Expression of type ExprTuple

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, ExprTuple, 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 = ExprTuple(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())

\left(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]\right)

stored_expr.style_options()

no style options

# display the expression information
stored_expr.expr_info()

	core type	sub-expressions	expression
0	ExprTuple	1
1	Lambda	parameter: 17 body: 3
2	ExprTuple	17
3	Operation	operator: 4 operand: 6
4	Literal
5	ExprTuple	6
6	Lambda	parameters: 20 body: 7
7	Conditional	value: 8 condition: 9
8	Operation	operator: 17 operand: 13
9	Operation	operator: 11 operands: 12
10	ExprTuple	13
11	Literal
12	ExprTuple	14, 15
13	Operation	operator: 23 operand: 22
14	Operation	operator: 17 operand: 21
15	Operation	operator: 19 operands: 20
16	ExprTuple	22
17	Variable
18	ExprTuple	21
19	Literal
20	ExprTuple	25, 22
21	Operation	operator: 23 operand: 25
22	Variable
23	Literal
24	ExprTuple	25
25	Variable