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Expression of type ExprTuple

from the theory of proveit.physics.quantum.circuits

In [1]:
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
In [2]:
# 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:
In [3]:
# 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
In [4]:
# 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)
In [5]:
stored_expr.style_options()
no style options
In [6]:
# display the expression information
stored_expr.expr_info()
 core typesub-expressionsexpression
0ExprTuple1
1Lambdaparameter: 17
body: 3
2ExprTuple17
3Operationoperator: 4
operand: 6
4Literal
5ExprTuple6
6Lambdaparameters: 20
body: 7
7Conditionalvalue: 8
condition: 9
8Operationoperator: 17
operand: 13
9Operationoperator: 11
operands: 12
10ExprTuple13
11Literal
12ExprTuple14, 15
13Operationoperator: 23
operand: 22
14Operationoperator: 17
operand: 21
15Operationoperator: 19
operands: 20
16ExprTuple22
17Variable
18ExprTuple21
19Literal
20ExprTuple25, 22
21Operationoperator: 23
operand: 25
22Variable
23Literal
24ExprTuple25
25Variable