Expression of type InSet

from the theory of proveit.physics.quantum.circuits

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 Lambda, n
from proveit.logic import Bijections, InSet, SetOfAll
from proveit.physics.quantum import m_bit_interval
from proveit.physics.quantum.circuits import register_meas

# build up the expression from sub-expressions
expr = InSet(Lambda(n, register_meas), Bijections(m_bit_interval, SetOfAll(instance_param_or_params = [n], instance_element = register_meas, domain = m_bit_interval))).with_wrapping_at(2)

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())

\begin{array}{c} \begin{array}{l} \left[n \mapsto \left(\begin{array}{c} \Qcircuit@C=1em @R=.7em{
\multiqin{3}{\lvert \psi \rangle} & \meter & \multiqout{3}{\lvert n \rangle_{m}} \\
\ghostqin{\lvert \psi \rangle} & \meter & \ghostqout{\lvert n \rangle_{m}} \\
\ghostqin{\lvert \psi \rangle} & \measure{\begin{array}{c}:\\ \left(m - 3\right) \times \\:\end{array}} \qw & \ghostqout{\lvert n \rangle_{m}} \\
\ghostqin{\lvert \psi \rangle} & \meter & \ghostqout{\lvert n \rangle_{m}}
} \end{array}\right)\right] \in  \\ \left[\{0~\ldotp \ldotp~2^{m} - 1\} \xrightarrow[\text{onto}]{\text{1-to-1}} \left\{\begin{array}{c} \Qcircuit@C=1em @R=.7em{
\multiqin{3}{\lvert \psi \rangle} & \meter & \multiqout{3}{\lvert n \rangle_{m}} \\
\ghostqin{\lvert \psi \rangle} & \meter & \ghostqout{\lvert n \rangle_{m}} \\
\ghostqin{\lvert \psi \rangle} & \measure{\begin{array}{c}:\\ \left(m - 3\right) \times \\:\end{array}} \qw & \ghostqout{\lvert n \rangle_{m}} \\
\ghostqin{\lvert \psi \rangle} & \meter & \ghostqout{\lvert n \rangle_{m}}
} \end{array}\right\}_{n \in \{0~\ldotp \ldotp~2^{m} - 1\}}\right] \end{array} \end{array}

stored_expr.style_options()

name	description	default	current value	related methods
operation	'infix' or 'function' style formatting	infix	infix
wrap_positions	position(s) at which wrapping is to occur; '2 n - 1' is after the nth operand, '2 n' is after the nth operation.	()	(2)	('with_wrapping_at', 'with_wrap_before_operator', 'with_wrap_after_operator', 'without_wrapping', 'wrap_positions')
justification	if any wrap positions are set, justify to the 'left', 'center', or 'right'	center	center	('with_justification',)
direction	Direction of the relation (normal or reversed)	normal	normal	('with_direction_reversed', 'is_reversed')

# display the expression information
stored_expr.expr_info()

	core type	sub-expressions	expression
0	Operation	operator: 16 operands: 1
1	ExprTuple	2, 3
2	Lambda	parameter: 65 body: 12
3	Operation	operator: 4 operands: 5
4	Literal
5	ExprTuple	21, 6
6	Operation	operator: 7 operand: 9
7	Literal
8	ExprTuple	9
9	Lambda	parameter: 65 body: 11
10	ExprTuple	65
11	Conditional	value: 12 condition: 13
12	Operation	operator: 14 operands: 15
13	Operation	operator: 16 operands: 17
14	Literal
15	ExprTuple	18, 19, 20
16	Literal
17	ExprTuple	65, 21
18	ExprTuple	22
19	ExprTuple	23
20	ExprTuple	24
21	Operation	operator: 56 operands: 25
22	ExprRange	lambda_map: 26 start_index: 62 end_index: 66
23	ExprRange	lambda_map: 27 start_index: 62 end_index: 66
24	ExprRange	lambda_map: 28 start_index: 62 end_index: 66
25	ExprTuple	29, 30
26	Lambda	parameter: 61 body: 31
27	Lambda	parameter: 61 body: 32
28	Lambda	parameter: 61 body: 34
29	Literal
30	Operation	operator: 35 operands: 36
31	Operation	operator: 40 operands: 37
32	Operation	operator: 38 operands: 39
33	ExprTuple	61
34	Operation	operator: 40 operands: 41
35	Literal
36	ExprTuple	42, 43
37	NamedExprs	element: 44 targets: 47
38	Literal
39	NamedExprs	basis: 45
40	Literal
41	NamedExprs	element: 46 targets: 47
42	Operation	operator: 48 operands: 49
43	Operation	operator: 50 operand: 62
44	Operation	operator: 52 operands: 53
45	Literal
46	Operation	operator: 54 operands: 55
47	Operation	operator: 56 operands: 57
48	Literal
49	ExprTuple	58, 66
50	Literal
51	ExprTuple	62
52	Literal
53	NamedExprs	state: 59 part: 61
54	Literal
55	NamedExprs	state: 60 part: 61
56	Literal
57	ExprTuple	62, 66
58	Literal
59	Variable
60	Operation	operator: 63 operands: 64
61	Variable
62	Literal
63	Literal
64	ExprTuple	65, 66
65	Variable
66	Variable