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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, S, k
from proveit.logic import Forall, NotEquals
from proveit.physics.quantum.circuits import MultiQubitElem, Output
In [2]:
# build up the expression from sub-expressions
expr = Forall(instance_param_or_params = [A, B, S], instance_expr = NotEquals(MultiQubitElem(element = Output(state = A, part = k), targets = S), MultiQubitElem(element = Output(state = B, part = k), targets = S)), condition = NotEquals(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_{A, B, S~|~A \neq B}~\left(\begin{array}{c} \Qcircuit@C=1em @R=.7em{
& & \qout{A~\mbox{part}~k~\mbox{on}~S} 
} \end{array} \neq \begin{array}{c} \Qcircuit@C=1em @R=.7em{
& & \qout{B~\mbox{part}~k~\mbox{on}~S} 
} \end{array}\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: 1
operand: 3
1Literal
2ExprTuple3
3Lambdaparameters: 4
body: 5
4ExprTuple22, 23, 18
5Conditionalvalue: 6
condition: 7
6Operationoperator: 9
operands: 8
7Operationoperator: 9
operands: 10
8ExprTuple11, 12
9Literal
10ExprTuple22, 23
11Operationoperator: 14
operands: 13
12Operationoperator: 14
operands: 15
13NamedExprselement: 16
targets: 18
14Literal
15NamedExprselement: 17
targets: 18
16Operationoperator: 20
operands: 19
17Operationoperator: 20
operands: 21
18Variable
19NamedExprsstate: 22
part: 24
20Literal
21NamedExprsstate: 23
part: 24
22Variable
23Variable
24Variable