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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, c
from proveit.linear_algebra import HilbertSpaces, Hspace, LinMap
from proveit.logic import Forall, InSet
from proveit.numbers import Complex
from proveit.physics.quantum import Qmult
In [2]:
# build up the expression from sub-expressions
sub_expr1 = LinMap(Hspace, X)
expr = Forall(instance_param_or_params = [c], instance_expr = Forall(instance_param_or_params = [Hspace, X], instance_expr = Forall(instance_param_or_params = [A], instance_expr = InSet(Qmult(c, A), sub_expr1), condition = InSet(Qmult(A), sub_expr1)), domain = HilbertSpaces), domain = Complex)
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_{c \in \mathbb{C}}~\left[\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(\left(c \thinspace A\right) \in \mathcal{L}\left(\mathcal{H}, X\right)\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: 14
operand: 2
1ExprTuple2
2Lambdaparameter: 39
body: 4
3ExprTuple39
4Conditionalvalue: 5
condition: 6
5Operationoperator: 14
operand: 9
6Operationoperator: 29
operands: 8
7ExprTuple9
8ExprTuple39, 10
9Lambdaparameters: 38
body: 11
10Literal
11Conditionalvalue: 12
condition: 13
12Operationoperator: 14
operand: 18
13Operationoperator: 16
operands: 17
14Literal
15ExprTuple18
16Literal
17ExprTuple19, 20
18Lambdaparameter: 40
body: 21
19Operationoperator: 23
operands: 22
20Operationoperator: 23
operands: 24
21Conditionalvalue: 25
condition: 26
22ExprTuple41, 27
23Literal
24ExprTuple42, 27
25Operationoperator: 29
operands: 28
26Operationoperator: 29
operands: 30
27Literal
28ExprTuple31, 33
29Literal
30ExprTuple32, 33
31Operationoperator: 35
operands: 34
32Operationoperator: 35
operand: 40
33Operationoperator: 37
operands: 38
34ExprTuple39, 40
35Literal
36ExprTuple40
37Literal
38ExprTuple41, 42
39Variable
40Variable
41Variable
42Variable