Expression of type ExprTuple

from the theory of proveit.physics.quantum.QPE

import proveit
# Automation is not needed when building an expression:
proveit.defaults.automation = False # This will speed things up.
proveit.defaults.inline_pngs = False # Makes files smaller.
%load_expr # Load the stored expression as 'stored_expr'
# import Expression classes needed to build the expression
from proveit import ExprTuple
from proveit.logic import Equals
from proveit.physics.quantum.QPE import _Omega, _sample_space

# build up the expression from sub-expressions
expr = ExprTuple(Equals(_sample_space, _Omega))

expr:

# check that the built expression is the same as the stored expression
assert expr == stored_expr
assert expr._style_id == stored_expr._style_id
print("Passed sanity check: expr matches stored_expr")

Passed sanity check: expr matches stored_expr

# Show the LaTeX representation of the expression for convenience if you need it.
print(stored_expr.latex())

\left(\left\{\begin{array}{c} \Qcircuit@C=1em @R=.7em{
\qin{\lvert + \rangle} & \multigate{4}{\textrm{QPE}\left(U, t\right)} & \meter & \multiqout{3}{\lvert m \rangle_{t}} \\
\qin{\lvert + \rangle} & \ghost{\textrm{QPE}\left(U, t\right)} & \meter & \ghostqout{\lvert m \rangle_{t}} \\
\qin{\begin{array}{c}:\\ \left(t - 3\right) \times \\:\end{array}} & \ghost{\textrm{QPE}\left(U, t\right)} & \measure{\begin{array}{c}:\\ \left(t - 3\right) \times \\:\end{array}} \qw & \ghostqout{\lvert m \rangle_{t}} \\
\qin{\lvert + \rangle} & \ghost{\textrm{QPE}\left(U, t\right)} & \meter & \ghostqout{\lvert m \rangle_{t}} \\
\qin{\lvert u \rangle} & \ghost{\textrm{QPE}\left(U, t\right)} & { /^{s} } \qw & \qout{\lvert u \rangle}
} \end{array}\right\}_{m \in \{0~\ldotp \ldotp~2^{t} - 1\}} = \Omega\right)

stored_expr.style_options()

no style options

# display the expression information
stored_expr.expr_info()

	core type	sub-expressions	expression
0	ExprTuple	1
1	Operation	operator: 2 operands: 3
2	Literal
3	ExprTuple	4, 5
4	Operation	operator: 6 operand: 8
5	Literal
6	Literal
7	ExprTuple	8
8	Lambda	parameter: 102 body: 10
9	ExprTuple	102
10	Conditional	value: 11 condition: 12
11	Operation	operator: 13 operands: 14
12	Operation	operator: 15 operands: 16
13	Literal
14	ExprTuple	17, 18, 19, 20
15	Literal
16	ExprTuple	102, 21
17	ExprTuple	22, 23
18	ExprTuple	24, 25
19	ExprTuple	26, 27
20	ExprTuple	28, 29
21	Operation	operator: 84 operands: 30
22	ExprRange	lambda_map: 31 start_index: 103 end_index: 104
23	ExprRange	lambda_map: 32 start_index: 103 end_index: 105
24	ExprRange	lambda_map: 33 start_index: 103 end_index: 104
25	ExprRange	lambda_map: 33 start_index: 92 end_index: 93
26	ExprRange	lambda_map: 34 start_index: 103 end_index: 104
27	ExprRange	lambda_map: 35 start_index: 103 end_index: 105
28	ExprRange	lambda_map: 36 start_index: 103 end_index: 104
29	ExprRange	lambda_map: 37 start_index: 103 end_index: 105
30	ExprTuple	38, 39
31	Lambda	parameter: 91 body: 40
32	Lambda	parameter: 91 body: 41
33	Lambda	parameter: 91 body: 42
34	Lambda	parameter: 91 body: 43
35	Lambda	parameter: 91 body: 44
36	Lambda	parameter: 91 body: 45
37	Lambda	parameter: 91 body: 47
38	Literal
39	Operation	operator: 99 operands: 48
40	Operation	operator: 76 operands: 49
41	Operation	operator: 56 operands: 50
42	Operation	operator: 56 operands: 51
43	Operation	operator: 52 operands: 53
44	Operation	operator: 77 operands: 54
45	Operation	operator: 56 operands: 55
46	ExprTuple	91
47	Operation	operator: 56 operands: 57
48	ExprTuple	58, 59
49	NamedExprs	state: 60
50	NamedExprs	element: 61 targets: 69
51	NamedExprs	element: 62 targets: 63
52	Literal
53	NamedExprs	basis: 64
54	NamedExprs	operation: 65
55	NamedExprs	element: 66 targets: 67
56	Literal
57	NamedExprs	element: 68 targets: 69
58	Operation	operator: 70 operands: 71
59	Operation	operator: 72 operand: 103
60	Operation	operator: 74 operand: 87
61	Operation	operator: 76 operands: 83
62	Operation	operator: 77 operands: 78
63	Operation	operator: 84 operands: 79
64	Literal
65	Literal
66	Operation	operator: 82 operands: 80
67	Operation	operator: 84 operands: 81
68	Operation	operator: 82 operands: 83
69	Operation	operator: 84 operands: 85
70	Literal
71	ExprTuple	86, 104
72	Literal
73	ExprTuple	103
74	Literal
75	ExprTuple	87
76	Literal
77	Literal
78	NamedExprs	operation: 88 part: 91
79	ExprTuple	103, 93
80	NamedExprs	state: 89 part: 91
81	ExprTuple	103, 104
82	Literal
83	NamedExprs	state: 90 part: 91
84	Literal
85	ExprTuple	92, 93
86	Literal
87	Literal
88	Operation	operator: 94 operands: 95
89	Operation	operator: 96 operands: 97
90	Literal
91	Variable
92	Operation	operator: 99 operands: 98
93	Operation	operator: 99 operands: 100
94	Literal
95	ExprTuple	101, 104
96	Literal
97	ExprTuple	102, 104
98	ExprTuple	104, 103
99	Literal
100	ExprTuple	104, 105
101	Literal
102	Variable
103	Literal
104	Literal
105	Literal