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Expression of type Conditional

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, Conditional, S, k
from proveit.logic import Forall, InSet, NotEquals
from proveit.numbers import NaturalPos
from proveit.physics.quantum.circuits import MultiQubitElem, Output
In [2]:
# build up the expression from sub-expressions
expr = Conditional(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)), InSet(k, NaturalPos))
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\{\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) \textrm{ if } k \in \mathbb{N}^+\right..
In [5]:
stored_expr.style_options()
namedescriptiondefaultcurrent valuerelated methods
condition_delimiter'comma' or 'and'commacomma('with_comma_delimiter', 'with_conjunction_delimiter')
In [6]:
# display the expression information
stored_expr.expr_info()
 core typesub-expressionsexpression
0Conditionalvalue: 1
condition: 2
1Operationoperator: 3
operand: 7
2Operationoperator: 5
operands: 6
3Literal
4ExprTuple7
5Literal
6ExprTuple29, 8
7Lambdaparameters: 9
body: 10
8Literal
9ExprTuple27, 28, 23
10Conditionalvalue: 11
condition: 12
11Operationoperator: 14
operands: 13
12Operationoperator: 14
operands: 15
13ExprTuple16, 17
14Literal
15ExprTuple27, 28
16Operationoperator: 19
operands: 18
17Operationoperator: 19
operands: 20
18NamedExprselement: 21
targets: 23
19Literal
20NamedExprselement: 22
targets: 23
21Operationoperator: 25
operands: 24
22Operationoperator: 25
operands: 26
23Variable
24NamedExprsstate: 27
part: 29
25Literal
26NamedExprsstate: 28
part: 29
27Variable
28Variable
29Variable