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Expression of type Conditional

from the theory of proveit.statistics

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 Conditional, Omega, x
from proveit.logic import Equals, InClass
from proveit.numbers import Sum, one
from proveit.statistics import Prob, SampleSpaces
In [2]:
# build up the expression from sub-expressions
expr = Conditional(Equals(Sum(index_or_indices = [x], summand = Prob(x), domain = Omega), one), InClass(Omega, SampleSpaces))
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\{\left[\sum_{x \in \Omega}~\textrm{Pr}\left(x\right)\right] = 1 \textrm{ if } \Omega \underset{{\scriptscriptstyle c}}{\in} \textrm{SampleSpaces}\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
operands: 4
2Operationoperator: 5
operands: 6
3Literal
4ExprTuple7, 8
5Literal
6ExprTuple21, 9
7Operationoperator: 10
operand: 12
8Literal
9Literal
10Literal
11ExprTuple12
12Lambdaparameter: 20
body: 13
13Conditionalvalue: 14
condition: 15
14Operationoperator: 16
operand: 20
15Operationoperator: 18
operands: 19
16Literal
17ExprTuple20
18Literal
19ExprTuple20, 21
20Variable
21Variable