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, x
from proveit.logic import Equals, SubsetEq
from proveit.numbers import Sum
from proveit.statistics import Prob

# build up the expression from sub-expressions
expr = Conditional(Equals(Prob(X), Sum(index_or_indices = [x], summand = Prob(x), domain = X)), SubsetEq(X, Omega))

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\{\textrm{Pr}\left(X\right) = \left[\sum_{x \in X}~\textrm{Pr}\left(x\right)\right] \textrm{ if } X \subseteq \Omega\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	22, 9
7	Operation	operator: 17 operand: 22
8	Operation	operator: 11 operand: 13
9	Variable
10	ExprTuple	22
11	Literal
12	ExprTuple	13
13	Lambda	parameter: 21 body: 14
14	Conditional	value: 15 condition: 16
15	Operation	operator: 17 operand: 21
16	Operation	operator: 19 operands: 20
17	Literal
18	ExprTuple	21
19	Literal
20	ExprTuple	21, 22
21	Variable
22	Variable