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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, B, Conditional, Lambda, X, Y
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
expr = Lambda([Hspace, X, Y], Conditional(Forall(instance_param_or_params = [A, B], instance_expr = InSet(Qmult(A, B), LinMap(Hspace, Y)), conditions = [InSet(Qmult(A), LinMap(X, Y)), InSet(Qmult(B), LinMap(Hspace, X))]), And(InClass(Hspace, HilbertSpaces), InClass(X, HilbertSpaces), InClass(Y, 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, Y\right) \mapsto \left\{\forall_{A, B~|~\left[A\right] \in \mathcal{L}\left(X, Y\right), \left[B\right] \in \mathcal{L}\left(\mathcal{H}, X\right)}~\left(\left(A \thinspace B\right) \in \mathcal{L}\left(\mathcal{H}, Y\right)\right) \textrm{ if } \mathcal{H} \underset{{\scriptscriptstyle c}}{\in} \textrm{HilbertSpaces} ,  X \underset{{\scriptscriptstyle c}}{\in} \textrm{HilbertSpaces} ,  Y \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: 1
body: 2
1ExprTuple45, 46, 43
2Conditionalvalue: 3
condition: 4
3Operationoperator: 5
operand: 8
4Operationoperator: 21
operands: 7
5Literal
6ExprTuple8
7ExprTuple9, 10, 11
8Lambdaparameters: 27
body: 12
9Operationoperator: 15
operands: 13
10Operationoperator: 15
operands: 14
11Operationoperator: 15
operands: 16
12Conditionalvalue: 17
condition: 18
13ExprTuple45, 19
14ExprTuple46, 19
15Literal
16ExprTuple43, 19
17Operationoperator: 30
operands: 20
18Operationoperator: 21
operands: 22
19Literal
20ExprTuple23, 24
21Literal
22ExprTuple25, 26
23Operationoperator: 38
operands: 27
24Operationoperator: 40
operands: 28
25Operationoperator: 30
operands: 29
26Operationoperator: 30
operands: 31
27ExprTuple42, 44
28ExprTuple45, 43
29ExprTuple32, 33
30Literal
31ExprTuple34, 35
32Operationoperator: 38
operand: 42
33Operationoperator: 40
operands: 37
34Operationoperator: 38
operand: 44
35Operationoperator: 40
operands: 41
36ExprTuple42
37ExprTuple46, 43
38Literal
39ExprTuple44
40Literal
41ExprTuple45, 46
42Variable
43Variable
44Variable
45Variable
46Variable