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Expression of type ExprTuple

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, ExprTuple, Lambda
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 = ExprTuple(Lambda(Hspace, 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(\mathcal{H} \mapsto \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..\right)
In [5]:
stored_expr.style_options()
no style options
In [6]:
# display the expression information
stored_expr.expr_info()
 core typesub-expressionsexpression
0ExprTuple1
1Lambdaparameter: 21
body: 3
2ExprTuple21
3Conditionalvalue: 4
condition: 5
4Operationoperator: 6
operand: 9
5Operationoperator: 14
operands: 8
6Literal
7ExprTuple9
8ExprTuple21, 10
9Lambdaparameter: 25
body: 11
10Literal
11Conditionalvalue: 12
condition: 13
12Operationoperator: 14
operands: 15
13Operationoperator: 16
operands: 17
14Literal
15ExprTuple18, 19
16Literal
17ExprTuple20, 21
18Operationoperator: 22
operand: 25
19Literal
20Operationoperator: 23
operand: 25
21Variable
22Literal
23Literal
24ExprTuple25
25Variable