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 ExprTuple, Lambda
from proveit.core_expr_types.expr_arrays import A11_to_Akl
from proveit.logic import Equals
from proveit.physics.quantum.circuits import circuit__psi_m__u_Akl_v, circuit__u_Akl_v
from proveit.statistics import Prob

# build up the expression from sub-expressions
expr = ExprTuple(Lambda([A11_to_Akl], Equals(Prob(circuit__u_Akl_v), Prob(circuit__psi_m__u_Akl_v)).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())

\left(\left(A_{1, 1}, A_{1, 2}, \ldots, A_{1, l}, A_{2, 1}, A_{2, 2}, \ldots, A_{2, l}, \ldots\ldots, A_{k, 1}, A_{k, 2}, \ldots, A_{k, l}\right) \mapsto \left(\begin{array}{c} \begin{array}{l} \textrm{Pr}\left(\begin{array}{c} \Qcircuit@C=1em @R=.7em{
\multiqin{3}{\lvert u \rangle} & \gate{A_{1, 1}} \qwx[1] & \gate{A_{2, 1}} \qwx[1] & \gate{\cdots} \qwx[1] & \gate{A_{k, 1}} \qwx[1] & \multiqout{3}{\lvert v \rangle} \\
\ghostqin{\lvert u \rangle} & \gate{A_{1, 2}} \qwx[1] & \gate{A_{2, 2}} \qwx[1] & \gate{\cdots} \qwx[1] & \gate{A_{k, 2}} \qwx[1] & \ghostqout{\lvert v \rangle} \\
\ghostqin{\lvert u \rangle} & \gate{\vdots} \qwx[1] & \gate{\vdots} \qwx[1] & \gate{\ddots} \qwx[1] & \gate{\vdots} \qwx[1] & \ghostqout{\lvert v \rangle} \\
\ghostqin{\lvert u \rangle} & \gate{A_{1, l}} & \gate{A_{2, l}} & \gate{\cdots} & \gate{A_{k, l}} & \ghostqout{\lvert v \rangle}
} \end{array}\right) =  \\ \textrm{Pr}\left(\begin{array}{c} \Qcircuit@C=1em @R=.7em{
\qin{\lvert \psi \rangle} & { /^{m} } \qw & { /^{m} } \qw & \gate{\cdots} & { /^{m} } \qw & \qout{\lvert \psi \rangle} \\
\multiqin{3}{\lvert u \rangle} & \gate{A_{1, 1}} \qwx[1] & \gate{A_{2, 1}} \qwx[1] & \gate{\cdots} \qwx[1] & \gate{A_{k, 1}} \qwx[1] & \multiqout{3}{\lvert v \rangle} \\
\ghostqin{\lvert u \rangle} & \gate{A_{1, 2}} \qwx[1] & \gate{A_{2, 2}} \qwx[1] & \gate{\cdots} \qwx[1] & \gate{A_{k, 2}} \qwx[1] & \ghostqout{\lvert v \rangle} \\
\ghostqin{\lvert u \rangle} & \gate{\vdots} \qwx[1] & \gate{\vdots} \qwx[1] & \gate{\ddots} \qwx[1] & \gate{\vdots} \qwx[1] & \ghostqout{\lvert v \rangle} \\
\ghostqin{\lvert u \rangle} & \gate{A_{1, l}} & \gate{A_{2, l}} & \gate{\cdots} & \gate{A_{k, l}} & \ghostqout{\lvert v \rangle}
} \end{array}\right) \end{array} \end{array}\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	4
3	Operation	operator: 5 operands: 6
4	ExprRange	lambda_map: 7 start_index: 93 end_index: 30
5	Literal
6	ExprTuple	8, 9
7	Lambda	parameter: 84 body: 47
8	Operation	operator: 11 operand: 13
9	Operation	operator: 11 operand: 14
10	ExprTuple	13
11	Literal
12	ExprTuple	14
13	Operation	operator: 16 operands: 15
14	Operation	operator: 16 operands: 17
15	ExprTuple	18, 19, 20
16	Literal
17	ExprTuple	21, 22, 23
18	ExprTuple	24
19	ExprRange	lambda_map: 25 start_index: 93 end_index: 30
20	ExprTuple	26
21	ExprTuple	27, 28
22	ExprRange	lambda_map: 29 start_index: 93 end_index: 30
23	ExprTuple	31, 32
24	ExprRange	lambda_map: 33 start_index: 93 end_index: 95
25	Lambda	parameter: 84 body: 34
26	ExprRange	lambda_map: 35 start_index: 93 end_index: 95
27	ExprRange	lambda_map: 36 start_index: 93 end_index: 94
28	ExprRange	lambda_map: 37 start_index: 93 end_index: 95
29	Lambda	parameter: 84 body: 39
30	Variable
31	ExprRange	lambda_map: 40 start_index: 93 end_index: 94
32	ExprRange	lambda_map: 41 start_index: 93 end_index: 95
33	Lambda	parameter: 87 body: 42
34	ExprTuple	47
35	Lambda	parameter: 87 body: 43
36	Lambda	parameter: 87 body: 44
37	Lambda	parameter: 87 body: 45
38	ExprTuple	84
39	ExprTuple	46, 47
40	Lambda	parameter: 87 body: 48
41	Lambda	parameter: 87 body: 49
42	Operation	operator: 57 operands: 50
43	Operation	operator: 57 operands: 51
44	Operation	operator: 57 operands: 52
45	Operation	operator: 57 operands: 53
46	ExprRange	lambda_map: 54 start_index: 93 end_index: 94
47	ExprRange	lambda_map: 55 start_index: 93 end_index: 95
48	Operation	operator: 57 operands: 56
49	Operation	operator: 57 operands: 58
50	NamedExprs	element: 61 targets: 59
51	NamedExprs	element: 67 targets: 59
52	NamedExprs	element: 60 targets: 66
53	NamedExprs	element: 61 targets: 68
54	Lambda	parameter: 87 body: 62
55	Lambda	parameter: 87 body: 64
56	NamedExprs	element: 65 targets: 66
57	Literal
58	NamedExprs	element: 67 targets: 68
59	Operation	operator: 80 operands: 69
60	Operation	operator: 70 operands: 76
61	Operation	operator: 70 operands: 71
62	Operation	operator: 72 operands: 73
63	ExprTuple	87
64	IndexedVar	variable: 74 indices: 75
65	Operation	operator: 78 operands: 76
66	Operation	operator: 80 operands: 77
67	Operation	operator: 78 operands: 79
68	Operation	operator: 80 operands: 81
69	ExprTuple	93, 95
70	Literal
71	NamedExprs	state: 82 part: 87
72	Literal
73	NamedExprs	operation: 83
74	Variable
75	ExprTuple	84, 87
76	NamedExprs	state: 85 part: 87
77	ExprTuple	93, 94
78	Literal
79	NamedExprs	state: 86 part: 87
80	Literal
81	ExprTuple	88, 89
82	Variable
83	Literal
84	Variable
85	Variable
86	Variable
87	Variable
88	Operation	operator: 91 operands: 90
89	Operation	operator: 91 operands: 92
90	ExprTuple	94, 93
91	Literal
92	ExprTuple	94, 95
93	Literal
94	Variable
95	Variable