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, Bijections, 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

# build up the expression from sub-expressions
expr = ExprTuple(Lambda([m, var_ket_psi], Conditional(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), 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\{\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} \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	88, 81
3	Conditional	value: 4 condition: 5
4	Operation	operator: 38 operands: 6
5	Operation	operator: 7 operands: 8
6	ExprTuple	9, 10
7	Literal
8	ExprTuple	11, 12, 13
9	Lambda	parameter: 87 body: 34
10	Operation	operator: 14 operands: 15
11	Operation	operator: 38 operands: 16
12	Operation	operator: 38 operands: 17
13	Operation	operator: 18 operands: 19
14	Literal
15	ExprTuple	43, 20
16	ExprTuple	88, 21
17	ExprTuple	81, 22
18	Literal
19	ExprTuple	23, 84
20	Operation	operator: 24 operand: 30
21	Literal
22	Operation	operator: 26 operands: 27
23	Operation	operator: 28 operand: 81
24	Literal
25	ExprTuple	30
26	Literal
27	ExprTuple	31, 64
28	Literal
29	ExprTuple	81
30	Lambda	parameter: 87 body: 33
31	Literal
32	ExprTuple	87
33	Conditional	value: 34 condition: 35
34	Operation	operator: 36 operands: 37
35	Operation	operator: 38 operands: 39
36	Literal
37	ExprTuple	40, 41, 42
38	Literal
39	ExprTuple	87, 43
40	ExprTuple	44
41	ExprTuple	45
42	ExprTuple	46
43	Operation	operator: 78 operands: 47
44	ExprRange	lambda_map: 48 start_index: 84 end_index: 88
45	ExprRange	lambda_map: 49 start_index: 84 end_index: 88
46	ExprRange	lambda_map: 50 start_index: 84 end_index: 88
47	ExprTuple	51, 52
48	Lambda	parameter: 83 body: 53
49	Lambda	parameter: 83 body: 54
50	Lambda	parameter: 83 body: 56
51	Literal
52	Operation	operator: 57 operands: 58
53	Operation	operator: 62 operands: 59
54	Operation	operator: 60 operands: 61
55	ExprTuple	83
56	Operation	operator: 62 operands: 63
57	Literal
58	ExprTuple	64, 65
59	NamedExprs	element: 66 targets: 69
60	Literal
61	NamedExprs	basis: 67
62	Literal
63	NamedExprs	element: 68 targets: 69
64	Operation	operator: 70 operands: 71
65	Operation	operator: 72 operand: 84
66	Operation	operator: 74 operands: 75
67	Literal
68	Operation	operator: 76 operands: 77
69	Operation	operator: 78 operands: 79
70	Literal
71	ExprTuple	80, 88
72	Literal
73	ExprTuple	84
74	Literal
75	NamedExprs	state: 81 part: 83
76	Literal
77	NamedExprs	state: 82 part: 83
78	Literal
79	ExprTuple	84, 88
80	Literal
81	Variable
82	Operation	operator: 85 operands: 86
83	Variable
84	Literal
85	Literal
86	ExprTuple	87, 88
87	Variable
88	Variable