| step type | requirements | statement |
0 | instantiation | 1, 2, 3 | ⊢ |
| : , : , : |
1 | theorem | | ⊢ |
| proveit.logic.equality.sub_left_side_into |
2 | instantiation | 4, 84, 5, 6* | ⊢ |
| : |
3 | instantiation | 115, 7 | ⊢ |
| : , : , : |
4 | axiom | | ⊢ |
| proveit.physics.quantum.QPE._psi_t_def |
5 | instantiation | 77, 8, 9 | ⊢ |
| : , : , : |
6 | instantiation | 106, 10, 11 | ⊢ |
| : , : , : |
7 | instantiation | 12, 13, 125, 14, 15*, 16* | ⊢ |
| : , : , : , : |
8 | instantiation | 17, 18, 105, 91 | ⊢ |
| : , : , : |
9 | instantiation | 19, 105, 20 | ⊢ |
| : , : |
10 | instantiation | 115, 21 | ⊢ |
| : , : , : |
11 | instantiation | 22, 54, 23 | ⊢ |
| : , : , : |
12 | theorem | | ⊢ |
| proveit.linear_algebra.addition.vec_sum_split_first |
13 | theorem | | ⊢ |
| proveit.numbers.number_sets.integers.zero_is_int |
14 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.less_0_1 |
15 | instantiation | 106, 24, 25 | ⊢ |
| : , : , : |
16 | instantiation | 106, 26, 27 | ⊢ |
| : , : , : |
17 | theorem | | ⊢ |
| proveit.numbers.addition.subtraction.subtract_from_add |
18 | theorem | | ⊢ |
| proveit.numbers.number_sets.complex_numbers.zero_is_complex |
19 | theorem | | ⊢ |
| proveit.numbers.addition.commutation |
20 | instantiation | 28, 105 | ⊢ |
| : |
21 | instantiation | 29, 84, 30 | ⊢ |
| : , : , : |
22 | axiom | | ⊢ |
| proveit.linear_algebra.tensors.unary_tensor_prod_def |
23 | instantiation | 53, 54, 31, 32 | ⊢ |
| : , : , : , : |
24 | instantiation | 115, 33 | ⊢ |
| : , : , : |
25 | instantiation | 34, 105, 43, 54 | ⊢ |
| : , : , : |
26 | instantiation | 115, 35 | ⊢ |
| : , : , : |
27 | instantiation | 36, 125, 37* | ⊢ |
| : , : |
28 | theorem | | ⊢ |
| proveit.numbers.negation.complex_closure |
29 | theorem | | ⊢ |
| proveit.core_expr_types.tuples.tuple_eq_via_elem_eq |
30 | instantiation | 115, 38 | ⊢ |
| : , : , : |
31 | instantiation | 39, 105, 40, 41 | ⊢ |
| : , : |
32 | instantiation | 42, 54, 43, 44 | ⊢ |
| : , : , : , : |
33 | instantiation | 106, 45, 46 | ⊢ |
| : , : , : |
34 | theorem | | ⊢ |
| proveit.linear_algebra.scalar_multiplication.one_as_scalar_mult_id |
35 | modus ponens | 47, 48 | ⊢ |
36 | axiom | | ⊢ |
| proveit.linear_algebra.addition.vec_sum_single |
37 | instantiation | 93, 69, 98, 70, 99, 118, 111, 102, 103 | ⊢ |
| : , : , : , : |
38 | instantiation | 115, 49 | ⊢ |
| : , : , : |
39 | theorem | | ⊢ |
| proveit.numbers.division.div_complex_closure |
40 | instantiation | 50, 118 | ⊢ |
| : |
41 | instantiation | 51, 63, 52 | ⊢ |
| : , : |
42 | theorem | | ⊢ |
| proveit.linear_algebra.addition.binary_closure |
43 | theorem | | ⊢ |
| proveit.physics.quantum.algebra.ket_zero_in_qubit_space |
44 | instantiation | 53, 54, 55, 56 | ⊢ |
| : , : , : , : |
45 | instantiation | 115, 57 | ⊢ |
| : , : , : |
46 | instantiation | 117, 66 | ⊢ |
| : |
47 | instantiation | 58, 84 | ⊢ |
| : , : , : , : , : , : |
48 | generalization | 59 | ⊢ |
49 | instantiation | 115, 60 | ⊢ |
| : , : , : |
50 | theorem | | ⊢ |
| proveit.numbers.exponentiation.sqrt_complex_closure |
51 | theorem | | ⊢ |
| proveit.numbers.exponentiation.exp_rational_non_zero__not_zero |
52 | instantiation | 61, 62, 63 | ⊢ |
| : , : |
53 | theorem | | ⊢ |
| proveit.linear_algebra.scalar_multiplication.scalar_mult_closure |
54 | instantiation | 64, 86 | ⊢ |
| : |
55 | instantiation | 65, 66, 67 | ⊢ |
| : , : |
56 | theorem | | ⊢ |
| proveit.physics.quantum.algebra.ket_one_in_qubit_space |
57 | instantiation | 68, 69, 98, 70, 99, 118, 111, 102, 103 | ⊢ |
| : , : , : , : |
58 | axiom | | ⊢ |
| proveit.core_expr_types.lambda_maps.lambda_substitution |
59 | instantiation | 115, 71 | ⊢ |
| : , : , : |
60 | instantiation | 115, 72 | ⊢ |
| : , : , : |
61 | theorem | | ⊢ |
| proveit.numbers.division.div_rational_nonzero_closure |
62 | instantiation | 131, 74, 73 | ⊢ |
| : , : , : |
63 | instantiation | 131, 74, 75 | ⊢ |
| : , : , : |
64 | theorem | | ⊢ |
| proveit.linear_algebra.complex_vec_set_is_vec_space |
65 | theorem | | ⊢ |
| proveit.numbers.exponentiation.exp_complex_closure |
66 | instantiation | 131, 121, 76 | ⊢ |
| : , : , : |
67 | instantiation | 77, 78, 79 | ⊢ |
| : , : , : |
68 | theorem | | ⊢ |
| proveit.numbers.multiplication.mult_zero_any |
69 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.nat4 |
70 | instantiation | 80 | ⊢ |
| : , : , : , : |
71 | instantiation | 115, 81 | ⊢ |
| : , : , : |
72 | instantiation | 106, 82, 83 | ⊢ |
| : , : , : |
73 | instantiation | 131, 85, 84 | ⊢ |
| : , : , : |
74 | theorem | | ⊢ |
| proveit.numbers.number_sets.rational_numbers.nonzero_int_within_rational_nonzero |
75 | instantiation | 131, 85, 86 | ⊢ |
| : , : , : |
76 | instantiation | 131, 123, 87 | ⊢ |
| : , : , : |
77 | theorem | | ⊢ |
| proveit.logic.equality.sub_right_side_into |
78 | instantiation | 110, 96, 88 | ⊢ |
| : , : |
79 | instantiation | 106, 89, 90 | ⊢ |
| : , : , : |
80 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.tuple_len_4_typical_eq |
81 | instantiation | 115, 91 | ⊢ |
| : , : , : |
82 | instantiation | 115, 92 | ⊢ |
| : , : , : |
83 | instantiation | 93, 94, 128, 95, 118, 111, 102, 103 | ⊢ |
| : , : , : , : |
84 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.posnat1 |
85 | theorem | | ⊢ |
| proveit.numbers.number_sets.integers.nat_pos_within_nonzero_int |
86 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.posnat2 |
87 | theorem | | ⊢ |
| proveit.numbers.number_sets.real_numbers.e_is_real_pos |
88 | instantiation | 110, 102, 103 | ⊢ |
| : , : |
89 | instantiation | 97, 128, 133, 98, 101, 99, 96, 102, 103 | ⊢ |
| : , : , : , : , : , : |
90 | instantiation | 97, 98, 133, 99, 100, 101, 118, 111, 102, 103 | ⊢ |
| : , : , : , : , : , : |
91 | instantiation | 104, 105 | ⊢ |
| : |
92 | instantiation | 106, 107, 108 | ⊢ |
| : , : , : |
93 | theorem | | ⊢ |
| proveit.numbers.multiplication.elim_one_any |
94 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.nat3 |
95 | instantiation | 109 | ⊢ |
| : , : , : |
96 | instantiation | 110, 118, 111 | ⊢ |
| : , : |
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 | 112 | ⊢ |
| : , : |
101 | instantiation | 112 | ⊢ |
| : , : |
102 | theorem | | ⊢ |
| proveit.numbers.number_sets.complex_numbers.i_is_complex |
103 | instantiation | 131, 121, 113 | ⊢ |
| : , : , : |
104 | theorem | | ⊢ |
| proveit.numbers.addition.elim_zero_left |
105 | instantiation | 131, 121, 114 | ⊢ |
| : , : , : |
106 | axiom | | ⊢ |
| proveit.logic.equality.equals_transitivity |
107 | instantiation | 115, 116 | ⊢ |
| : , : , : |
108 | instantiation | 117, 118 | ⊢ |
| : |
109 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.tuple_len_3_typical_eq |
110 | theorem | | ⊢ |
| proveit.numbers.multiplication.mult_complex_closure_bin |
111 | instantiation | 131, 121, 119 | ⊢ |
| : , : , : |
112 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.tuple_len_2_typical_eq |
113 | theorem | | ⊢ |
| proveit.physics.quantum.QPE._phase_is_real |
114 | instantiation | 131, 126, 120 | ⊢ |
| : , : , : |
115 | axiom | | ⊢ |
| proveit.logic.equality.substitution |
116 | theorem | | ⊢ |
| proveit.numbers.negation.negated_zero |
117 | theorem | | ⊢ |
| proveit.numbers.exponentiation.exp_zero_eq_one |
118 | instantiation | 131, 121, 122 | ⊢ |
| : , : , : |
119 | instantiation | 131, 123, 124 | ⊢ |
| : , : , : |
120 | instantiation | 131, 129, 125 | ⊢ |
| : , : , : |
121 | theorem | | ⊢ |
| proveit.numbers.number_sets.complex_numbers.real_within_complex |
122 | instantiation | 131, 126, 127 | ⊢ |
| : , : , : |
123 | theorem | | ⊢ |
| proveit.numbers.number_sets.real_numbers.real_pos_within_real |
124 | theorem | | ⊢ |
| proveit.numbers.number_sets.real_numbers.pi_is_real_pos |
125 | instantiation | 131, 132, 128 | ⊢ |
| : , : , : |
126 | theorem | | ⊢ |
| proveit.numbers.number_sets.real_numbers.rational_within_real |
127 | instantiation | 131, 129, 130 | ⊢ |
| : , : , : |
128 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.nat1 |
129 | theorem | | ⊢ |
| proveit.numbers.number_sets.rational_numbers.int_within_rational |
130 | instantiation | 131, 132, 133 | ⊢ |
| : , : , : |
131 | theorem | | ⊢ |
| proveit.logic.sets.inclusion.superset_membership_from_proper_subset |
132 | theorem | | ⊢ |
| proveit.numbers.number_sets.integers.nat_within_int |
133 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.nat2 |
*equality replacement requirements |