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Expression of type Lambda

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 A, Conditional, Lambda, X, c
from proveit.linear_algebra import HilbertSpaces, Hspace, LinMap
from proveit.logic import And, Forall, InClass, InSet
from proveit.physics.quantum import Qmult
In [2]:
# build up the expression from sub-expressions
sub_expr1 = LinMap(Hspace, X)
expr = Lambda([Hspace, X], Conditional(Forall(instance_param_or_params = [A], instance_expr = InSet(Qmult(A, c), sub_expr1), condition = InSet(Qmult(A), sub_expr1)), And(InClass(Hspace, HilbertSpaces), InClass(X, 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}, X\right) \mapsto \left\{\forall_{A~|~\left[A\right] \in \mathcal{L}\left(\mathcal{H}, X\right)}~\left(\left(A \thinspace c\right) \in \mathcal{L}\left(\mathcal{H}, X\right)\right) \textrm{ if } \mathcal{H} \underset{{\scriptscriptstyle c}}{\in} \textrm{HilbertSpaces} ,  X \underset{{\scriptscriptstyle c}}{\in} \textrm{HilbertSpaces}\right..
In [5]:
stored_expr.style_options()
no style options
In [6]:
# display the expression information
stored_expr.expr_info()
 core typesub-expressionsexpression
0Lambdaparameters: 28
body: 1
1Conditionalvalue: 2
condition: 3
2Operationoperator: 4
operand: 8
3Operationoperator: 6
operands: 7
4Literal
5ExprTuple8
6Literal
7ExprTuple9, 10
8Lambdaparameter: 30
body: 11
9Operationoperator: 13
operands: 12
10Operationoperator: 13
operands: 14
11Conditionalvalue: 15
condition: 16
12ExprTuple31, 17
13Literal
14ExprTuple32, 17
15Operationoperator: 19
operands: 18
16Operationoperator: 19
operands: 20
17Literal
18ExprTuple21, 23
19Literal
20ExprTuple22, 23
21Operationoperator: 25
operands: 24
22Operationoperator: 25
operand: 30
23Operationoperator: 27
operands: 28
24ExprTuple30, 29
25Literal
26ExprTuple30
27Literal
28ExprTuple31, 32
29Variable
30Variable
31Variable
32Variable