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, Function, Lambda, Q
from proveit.logic import And
from proveit.physics.quantum.circuits import QcircuitEquiv
from proveit.statistics import Prob

# build up the expression from sub-expressions
expr = Lambda([A, B], Conditional(Function(Q, [Prob(B)]), And(Function(Q, [Prob(A)]), QcircuitEquiv(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\{Q\left(\textrm{Pr}\left(B\right)\right) \textrm{ if } Q\left(\textrm{Pr}\left(A\right)\right) ,  A \cong 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: 14 body: 1
1	Conditional	value: 2 condition: 3
2	Operation	operator: 11 operand: 7
3	Operation	operator: 5 operands: 6
4	ExprTuple	7
5	Literal
6	ExprTuple	8, 9
7	Operation	operator: 17 operand: 16
8	Operation	operator: 11 operand: 15
9	Operation	operator: 13 operands: 14
10	ExprTuple	16
11	Variable
12	ExprTuple	15
13	Literal
14	ExprTuple	19, 16
15	Operation	operator: 17 operand: 19
16	Variable
17	Literal
18	ExprTuple	19
19	Variable