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, i, j, m
from proveit.core_expr_types import U_1_to_i, V_1_to_j
from proveit.logic import And, Equals, Forall, Implies, InSet
from proveit.numbers import NaturalPos, one
from proveit.physics.quantum import m_ket_domain, var_ket_psi
from proveit.physics.quantum.circuits import circuit_Ui_Vj, circuit_Ui_psi_m, circuit_psi_m_Vj
from proveit.statistics import Prob

# build up the expression from sub-expressions
expr = ExprTuple(Lambda([i, j, m], Conditional(Forall(instance_param_or_params = [var_ket_psi], instance_expr = Forall(instance_param_or_params = [U_1_to_i, V_1_to_j], instance_expr = Implies(Equals(Prob(circuit_Ui_psi_m), one), Equals(Prob(circuit_Ui_Vj), Prob(circuit_psi_m_Vj)).with_wrapping_at(2)).with_wrapping_at(2)).with_wrapping(), domain = m_ket_domain).with_wrapping(), And(InSet(i, NaturalPos), InSet(j, NaturalPos), InSet(m, NaturalPos)))))

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