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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, B, X, Y
from proveit.linear_algebra import HilbertSpaces, Hspace, LinMap
from proveit.logic import Forall, InSet
from proveit.physics.quantum import Qmult
In [2]:
# build up the expression from sub-expressions
expr = Forall(instance_param_or_params = [Hspace, X, Y], instance_expr = 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))]), 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, Y \underset{{\scriptscriptstyle c}}{\in} \textrm{HilbertSpaces}}~\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)\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: 7
operand: 2
1ExprTuple2
2Lambdaparameters: 3
body: 4
3ExprTuple47, 48, 45
4Conditionalvalue: 5
condition: 6
5Operationoperator: 7
operand: 10
6Operationoperator: 23
operands: 9
7Literal
8ExprTuple10
9ExprTuple11, 12, 13
10Lambdaparameters: 29
body: 14
11Operationoperator: 17
operands: 15
12Operationoperator: 17
operands: 16
13Operationoperator: 17
operands: 18
14Conditionalvalue: 19
condition: 20
15ExprTuple47, 21
16ExprTuple48, 21
17Literal
18ExprTuple45, 21
19Operationoperator: 32
operands: 22
20Operationoperator: 23
operands: 24
21Literal
22ExprTuple25, 26
23Literal
24ExprTuple27, 28
25Operationoperator: 40
operands: 29
26Operationoperator: 42
operands: 30
27Operationoperator: 32
operands: 31
28Operationoperator: 32
operands: 33
29ExprTuple44, 46
30ExprTuple47, 45
31ExprTuple34, 35
32Literal
33ExprTuple36, 37
34Operationoperator: 40
operand: 44
35Operationoperator: 42
operands: 39
36Operationoperator: 40
operand: 46
37Operationoperator: 42
operands: 43
38ExprTuple44
39ExprTuple48, 45
40Literal
41ExprTuple46
42Literal
43ExprTuple47, 48
44Variable
45Variable
46Variable
47Variable
48Variable