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 A, B, Conditional, Omega
from proveit.logic import And, SubsetEq
from proveit.numbers import LessEq
from proveit.statistics import Prob

# build up the expression from sub-expressions
expr = Conditional(LessEq(Prob(A), Prob(B)), And(SubsetEq(A, B), SubsetEq(B, Omega)).with_total_ordering_style())

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(A\right) \leq \textrm{Pr}\left(B\right) \textrm{ if } A \subseteq B ,  B \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	9, 10
7	Operation	operator: 12 operand: 17
8	Operation	operator: 12 operand: 18
9	Operation	operator: 15 operands: 14
10	Operation	operator: 15 operands: 16
11	ExprTuple	17
12	Literal
13	ExprTuple	18
14	ExprTuple	17, 18
15	Literal
16	ExprTuple	18, 19
17	Variable
18	Variable
19	Variable