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__u_Akl_v, circuit__u_Akl_v__psi_m
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__u_Akl_v__psi_m)).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{
\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} \\
\qin{\lvert \psi \rangle} & { /^{m} } \qw & { /^{m} } \qw & \gate{\cdots} & { /^{m} } \qw & \qout{\lvert \psi \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: 83 end_index: 28
5	Literal
6	ExprTuple	8, 9
7	Lambda	parameter: 73 body: 40
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	25
19	ExprRange	lambda_map: 24 start_index: 83 end_index: 28
20	ExprTuple	29
21	ExprTuple	25, 26
22	ExprRange	lambda_map: 27 start_index: 83 end_index: 28
23	ExprTuple	29, 30
24	Lambda	parameter: 73 body: 31
25	ExprRange	lambda_map: 32 start_index: 83 end_index: 84
26	ExprRange	lambda_map: 33 start_index: 83 end_index: 85
27	Lambda	parameter: 73 body: 35
28	Variable
29	ExprRange	lambda_map: 36 start_index: 83 end_index: 84
30	ExprRange	lambda_map: 37 start_index: 83 end_index: 85
31	ExprTuple	40
32	Lambda	parameter: 77 body: 38
33	Lambda	parameter: 77 body: 39
34	ExprTuple	73
35	ExprTuple	40, 41
36	Lambda	parameter: 77 body: 42
37	Lambda	parameter: 77 body: 43
38	Operation	operator: 49 operands: 44
39	Operation	operator: 49 operands: 45
40	ExprRange	lambda_map: 46 start_index: 83 end_index: 84
41	ExprRange	lambda_map: 47 start_index: 83 end_index: 85
42	Operation	operator: 49 operands: 48
43	Operation	operator: 49 operands: 50
44	NamedExprs	element: 51 targets: 57
45	NamedExprs	element: 52 targets: 59
46	Lambda	parameter: 77 body: 53
47	Lambda	parameter: 77 body: 55
48	NamedExprs	element: 56 targets: 57
49	Literal
50	NamedExprs	element: 58 targets: 59
51	Operation	operator: 61 operands: 60
52	Operation	operator: 61 operands: 69
53	IndexedVar	variable: 62 indices: 63
54	ExprTuple	77
55	Operation	operator: 64 operands: 65
56	Operation	operator: 68 operands: 66
57	Operation	operator: 70 operands: 67
58	Operation	operator: 68 operands: 69
59	Operation	operator: 70 operands: 71
60	NamedExprs	state: 72 part: 77
61	Literal
62	Variable
63	ExprTuple	73, 77
64	Literal
65	NamedExprs	operation: 74
66	NamedExprs	state: 75 part: 77
67	ExprTuple	83, 84
68	Literal
69	NamedExprs	state: 76 part: 77
70	Literal
71	ExprTuple	78, 79
72	Variable
73	Variable
74	Literal
75	Variable
76	Variable
77	Variable
78	Operation	operator: 81 operands: 80
79	Operation	operator: 81 operands: 82
80	ExprTuple	84, 83
81	Literal
82	ExprTuple	84, 85
83	Literal
84	Variable
85	Variable