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
from proveit.logic import Forall, InClass, InSet
from proveit.statistics import Prob, SampleSpaces, prob_domain

# build up the expression from sub-expressions
expr = Conditional(Forall(instance_param_or_params = [x], instance_expr = InSet(Prob(x), prob_domain), domain = 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_{x \in \Omega}~\left(\textrm{Pr}\left(x\right) \in \left[0,1\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	17, 8
7	Lambda	parameter: 22 body: 9
8	Literal
9	Conditional	value: 10 condition: 11
10	Operation	operator: 13 operands: 12
11	Operation	operator: 13 operands: 14
12	ExprTuple	15, 16
13	Literal
14	ExprTuple	22, 17
15	Operation	operator: 18 operand: 22
16	Operation	operator: 20 operands: 21
17	Variable
18	Literal
19	ExprTuple	22
20	Literal
21	ExprTuple	23, 24
22	Variable
23	Literal
24	Literal