Common each_x_in_S of type ExprRange

from the theory of proveit.logic.sets

import proveit
# Automation is not needed when only 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 the special expression
from proveit.logic.sets import each_x_in_S

# check that the built expression is the same as the stored expression
assert each_x_in_S == stored_expr
assert each_x_in_S._style_id == stored_expr._style_id
print("Passed sanity check: each_x_in_S matches stored_expr")

Passed sanity check: each_x_in_S matches stored_expr

# Show the LaTeX representation of the expression for convenience if you need it.
print(stored_expr.latex())

\left(x_{1} \in S\right), \left(x_{2} \in S\right), \ldots, \left(x_{n} \in S\right)

stored_expr.style_options()

name	description	default	current value	related methods
parameterization	'implicit' (default for LaTeX formatting) hides the parameter the ExprRange so the parameterization may be ambiguous (e.g., x_{1+1}, ..., x_{n+1}); 'explicit' (default for string formatting) reveals the parameterization (e.g. x_{1+1}, ..x_{k+1}.., x_{n+1}).	None	None/False	('with_explicit_parameterization', 'with_implicit_parameterization', 'with_default_parameterization_style')
front_expansion	The number of instances to display at the front of the range (e.g., before the ellipsis). Default is 2.	2	2	('with_front_expansion', 'get_front_expansion')
back_expansion	The number of instances to display at the back of the range (e.g., after the ellipsis). Default is 1.	1	1	('with_back_expansion', 'get_back_expansion')
order	The default order is 'increasing' (a_1 ... a_3) but to represent a 'decreasing' ExprRange (a_6 ... a_2) the order must be set to 'decreasing'	increasing	increasing	('with_decreasing_order', 'with_increasing_order')
wrap_positions	position(s) at which wrapping is to occur; 'n' is after the nth comma.	()	()	('with_wrapping_at',)
case_simplify	If 'True', simplify formatted instances that are ConditionalSets under proper index assumptions	False	False	('with_case_simplification',)

# display the expression information
stored_expr.expr_info()

	core type	sub-expressions	expression
0	ExprRange	lambda_map: 1 start_index: 2 end_index: 3
1	Lambda	parameter: 11 body: 4
2	Literal
3	Variable
4	Operation	operator: 5 operands: 6
5	Literal
6	ExprTuple	7, 8
7	IndexedVar	variable: 9 index: 11
8	Variable
9	Variable
10	ExprTuple	11
11	Variable