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Expression of type Forall

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, Function, X
from proveit.linear_algebra import LinMap
from proveit.logic import Equals, Forall, InSet
from proveit.physics.quantum import HilbertSpaces, Qmult, var_ket_psi
from proveit.physics.quantum.algebra import Hspace
In [2]:
# build up the expression from sub-expressions
sub_expr1 = [var_ket_psi]
sub_expr2 = Qmult(A)
expr = Forall(instance_param_or_params = [Hspace, X], instance_expr = Forall(instance_param_or_params = [A], instance_expr = Forall(instance_param_or_params = sub_expr1, instance_expr = Equals(Qmult(A, var_ket_psi), Function(sub_expr2, sub_expr1)), domain = Hspace), condition = InSet(sub_expr2, LinMap(Hspace, X))), domain = HilbertSpaces)
Out[2]:
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())
\forall_{\mathcal{H}, X \underset{{\scriptscriptstyle c}}{\in} \textrm{HilbertSpaces}}~\left[\forall_{A~|~\left[A\right] \in \mathcal{L}\left(\mathcal{H}, X\right)}~\left[\forall_{\lvert \psi \rangle \in \mathcal{H}}~\left(\left(A \thinspace \lvert \psi \rangle\right) = \left[A\right]\left(\lvert \psi \rangle\right)\right)\right]\right]
In [5]:
stored_expr.style_options()
Out[5]:
namedescriptiondefaultcurrent valuerelated methods
with_wrappingIf 'True', wrap the Expression after the parametersNoneNone/False('with_wrapping',)
condition_wrappingWrap 'before' or 'after' the condition (or None).NoneNone/False('with_wrap_after_condition', 'with_wrap_before_condition')
wrap_paramsIf 'True', wraps every two parameters AND wraps the Expression after the parametersNoneNone/False('with_params',)
justificationjustify to the 'left', 'center', or 'right' in the array cellscentercenter('with_justification',)
In [6]:
# display the expression information
stored_expr.expr_info()
Out[6]:
 core typesub-expressionsexpression
0Operationoperator: 19
operand: 2
1ExprTuple2
2Lambdaparameters: 26
body: 3
3Conditionalvalue: 4
condition: 5
4Operationoperator: 19
operand: 9
5Operationoperator: 7
operands: 8
6ExprTuple9
7Literal
8ExprTuple10, 11
9Lambdaparameter: 43
body: 12
10Operationoperator: 14
operands: 13
11Operationoperator: 14
operands: 15
12Conditionalvalue: 16
condition: 17
13ExprTuple36, 18
14Literal
15ExprTuple29, 18
16Operationoperator: 19
operand: 22
17Operationoperator: 32
operands: 21
18Literal
19Literal
20ExprTuple22
21ExprTuple38, 23
22Lambdaparameter: 42
body: 24
23Operationoperator: 25
operands: 26
24Conditionalvalue: 27
condition: 28
25Literal
26ExprTuple36, 29
27Operationoperator: 30
operands: 31
28Operationoperator: 32
operands: 33
29Variable
30Literal
31ExprTuple34, 35
32Literal
33ExprTuple42, 36
34Operationoperator: 40
operands: 37
35Operationoperator: 38
operand: 42
36Variable
37ExprTuple43, 42
38Operationoperator: 40
operand: 43
39ExprTuple42
40Literal
41ExprTuple43
42Variable
43Variable