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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, InSet
from proveit.physics.quantum import QmultCodomain, bra_varphi, ket_varphi, varphi
In [2]:
# build up the expression from sub-expressions
expr = Conditional(Forall(instance_param_or_params = [varphi], instance_expr = InClass(bra_varphi, QmultCodomain), condition = InSet(ket_varphi, 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_{\varphi~|~\lvert \varphi \rangle \in \mathcal{H}}~\left(\langle \varphi \rvert \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: 11
operands: 5
3Literal
4ExprTuple6
5ExprTuple18, 7
6Lambdaparameter: 22
body: 8
7Literal
8Conditionalvalue: 9
condition: 10
9Operationoperator: 11
operands: 12
10Operationoperator: 13
operands: 14
11Literal
12ExprTuple15, 16
13Literal
14ExprTuple17, 18
15Operationoperator: 19
operand: 22
16Literal
17Operationoperator: 20
operand: 22
18Variable
19Literal
20Literal
21ExprTuple22
22Variable