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 import U_1_to_i, V_1_to_j
from proveit.logic import Equals, Implies
from proveit.numbers import one
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([U_1_to_i, V_1_to_j], 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)))

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(U_{1}, U_{2}, \ldots, U_{i}, V_{1}, V_{2}, \ldots, V_{j}\right) \mapsto \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)\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	26, 28
3	Operation	operator: 4 operands: 5
4	Literal
5	ExprTuple	6, 7
6	Operation	operator: 9 operands: 8
7	Operation	operator: 9 operands: 10
8	ExprTuple	11, 57
9	Literal
10	ExprTuple	12, 13
11	Operation	operator: 16 operand: 18
12	Operation	operator: 16 operand: 19
13	Operation	operator: 16 operand: 20
14	ExprTuple	18
15	ExprTuple	19
16	Literal
17	ExprTuple	20
18	Operation	operator: 23 operands: 21
19	Operation	operator: 23 operands: 22
20	Operation	operator: 23 operands: 24
21	ExprTuple	26, 25
22	ExprTuple	26, 28
23	Literal
24	ExprTuple	27, 28
25	ExprTuple	29
26	ExprRange	lambda_map: 30 start_index: 57 end_index: 31
27	ExprTuple	32
28	ExprRange	lambda_map: 33 start_index: 57 end_index: 34
29	ExprRange	lambda_map: 35 start_index: 57 end_index: 58
30	Lambda	parameter: 56 body: 36
31	Variable
32	ExprRange	lambda_map: 37 start_index: 57 end_index: 58
33	Lambda	parameter: 56 body: 38
34	Variable
35	Lambda	parameter: 56 body: 39
36	IndexedVar	variable: 40 index: 56
37	Lambda	parameter: 56 body: 41
38	IndexedVar	variable: 42 index: 56
39	Operation	operator: 45 operands: 44
40	Variable
41	Operation	operator: 45 operands: 46
42	Variable
43	ExprTuple	56
44	NamedExprs	element: 47 targets: 49
45	Literal
46	NamedExprs	element: 48 targets: 49
47	Operation	operator: 50 operands: 52
48	Operation	operator: 51 operands: 52
49	Operation	operator: 53 operands: 54
50	Literal
51	Literal
52	NamedExprs	state: 55 part: 56
53	Literal
54	ExprTuple	57, 58
55	Variable
56	Variable
57	Literal
58	Variable