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 A, B, Lambda, S, k
from proveit.logic import Equals
from proveit.physics.quantum.circuits import Input, MultiQubitElem

# build up the expression from sub-expressions
expr = Lambda([A, B, S], Equals(Equals(MultiQubitElem(element = Input(state = A, part = k), targets = S), MultiQubitElem(element = Input(state = B, part = k), targets = S)), Equals(A, B)))

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(A, B, S\right) \mapsto \left(\left(\begin{array}{c} \Qcircuit@C=1em @R=.7em{
& \qin{A~\mbox{part}~k~\mbox{on}~S} & \qw 
} \end{array} = \begin{array}{c} \Qcircuit@C=1em @R=.7em{
& \qin{B~\mbox{part}~k~\mbox{on}~S} & \qw 
} \end{array}\right) = \left(A = B\right)\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	20, 21, 16
2	Operation	operator: 7 operands: 3
3	ExprTuple	4, 5
4	Operation	operator: 7 operands: 6
5	Operation	operator: 7 operands: 8
6	ExprTuple	9, 10
7	Literal
8	ExprTuple	20, 21
9	Operation	operator: 12 operands: 11
10	Operation	operator: 12 operands: 13
11	NamedExprs	element: 14 targets: 16
12	Literal
13	NamedExprs	element: 15 targets: 16
14	Operation	operator: 18 operands: 17
15	Operation	operator: 18 operands: 19
16	Variable
17	NamedExprs	state: 20 part: 22
18	Literal
19	NamedExprs	state: 21 part: 22
20	Variable
21	Variable
22	Variable