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, b
from proveit.logic import Bijections, InSet, Set, SetOfAll
from proveit.numbers import one, zero
from proveit.physics.quantum.circuits import qubit_meas

# build up the expression from sub-expressions
sub_expr1 = Set(zero, one)
expr = InSet(Lambda(b, qubit_meas), Bijections(sub_expr1, SetOfAll(instance_param_or_params = [b], instance_element = qubit_meas, domain = sub_expr1))).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[b \mapsto \left(\begin{array}{c} \Qcircuit@C=1em @R=.7em{
\qin{\lvert \psi \rangle} & \meter & \qout{\lvert b \rangle}
} \end{array}\right)\right] \in  \\ \left[\left\{0, 1\right\} \xrightarrow[\text{onto}]{\text{1-to-1}} \left\{\begin{array}{c} \Qcircuit@C=1em @R=.7em{
\qin{\lvert \psi \rangle} & \meter & \qout{\lvert b \rangle}
} \end{array}\right\}_{b \in \left\{0, 1\right\}}\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: 15 operands: 1
1	ExprTuple	2, 3
2	Lambda	parameter: 39 body: 11
3	Operation	operator: 4 operands: 5
4	Literal
5	ExprTuple	20, 6
6	Operation	operator: 7 operand: 9
7	Literal
8	ExprTuple	9
9	Lambda	parameter: 39 body: 10
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
15	Literal
16	ExprTuple	39, 20
17	ExprTuple	21
18	ExprTuple	22
19	ExprTuple	23
20	Operation	operator: 24 operands: 25
21	Operation	operator: 26 operands: 27
22	Operation	operator: 28 operands: 29
23	Operation	operator: 30 operands: 31
24	Literal
25	ExprTuple	32, 33
26	Literal
27	NamedExprs	state: 34
28	Literal
29	NamedExprs	basis: 35
30	Literal
31	NamedExprs	state: 36
32	Literal
33	Literal
34	Variable
35	Literal
36	Operation	operator: 37 operand: 39
37	Literal
38	ExprTuple	39
39	Variable