Expression of type InSet

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 x
from proveit.logic import InSet
from proveit.logic.sets import general_comprehension_fyn

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

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())

x \in \left\{f\left(y_{1}, y_{2}, \ldots, y_{n}\right)~|~Q\left(y_{1}, y_{2}, \ldots, y_{n}\right)\right\}_{\left(y_{1} \in S_{1}\right), \left(y_{2} \in S_{2}\right), \ldots, \left(y_{n} \in S_{n}\right)}

stored_expr.style_options()

name	description	default	current value	related methods
operation	'infix' or 'function' style formatting	infix	infix
wrap_positions	position(s) at which wrapping is to occur; '2 n - 1' is after the nth operand, '2 n' is after the nth operation.	()	()	('with_wrapping_at', 'with_wrap_before_operator', 'with_wrap_after_operator', 'without_wrapping', 'wrap_positions')
justification	if any wrap positions are set, justify to the 'left', 'center', or 'right'	center	center	('with_justification',)
direction	Direction of the relation (normal or reversed)	normal	normal	('with_direction_reversed', 'is_reversed')

# display the expression information
stored_expr.expr_info()

	core type	sub-expressions	expression
0	Operation	operator: 20 operands: 1
1	ExprTuple	2, 3
2	Variable
3	Operation	operator: 4 operand: 6
4	Literal
5	ExprTuple	6
6	Lambda	parameters: 17 body: 7
7	Conditional	value: 8 condition: 9
8	Operation	operator: 10 operands: 17
9	Operation	operator: 11 operands: 12
10	Variable
11	Literal
12	ExprTuple	13, 14
13	ExprRange	lambda_map: 15 start_index: 23 end_index: 24
14	Operation	operator: 16 operands: 17
15	Lambda	parameter: 30 body: 18
16	Variable
17	ExprTuple	19
18	Operation	operator: 20 operands: 21
19	ExprRange	lambda_map: 22 start_index: 23 end_index: 24
20	Literal
21	ExprTuple	26, 25
22	Lambda	parameter: 30 body: 26
23	Literal
24	Variable
25	IndexedVar	variable: 27 index: 30
26	IndexedVar	variable: 28 index: 30
27	Variable
28	Variable
29	ExprTuple	30
30	Variable