Expression of type ExprTuple

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 Conditional, ExprTuple, Lambda, m, n
from proveit.logic import And, InClass, InSet, SetOfAll
from proveit.numbers import NaturalPos
from proveit.physics.quantum import m_bit_interval, m_ket_domain, normalized_var_ket_psi, var_ket_psi
from proveit.physics.quantum.circuits import register_meas
from proveit.statistics import SampleSpaces

# build up the expression from sub-expressions
expr = ExprTuple(Lambda([m, var_ket_psi], Conditional(InClass(SetOfAll(instance_param_or_params = [n], instance_element = register_meas, domain = m_bit_interval), SampleSpaces), And(InSet(m, NaturalPos), InSet(var_ket_psi, m_ket_domain), normalized_var_ket_psi))))

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(m, \lvert \psi \rangle\right) \mapsto \left\{\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\}} \underset{{\scriptscriptstyle c}}{\in} \textrm{SampleSpaces} \textrm{ if } m \in \mathbb{N}^+ ,  \lvert \psi \rangle \in \mathbb{C}^{2^{m}} ,  \left \|\lvert \psi \rangle\right \| = 1\right..\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	Lambda	parameters: 2 body: 3
2	ExprTuple	86, 79
3	Conditional	value: 4 condition: 5
4	Operation	operator: 6 operands: 7
5	Operation	operator: 8 operands: 9
6	Literal
7	ExprTuple	10, 11
8	Literal
9	ExprTuple	12, 13, 14
10	Operation	operator: 15 operand: 21
11	Literal
12	Operation	operator: 36 operands: 17
13	Operation	operator: 36 operands: 18
14	Operation	operator: 19 operands: 20
15	Literal
16	ExprTuple	21
17	ExprTuple	86, 22
18	ExprTuple	79, 23
19	Literal
20	ExprTuple	24, 82
21	Lambda	parameter: 85 body: 26
22	Literal
23	Operation	operator: 27 operands: 28
24	Operation	operator: 29 operand: 79
25	ExprTuple	85
26	Conditional	value: 31 condition: 32
27	Literal
28	ExprTuple	33, 62
29	Literal
30	ExprTuple	79
31	Operation	operator: 34 operands: 35
32	Operation	operator: 36 operands: 37
33	Literal
34	Literal
35	ExprTuple	38, 39, 40
36	Literal
37	ExprTuple	85, 41
38	ExprTuple	42
39	ExprTuple	43
40	ExprTuple	44
41	Operation	operator: 76 operands: 45
42	ExprRange	lambda_map: 46 start_index: 82 end_index: 86
43	ExprRange	lambda_map: 47 start_index: 82 end_index: 86
44	ExprRange	lambda_map: 48 start_index: 82 end_index: 86
45	ExprTuple	49, 50
46	Lambda	parameter: 81 body: 51
47	Lambda	parameter: 81 body: 52
48	Lambda	parameter: 81 body: 54
49	Literal
50	Operation	operator: 55 operands: 56
51	Operation	operator: 60 operands: 57
52	Operation	operator: 58 operands: 59
53	ExprTuple	81
54	Operation	operator: 60 operands: 61
55	Literal
56	ExprTuple	62, 63
57	NamedExprs	element: 64 targets: 67
58	Literal
59	NamedExprs	basis: 65
60	Literal
61	NamedExprs	element: 66 targets: 67
62	Operation	operator: 68 operands: 69
63	Operation	operator: 70 operand: 82
64	Operation	operator: 72 operands: 73
65	Literal
66	Operation	operator: 74 operands: 75
67	Operation	operator: 76 operands: 77
68	Literal
69	ExprTuple	78, 86
70	Literal
71	ExprTuple	82
72	Literal
73	NamedExprs	state: 79 part: 81
74	Literal
75	NamedExprs	state: 80 part: 81
76	Literal
77	ExprTuple	82, 86
78	Literal
79	Variable
80	Operation	operator: 83 operands: 84
81	Variable
82	Literal
83	Literal
84	ExprTuple	85, 86
85	Variable
86	Variable