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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, InnerProd
from proveit.logic import Equals, Forall, InClass, InSet
from proveit.physics.quantum import bra_varphi, ket_varphi, var_ket_psi, varphi
In [2]:
# build up the expression from sub-expressions
expr = ExprTuple(Lambda(Hspace, Conditional(Forall(instance_param_or_params = [varphi], instance_expr = Equals(bra_varphi, Lambda(var_ket_psi, Conditional(InnerProd(ket_varphi, var_ket_psi), InSet(var_ket_psi, Hspace)))), 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 = \left[\lvert \psi \rangle \mapsto \left\{\left \langle \lvert \varphi \rangle, \lvert \psi \rangle\right \rangle \textrm{ if } \lvert \psi \rangle \in \mathcal{H}\right..\right]\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: 31
body: 3
2ExprTuple31
3Conditionalvalue: 4
condition: 5
4Operationoperator: 6
operand: 10
5Operationoperator: 8
operands: 9
6Literal
7ExprTuple10
8Literal
9ExprTuple31, 11
10Lambdaparameter: 34
body: 12
11Literal
12Conditionalvalue: 13
condition: 14
13Operationoperator: 15
operands: 16
14Operationoperator: 27
operands: 17
15Literal
16ExprTuple18, 19
17ExprTuple29, 31
18Operationoperator: 20
operand: 34
19Lambdaparameter: 30
body: 22
20Literal
21ExprTuple30
22Conditionalvalue: 23
condition: 24
23Operationoperator: 25
operands: 26
24Operationoperator: 27
operands: 28
25Literal
26ExprTuple29, 30
27Literal
28ExprTuple30, 31
29Operationoperator: 32
operand: 34
30Variable
31Variable
32Literal
33ExprTuple34
34Variable