Expression of type Lambda

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 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 = 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(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)

stored_expr.style_options()

no style options

# display the expression information
stored_expr.expr_info()

	core type	sub-expressions	expression
0	Lambda	parameters: 1 body: 2
1	ExprTuple	25, 27
2	Operation	operator: 3 operands: 4
3	Literal
4	ExprTuple	5, 6
5	Operation	operator: 8 operands: 7
6	Operation	operator: 8 operands: 9
7	ExprTuple	10, 56
8	Literal
9	ExprTuple	11, 12
10	Operation	operator: 15 operand: 17
11	Operation	operator: 15 operand: 18
12	Operation	operator: 15 operand: 19
13	ExprTuple	17
14	ExprTuple	18
15	Literal
16	ExprTuple	19
17	Operation	operator: 22 operands: 20
18	Operation	operator: 22 operands: 21
19	Operation	operator: 22 operands: 23
20	ExprTuple	25, 24
21	ExprTuple	25, 27
22	Literal
23	ExprTuple	26, 27
24	ExprTuple	28
25	ExprRange	lambda_map: 29 start_index: 56 end_index: 30
26	ExprTuple	31
27	ExprRange	lambda_map: 32 start_index: 56 end_index: 33
28	ExprRange	lambda_map: 34 start_index: 56 end_index: 57
29	Lambda	parameter: 55 body: 35
30	Variable
31	ExprRange	lambda_map: 36 start_index: 56 end_index: 57
32	Lambda	parameter: 55 body: 37
33	Variable
34	Lambda	parameter: 55 body: 38
35	IndexedVar	variable: 39 index: 55
36	Lambda	parameter: 55 body: 40
37	IndexedVar	variable: 41 index: 55
38	Operation	operator: 44 operands: 43
39	Variable
40	Operation	operator: 44 operands: 45
41	Variable
42	ExprTuple	55
43	NamedExprs	element: 46 targets: 48
44	Literal
45	NamedExprs	element: 47 targets: 48
46	Operation	operator: 49 operands: 51
47	Operation	operator: 50 operands: 51
48	Operation	operator: 52 operands: 53
49	Literal
50	Literal
51	NamedExprs	state: 54 part: 55
52	Literal
53	ExprTuple	56, 57
54	Variable
55	Variable
56	Literal
57	Variable