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Expression of type Conditional

from the theory of proveit.physics.quantum.algebra

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 Conditional
from proveit.linear_algebra import HilbertSpaces, Hspace
from proveit.logic import Forall, InClass
from proveit.physics.quantum import QmultCodomain, var_ket_psi
In [2]:
# build up the expression from sub-expressions
expr = Conditional(Forall(instance_param_or_params = [var_ket_psi], instance_expr = InClass(var_ket_psi, QmultCodomain), domain = Hspace), InClass(Hspace, HilbertSpaces))
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_{\lvert \psi \rangle \in \mathcal{H}}~\left(\lvert \psi \rangle \underset{{\scriptscriptstyle c}}{\in} \mathcal{Q^*}\right) \textrm{ if } \mathcal{H} \underset{{\scriptscriptstyle c}}{\in} \textrm{HilbertSpaces}\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: 6
2Operationoperator: 12
operands: 5
3Literal
4ExprTuple6
5ExprTuple18, 7
6Lambdaparameter: 17
body: 9
7Literal
8ExprTuple17
9Conditionalvalue: 10
condition: 11
10Operationoperator: 12
operands: 13
11Operationoperator: 14
operands: 15
12Literal
13ExprTuple17, 16
14Literal
15ExprTuple17, 18
16Literal
17Variable
18Variable