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

# build up the expression from sub-expressions
expr = Lambda(Q, Forall(instance_param_or_params = [A, B], instance_expr = Function(Q, [Prob(B)]), conditions = [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())

Q \mapsto \left[\forall_{A, B~|~Q\left(\textrm{Pr}\left(A\right)\right), A \cong B}~Q\left(\textrm{Pr}\left(B\right)\right)\right]

stored_expr.style_options()

no style options

# display the expression information
stored_expr.expr_info()

	core type	sub-expressions	expression
0	Lambda	parameter: 16 body: 2
1	ExprTuple	16
2	Operation	operator: 3 operand: 5
3	Literal
4	ExprTuple	5
5	Lambda	parameters: 19 body: 6
6	Conditional	value: 7 condition: 8
7	Operation	operator: 16 operand: 12
8	Operation	operator: 10 operands: 11
9	ExprTuple	12
10	Literal
11	ExprTuple	13, 14
12	Operation	operator: 22 operand: 21
13	Operation	operator: 16 operand: 20
14	Operation	operator: 18 operands: 19
15	ExprTuple	21
16	Variable
17	ExprTuple	20
18	Literal
19	ExprTuple	24, 21
20	Operation	operator: 22 operand: 24
21	Variable
22	Literal
23	ExprTuple	24
24	Variable