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, Conditional, Lambda, S, k
from proveit.logic import NotEquals
from proveit.physics.quantum.circuits import MultiQubitElem, Output

# build up the expression from sub-expressions
expr = Lambda([A, B, S], Conditional(NotEquals(MultiQubitElem(element = Output(state = A, part = k), targets = S), MultiQubitElem(element = Output(state = B, part = k), targets = S)), NotEquals(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\{\begin{array}{c} \Qcircuit@C=1em @R=.7em{
& & \qout{A~\mbox{part}~k~\mbox{on}~S} 
} \end{array} \neq \begin{array}{c} \Qcircuit@C=1em @R=.7em{
& & \qout{B~\mbox{part}~k~\mbox{on}~S} 
} \end{array} \textrm{ if } A \neq B\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	19, 20, 15
2	Conditional	value: 3 condition: 4
3	Operation	operator: 6 operands: 5
4	Operation	operator: 6 operands: 7
5	ExprTuple	8, 9
6	Literal
7	ExprTuple	19, 20
8	Operation	operator: 11 operands: 10
9	Operation	operator: 11 operands: 12
10	NamedExprs	element: 13 targets: 15
11	Literal
12	NamedExprs	element: 14 targets: 15
13	Operation	operator: 17 operands: 16
14	Operation	operator: 17 operands: 18
15	Variable
16	NamedExprs	state: 19 part: 21
17	Literal
18	NamedExprs	state: 20 part: 21
19	Variable
20	Variable
21	Variable