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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 LinMap
from proveit.logic import Equals, Forall
from proveit.physics.quantum import HilbertSpaces, Qmult
from proveit.physics.quantum.algebra import Hspace
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 = Equals(Qmult(A), A), domain = 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 \in \mathcal{L}\left(\mathcal{H}, X\right)}~\left(\left[A\right] = A\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: 6
operand: 2
1ExprTuple2
2Lambdaparameters: 29
body: 3
3Conditionalvalue: 4
condition: 5
4Operationoperator: 6
operand: 10
5Operationoperator: 8
operands: 9
6Literal
7ExprTuple10
8Literal
9ExprTuple11, 12
10Lambdaparameter: 30
body: 13
11Operationoperator: 15
operands: 14
12Operationoperator: 15
operands: 16
13Conditionalvalue: 17
condition: 18
14ExprTuple31, 19
15Literal
16ExprTuple32, 19
17Operationoperator: 20
operands: 21
18Operationoperator: 22
operands: 23
19Literal
20Literal
21ExprTuple24, 30
22Literal
23ExprTuple30, 25
24Operationoperator: 26
operand: 30
25Operationoperator: 28
operands: 29
26Literal
27ExprTuple30
28Literal
29ExprTuple31, 32
30Variable
31Variable
32Variable