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Expression of type Conditional

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, Conditional, X, c
from proveit.linear_algebra import HilbertSpaces, Hspace, LinMap
from proveit.logic import And, Forall, InClass, InSet
from proveit.physics.quantum import Qmult
In [2]:
# build up the expression from sub-expressions
sub_expr1 = LinMap(Hspace, X)
expr = Conditional(Forall(instance_param_or_params = [A], instance_expr = InSet(Qmult(c, A), sub_expr1), condition = InSet(Qmult(A), sub_expr1)), And(InClass(Hspace, HilbertSpaces), InClass(X, 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())
\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) \textrm{ if } \mathcal{H} \underset{{\scriptscriptstyle c}}{\in} \textrm{HilbertSpaces} ,  X \underset{{\scriptscriptstyle c}}{\in} \textrm{HilbertSpaces}\right..
In [5]:
stored_expr.style_options()
namedescriptiondefaultcurrent valuerelated methods
condition_delimiter'comma' or 'and'commacomma('with_comma_delimiter', 'with_conjunction_delimiter')
In [6]:
# display the expression information
stored_expr.expr_info()
 core typesub-expressionsexpression
0Conditionalvalue: 1
condition: 2
1Operationoperator: 3
operand: 7
2Operationoperator: 5
operands: 6
3Literal
4ExprTuple7
5Literal
6ExprTuple8, 9
7Lambdaparameter: 29
body: 10
8Operationoperator: 12
operands: 11
9Operationoperator: 12
operands: 13
10Conditionalvalue: 14
condition: 15
11ExprTuple30, 16
12Literal
13ExprTuple31, 16
14Operationoperator: 18
operands: 17
15Operationoperator: 18
operands: 19
16Literal
17ExprTuple20, 22
18Literal
19ExprTuple21, 22
20Operationoperator: 24
operands: 23
21Operationoperator: 24
operand: 29
22Operationoperator: 26
operands: 27
23ExprTuple28, 29
24Literal
25ExprTuple29
26Literal
27ExprTuple30, 31
28Variable
29Variable
30Variable
31Variable