Expression of type ExprTuple

from the theory of proveit.logic.sets.intersection

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 ExprTuple, x
from proveit.core_expr_types import Q__y_1_to_n, R__y_1_to_n, S_1_to_n, y_1_to_n
from proveit.logic import Forall, InSet
from proveit.logic.sets import general_intersectall_Ryn

# build up the expression from sub-expressions
expr = ExprTuple(InSet(x, general_intersectall_Ryn), Forall(instance_param_or_params = [y_1_to_n], instance_expr = InSet(x, R__y_1_to_n), domains = [S_1_to_n], condition = Q__y_1_to_n))

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 \left[\bigcap_{\left(y_{1} \in S_{1}\right), \left(y_{2} \in S_{2}\right), \ldots, \left(y_{n} \in S_{n}\right)~|~Q\left(y_{1}, y_{2}, \ldots, y_{n}\right)}~R\left(y_{1}, y_{2}, \ldots, y_{n}\right)\right], \forall_{\left(y_{1} \in S_{1}\right), \left(y_{2} \in S_{2}\right), \ldots, \left(y_{n} \in S_{n}\right)~|~Q\left(y_{1}, y_{2}, \ldots, y_{n}\right)}~\left(x \in R\left(y_{1}, y_{2}, \ldots, y_{n}\right)\right)\right)

stored_expr.style_options()

name	description	default	current value	related methods
wrap_positions	position(s) at which wrapping is to occur; 'n' is after the nth comma.	()	()	('with_wrapping_at',)
justification	if any wrap positions are set, justify to the 'left', 'center', or 'right'	left	left	('with_justification',)

# display the expression information
stored_expr.expr_info()

	core type	sub-expressions	expression
0	ExprTuple	1, 2
1	Operation	operator: 28 operands: 3
2	Operation	operator: 4 operand: 7
3	ExprTuple	16, 6
4	Literal
5	ExprTuple	7
6	Operation	operator: 8 operand: 11
7	Lambda	parameters: 25 body: 10
8	Literal
9	ExprTuple	11
10	Conditional	value: 12 condition: 15
11	Lambda	parameters: 25 body: 13
12	Operation	operator: 28 operands: 14
13	Conditional	value: 17 condition: 15
14	ExprTuple	16, 17
15	Operation	operator: 18 operands: 19
16	Variable
17	Operation	operator: 20 operands: 25
18	Literal
19	ExprTuple	21, 22
20	Variable
21	ExprRange	lambda_map: 23 start_index: 31 end_index: 32
22	Operation	operator: 24 operands: 25
23	Lambda	parameter: 38 body: 26
24	Variable
25	ExprTuple	27
26	Operation	operator: 28 operands: 29
27	ExprRange	lambda_map: 30 start_index: 31 end_index: 32
28	Literal
29	ExprTuple	34, 33
30	Lambda	parameter: 38 body: 34
31	Literal
32	Variable
33	IndexedVar	variable: 35 index: 38
34	IndexedVar	variable: 36 index: 38
35	Variable
36	Variable
37	ExprTuple	38
38	Variable