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
from proveit.core_expr_types.expr_arrays import A11_to_Akl
from proveit.logic import Equals, Forall, InSet
from proveit.physics.quantum import m_ket_domain, var_ket_psi
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(var_ket_psi, Conditional(Forall(instance_param_or_params = [A11_to_Akl], instance_expr = Equals(Prob(circuit__u_Akl_v), Prob(circuit__psi_m__u_Akl_v)).with_wrapping_at(2)).with_wrapping(), InSet(var_ket_psi, m_ket_domain))))

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(\lvert \psi \rangle \mapsto \left\{\begin{array}{l}\forall_{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}}~\\
\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)\end{array} \textrm{ if } \lvert \psi \rangle \in \mathbb{C}^{2^{m}}\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	parameter: 102 body: 3
2	ExprTuple	102
3	Conditional	value: 4 condition: 5
4	Operation	operator: 6 operand: 10
5	Operation	operator: 8 operands: 9
6	Literal
7	ExprTuple	10
8	Literal
9	ExprTuple	102, 11
10	Lambda	parameters: 12 body: 13
11	Operation	operator: 14 operands: 15
12	ExprTuple	16
13	Operation	operator: 17 operands: 18
14	Literal
15	ExprTuple	19, 20
16	ExprRange	lambda_map: 21 start_index: 110 end_index: 47
17	Literal
18	ExprTuple	22, 23
19	Literal
20	Operation	operator: 24 operands: 25
21	Lambda	parameter: 101 body: 64
22	Operation	operator: 27 operand: 30
23	Operation	operator: 27 operand: 31
24	Literal
25	ExprTuple	29, 111
26	ExprTuple	30
27	Literal
28	ExprTuple	31
29	Literal
30	Operation	operator: 33 operands: 32
31	Operation	operator: 33 operands: 34
32	ExprTuple	35, 36, 37
33	Literal
34	ExprTuple	38, 39, 40
35	ExprTuple	41
36	ExprRange	lambda_map: 42 start_index: 110 end_index: 47
37	ExprTuple	43
38	ExprTuple	44, 45
39	ExprRange	lambda_map: 46 start_index: 110 end_index: 47
40	ExprTuple	48, 49
41	ExprRange	lambda_map: 50 start_index: 110 end_index: 112
42	Lambda	parameter: 101 body: 51
43	ExprRange	lambda_map: 52 start_index: 110 end_index: 112
44	ExprRange	lambda_map: 53 start_index: 110 end_index: 111
45	ExprRange	lambda_map: 54 start_index: 110 end_index: 112
46	Lambda	parameter: 101 body: 56
47	Variable
48	ExprRange	lambda_map: 57 start_index: 110 end_index: 111
49	ExprRange	lambda_map: 58 start_index: 110 end_index: 112
50	Lambda	parameter: 104 body: 59
51	ExprTuple	64
52	Lambda	parameter: 104 body: 60
53	Lambda	parameter: 104 body: 61
54	Lambda	parameter: 104 body: 62
55	ExprTuple	101
56	ExprTuple	63, 64
57	Lambda	parameter: 104 body: 65
58	Lambda	parameter: 104 body: 66
59	Operation	operator: 74 operands: 67
60	Operation	operator: 74 operands: 68
61	Operation	operator: 74 operands: 69
62	Operation	operator: 74 operands: 70
63	ExprRange	lambda_map: 71 start_index: 110 end_index: 111
64	ExprRange	lambda_map: 72 start_index: 110 end_index: 112
65	Operation	operator: 74 operands: 73
66	Operation	operator: 74 operands: 75
67	NamedExprs	element: 78 targets: 76
68	NamedExprs	element: 84 targets: 76
69	NamedExprs	element: 77 targets: 83
70	NamedExprs	element: 78 targets: 85
71	Lambda	parameter: 104 body: 79
72	Lambda	parameter: 104 body: 81
73	NamedExprs	element: 82 targets: 83
74	Literal
75	NamedExprs	element: 84 targets: 85
76	Operation	operator: 97 operands: 86
77	Operation	operator: 87 operands: 93
78	Operation	operator: 87 operands: 88
79	Operation	operator: 89 operands: 90
80	ExprTuple	104
81	IndexedVar	variable: 91 indices: 92
82	Operation	operator: 95 operands: 93
83	Operation	operator: 97 operands: 94
84	Operation	operator: 95 operands: 96
85	Operation	operator: 97 operands: 98
86	ExprTuple	110, 112
87	Literal
88	NamedExprs	state: 99 part: 104
89	Literal
90	NamedExprs	operation: 100
91	Variable
92	ExprTuple	101, 104
93	NamedExprs	state: 102 part: 104
94	ExprTuple	110, 111
95	Literal
96	NamedExprs	state: 103 part: 104
97	Literal
98	ExprTuple	105, 106
99	Variable
100	Literal
101	Variable
102	Variable
103	Variable
104	Variable
105	Operation	operator: 108 operands: 107
106	Operation	operator: 108 operands: 109
107	ExprTuple	111, 110
108	Literal
109	ExprTuple	111, 112
110	Literal
111	Variable
112	Variable