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
from proveit.logic import Equals
from proveit.physics.quantum.circuits import Output

# build up the expression from sub-expressions
expr = Lambda([A, B], Equals(Equals(Output(state = A), Output(state = B)), 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\right) \mapsto \left(\left(\begin{array}{c} \Qcircuit@C=1em @R=.7em{
& & \qout{A} 
} \end{array} = \begin{array}{c} \Qcircuit@C=1em @R=.7em{
& & \qout{B} 
} \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: 7 body: 1
1	Operation	operator: 6 operands: 2
2	ExprTuple	3, 4
3	Operation	operator: 6 operands: 5
4	Operation	operator: 6 operands: 7
5	ExprTuple	8, 9
6	Literal
7	ExprTuple	13, 14
8	Operation	operator: 11 operands: 10
9	Operation	operator: 11 operands: 12
10	NamedExprs	state: 13
11	Literal
12	NamedExprs	state: 14
13	Variable
14	Variable