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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, X
from proveit.linear_algebra import HilbertSpaces, Hspace, LinMap
from proveit.logic import Forall, InClass, InSet
from proveit.physics.quantum import Qmult, QmultCodomain, var_ket_psi
In [2]:
# build up the expression from sub-expressions
expr = Forall(instance_param_or_params = [Hspace, X], instance_expr = Forall(instance_param_or_params = [A], instance_expr = Forall(instance_param_or_params = [var_ket_psi], instance_expr = InClass(Qmult(A, var_ket_psi), QmultCodomain), domain = Hspace), condition = InSet(Qmult(A), LinMap(Hspace, X))), domain = 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())
\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) \underset{{\scriptscriptstyle c}}{\in} \mathcal{Q^*}\right)\right]\right]
In [5]:
stored_expr.style_options()
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()
 core typesub-expressionsexpression
0Operationoperator: 18
operand: 2
1ExprTuple2
2Lambdaparameters: 28
body: 3
3Conditionalvalue: 4
condition: 5
4Operationoperator: 18
operand: 9
5Operationoperator: 7
operands: 8
6ExprTuple9
7Literal
8ExprTuple10, 11
9Lambdaparameter: 41
body: 12
10Operationoperator: 32
operands: 13
11Operationoperator: 32
operands: 14
12Conditionalvalue: 15
condition: 16
13ExprTuple38, 17
14ExprTuple31, 17
15Operationoperator: 18
operand: 21
16Operationoperator: 34
operands: 20
17Literal
18Literal
19ExprTuple21
20ExprTuple22, 23
21Lambdaparameter: 42
body: 25
22Operationoperator: 39
operand: 41
23Operationoperator: 27
operands: 28
24ExprTuple42
25Conditionalvalue: 29
condition: 30
26ExprTuple41
27Literal
28ExprTuple38, 31
29Operationoperator: 32
operands: 33
30Operationoperator: 34
operands: 35
31Variable
32Literal
33ExprTuple36, 37
34Literal
35ExprTuple42, 38
36Operationoperator: 39
operands: 40
37Literal
38Variable
39Literal
40ExprTuple41, 42
41Variable
42Variable