Expression of type Conditional

from the theory of proveit.logic.sets.comprehension

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, S, x
from proveit.logic import InSet
from proveit.logic.sets import basic_comprehension_y

# build up the expression from sub-expressions
expr = Conditional(InSet(x, S), InSet(x, basic_comprehension_y))

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\{x \in S \textrm{ if } x \in \left\{y~|~Q\left(y\right)\right\}_{y \in S}\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: 16 operands: 3
2	Operation	operator: 16 operands: 4
3	ExprTuple	5, 20
4	ExprTuple	5, 6
5	Variable
6	Operation	operator: 7 operand: 9
7	Literal
8	ExprTuple	9
9	Lambda	parameter: 21 body: 10
10	Conditional	value: 21 condition: 11
11	Operation	operator: 12 operands: 13
12	Literal
13	ExprTuple	14, 15
14	Operation	operator: 16 operands: 17
15	Operation	operator: 18 operand: 21
16	Literal
17	ExprTuple	21, 20
18	Variable
19	ExprTuple	21
20	Variable
21	Variable