Expression of type Conditional

from the theory of proveit.statistics

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

# 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:

# 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

# 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..

stored_expr.style_options()

name	description	default	current value	related methods
condition_delimiter	'comma' or 'and'	comma	comma	('with_comma_delimiter', 'with_conjunction_delimiter')

# display the expression information
stored_expr.expr_info()

	core type	sub-expressions	expression
0	Conditional	value: 1 condition: 2
1	Operation	operator: 3 operands: 4
2	Operation	operator: 5 operands: 6
3	Literal
4	ExprTuple	7, 8
5	Literal
6	ExprTuple	21, 9
7	Operation	operator: 10 operand: 12
8	Literal
9	Literal
10	Literal
11	ExprTuple	12
12	Lambda	parameter: 20 body: 13
13	Conditional	value: 14 condition: 15
14	Operation	operator: 16 operand: 20
15	Operation	operator: 18 operands: 19
16	Literal
17	ExprTuple	20
18	Literal
19	ExprTuple	20, 21
20	Variable
21	Variable