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, S
from proveit.logic import Difference, Equals, SubsetEq
from proveit.numbers import one, subtract
from proveit.statistics import Prob

# build up the expression from sub-expressions
expr = Conditional(Equals(Prob(Difference(Omega, S)), subtract(one, Prob(S))), SubsetEq(S, 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(\Omega - S\right) = \left(1 - \textrm{Pr}\left(S\right)\right) \textrm{ if } S \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	23, 19
7	Operation	operator: 21 operand: 12
8	Operation	operator: 10 operands: 11
9	ExprTuple	12
10	Literal
11	ExprTuple	13, 14
12	Operation	operator: 15 operands: 16
13	Literal
14	Operation	operator: 17 operand: 20
15	Literal
16	ExprTuple	19, 23
17	Literal
18	ExprTuple	20
19	Variable
20	Operation	operator: 21 operand: 23
21	Literal
22	ExprTuple	23
23	Variable