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

# build up the expression from sub-expressions
expr = Conditional(Forall(instance_param_or_params = [A, B], instance_expr = LessEq(Prob(A), Prob(B)), condition = And(SubsetEq(A, B), SubsetEq(B, Omega)).with_total_ordering_style()), 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_{A, B~|~A \subseteq B, B \subseteq \Omega}~\left(\textrm{Pr}\left(A\right) \leq \textrm{Pr}\left(B\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	parameters: 23 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	18, 19
16	Operation	operator: 21 operand: 26
17	Operation	operator: 21 operand: 27
18	Operation	operator: 24 operands: 23
19	Operation	operator: 24 operands: 25
20	ExprTuple	26
21	Literal
22	ExprTuple	27
23	ExprTuple	26, 27
24	Literal
25	ExprTuple	27, 28
26	Variable
27	Variable
28	Variable