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, Forall, InClass, SubsetEq
from proveit.numbers import one, subtract
from proveit.statistics import Prob, SampleSpaces

# build up the expression from sub-expressions
expr = Conditional(Forall(instance_param_or_params = [S], instance_expr = Equals(Prob(Difference(Omega, S)), subtract(one, Prob(S))), condition = SubsetEq(S, Omega)), 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\{\forall_{S~|~S \subseteq \Omega}~\left(\textrm{Pr}\left(\Omega - S\right) = \left(1 - \textrm{Pr}\left(S\right)\right)\right) \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 operand: 7
2	Operation	operator: 5 operands: 6
3	Literal
4	ExprTuple	7
5	Literal
6	ExprTuple	28, 8
7	Lambda	parameter: 32 body: 9
8	Literal
9	Conditional	value: 10 condition: 11
10	Operation	operator: 12 operands: 13
11	Operation	operator: 14 operands: 15
12	Literal
13	ExprTuple	16, 17
14	Literal
15	ExprTuple	32, 28
16	Operation	operator: 30 operand: 21
17	Operation	operator: 19 operands: 20
18	ExprTuple	21
19	Literal
20	ExprTuple	22, 23
21	Operation	operator: 24 operands: 25
22	Literal
23	Operation	operator: 26 operand: 29
24	Literal
25	ExprTuple	28, 32
26	Literal
27	ExprTuple	29
28	Variable
29	Operation	operator: 30 operand: 32
30	Literal
31	ExprTuple	32
32	Variable