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Expression of type Forall

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, Function, 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 = Forall(instance_param_or_params = [Q], instance_expr = 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())
\forall_{Q}~\left[\forall_{A, B~|~Q\left(\textrm{Pr}\left(A\right)\right), A \cong B}~Q\left(\textrm{Pr}\left(B\right)\right)\right]
In [5]:
stored_expr.style_options()
namedescriptiondefaultcurrent valuerelated methods
with_wrappingIf 'True', wrap the Expression after the parametersNoneNone/False('with_wrapping',)
condition_wrappingWrap 'before' or 'after' the condition (or None).NoneNone/False('with_wrap_after_condition', 'with_wrap_before_condition')
wrap_paramsIf 'True', wraps every two parameters AND wraps the Expression after the parametersNoneNone/False('with_params',)
justificationjustify to the 'left', 'center', or 'right' in the array cellscentercenter('with_justification',)
In [6]:
# display the expression information
stored_expr.expr_info()
 core typesub-expressionsexpression
0Operationoperator: 5
operand: 2
1ExprTuple2
2Lambdaparameter: 18
body: 4
3ExprTuple18
4Operationoperator: 5
operand: 7
5Literal
6ExprTuple7
7Lambdaparameters: 21
body: 8
8Conditionalvalue: 9
condition: 10
9Operationoperator: 18
operand: 14
10Operationoperator: 12
operands: 13
11ExprTuple14
12Literal
13ExprTuple15, 16
14Operationoperator: 24
operand: 23
15Operationoperator: 18
operand: 22
16Operationoperator: 20
operands: 21
17ExprTuple23
18Variable
19ExprTuple22
20Literal
21ExprTuple26, 23
22Operationoperator: 24
operand: 26
23Variable
24Literal
25ExprTuple26
26Variable