_in_nats |
99 | theorem | | ⊢ |
| proveit.core_expr_types.tuples.tuple_len_0_typical_eq |
100 | instantiation | 115 | ⊢ |
| : , : |
101 | instantiation | 153, 124, 116 | , ⊢ |
| : , : , : |
102 | instantiation | 153, 124, 117 | ⊢ |
| : , : , : |
103 | instantiation | 153, 124, 118 | ⊢ |
| : , : , : |
104 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.tuple_len_3_typical_eq |
105 | theorem | | ⊢ |
| proveit.numbers.number_sets.real_numbers.rational_nonzero_within_real_nonzero |
106 | instantiation | 153, 119, 120 | ⊢ |
| : , : , : |
107 | theorem | | ⊢ |
| proveit.logic.sets.inclusion.relax_proper_subset |
108 | theorem | | ⊢ |
| proveit.numbers.number_sets.real_numbers.nat_pos_within_real |
109 | theorem | | ⊢ |
| proveit.numbers.number_sets.rational_numbers.rational_pos_within_rational |
110 | instantiation | 121, 122, 123 | ⊢ |
| : , : |
111 | instantiation | 153, 136, 143 | ⊢ |
| : , : , : |
112 | theorem | | ⊢ |
| proveit.numbers.multiplication.mult_complex_closure_bin |
113 | theorem | | ⊢ |
| proveit.numbers.number_sets.complex_numbers.i_is_complex |
114 | instantiation | 153, 124, 125 | ⊢ |
| : , : , : |
115 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.tuple_len_2_typical_eq |
116 | instantiation | 153, 127, 126 | , ⊢ |
| : , : , : |
117 | instantiation | 153, 127, 128 | ⊢ |
| : , : , : |
118 | instantiation | 153, 129, 130 | ⊢ |
| : , : , : |
119 | theorem | | ⊢ |
| proveit.numbers.number_sets.rational_numbers.nonzero_int_within_rational_nonzero |
120 | instantiation | 153, 131, 134 | ⊢ |
| : , : , : |
121 | theorem | | ⊢ |
| proveit.numbers.division.div_rational_pos_closure |
122 | instantiation | 153, 133, 132 | ⊢ |
| : , : , : |
123 | instantiation | 153, 133, 134 | ⊢ |
| : , : , : |
124 | theorem | | ⊢ |
| proveit.numbers.number_sets.complex_numbers.real_within_complex |
125 | theorem | | ⊢ |
| proveit.physics.quantum.QPE._phase_is_real |
126 | instantiation | 153, 136, 135 | , ⊢ |
| : , : , : |
127 | theorem | | ⊢ |
| proveit.numbers.number_sets.real_numbers.rational_within_real |
128 | instantiation | 153, 136, 146 | ⊢ |
| : , : , : |
129 | theorem | | ⊢ |
| proveit.numbers.number_sets.real_numbers.real_pos_within_real |
130 | theorem | | ⊢ |
| proveit.numbers.number_sets.real_numbers.pi_is_real_pos |
131 | theorem | | ⊢ |
| proveit.numbers.number_sets.integers.nat_pos_within_nonzero_int |
132 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.posnat1 |
133 | theorem | | ⊢ |
| proveit.numbers.number_sets.rational_numbers.nat_pos_within_rational_pos |
134 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.posnat2 |
135 | instantiation | 153, 137, 138 | , ⊢ |
| : , : , : |
136 | theorem | | ⊢ |
| proveit.numbers.number_sets.rational_numbers.int_within_rational |
137 | instantiation | 139, 140, 141 | ⊢ |
| : , : |
138 | assumption | | ⊢ |
139 | theorem | | ⊢ |
| proveit.numbers.number_sets.integers.int_interval_within_int |
140 | theorem | | ⊢ |
| proveit.numbers.number_sets.integers.zero_is_int |
141 | instantiation | 142, 143, 144 | ⊢ |
| : , : |
142 | theorem | | ⊢ |
| proveit.numbers.addition.add_int_closure_bin |
143 | instantiation | 145, 146, 147 | ⊢ |
| : , : |
144 | instantiation | 148, 149 | ⊢ |
| : |
145 | theorem | | ⊢ |
| proveit.numbers.exponentiation.exp_int_closure |
146 | instantiation | 153, 154, 150 | ⊢ |
| : , : , : |
147 | instantiation | 153, 151, 152 | ⊢ |
| : , : , : |
148 | theorem | | ⊢ |
| proveit.numbers.negation.int_closure |
149 | instantiation | 153, 154, 155 | ⊢ |
| : , : , : |
150 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.nat2 |
151 | theorem | | ⊢ |
| proveit.numbers.number_sets.natural_numbers.nat_pos_within_nat |
152 | assumption | | ⊢ |
153 | theorem | | ⊢ |
| proveit.logic.sets.inclusion.superset_membership_from_proper_subset |
154 | theorem | | ⊢ |
| proveit.numbers.number_sets.integers.nat_within_int |
155 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.nat1 |
*equality replacement requirements |