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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, c
from proveit.linear_algebra import HilbertSpaces, Hspace
from proveit.logic import Forall, InSet
from proveit.numbers import Complex
from proveit.physics.quantum import Qmult, var_ket_psi
In [2]:
# build up the expression from sub-expressions
expr = ExprTuple(Lambda(c, Conditional(Forall(instance_param_or_params = [Hspace], instance_expr = Forall(instance_param_or_params = [var_ket_psi], instance_expr = InSet(Qmult(c, var_ket_psi), Hspace), domain = Hspace), domain = HilbertSpaces), InSet(c, Complex))))
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(c \mapsto \left\{\forall_{\mathcal{H} \underset{{\scriptscriptstyle c}}{\in} \textrm{HilbertSpaces}}~\left[\forall_{\lvert \psi \rangle \in \mathcal{H}}~\left(\left(c \thinspace \lvert \psi \rangle\right) \in \mathcal{H}\right)\right] \textrm{ if } c \in \mathbb{C}\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: 14
operand: 8
5Operationoperator: 25
operands: 7
6ExprTuple8
7ExprTuple31, 9
8Lambdaparameter: 28
body: 11
9Literal
10ExprTuple28
11Conditionalvalue: 12
condition: 13
12Operationoperator: 14
operand: 18
13Operationoperator: 16
operands: 17
14Literal
15ExprTuple18
16Literal
17ExprTuple28, 19
18Lambdaparameter: 32
body: 21
19Literal
20ExprTuple32
21Conditionalvalue: 22
condition: 23
22Operationoperator: 25
operands: 24
23Operationoperator: 25
operands: 26
24ExprTuple27, 28
25Literal
26ExprTuple32, 28
27Operationoperator: 29
operands: 30
28Variable
29Literal
30ExprTuple31, 32
31Variable
32Variable