Expression of type ExprTuple

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 ExprTuple, x
from proveit.core_expr_types import Q__y_1_to_n, S_1_to_n, f__y_1_to_n, y_1_to_n
from proveit.logic import Equals, Exists, InSet
from proveit.logic.sets import general_comprehension_fyn

# build up the expression from sub-expressions
expr = ExprTuple(Exists(instance_param_or_params = [y_1_to_n], instance_expr = Equals(x, f__y_1_to_n), domains = [S_1_to_n], condition = Q__y_1_to_n), 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())

\left(\exists_{\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 = f\left(y_{1}, y_{2}, \ldots, y_{n}\right)\right), 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)}\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: 3 operand: 6
2	Operation	operator: 29 operands: 5
3	Literal
4	ExprTuple	6
5	ExprTuple	16, 7
6	Lambda	parameters: 26 body: 8
7	Operation	operator: 9 operand: 12
8	Conditional	value: 11 condition: 18
9	Literal
10	ExprTuple	12
11	Operation	operator: 13 operands: 14
12	Lambda	parameters: 26 body: 15
13	Literal
14	ExprTuple	16, 17
15	Conditional	value: 17 condition: 18
16	Variable
17	Operation	operator: 19 operands: 26
18	Operation	operator: 20 operands: 21
19	Variable
20	Literal
21	ExprTuple	22, 23
22	ExprRange	lambda_map: 24 start_index: 32 end_index: 33
23	Operation	operator: 25 operands: 26
24	Lambda	parameter: 39 body: 27
25	Variable
26	ExprTuple	28
27	Operation	operator: 29 operands: 30
28	ExprRange	lambda_map: 31 start_index: 32 end_index: 33
29	Literal
30	ExprTuple	35, 34
31	Lambda	parameter: 39 body: 35
32	Literal
33	Variable
34	IndexedVar	variable: 36 index: 39
35	IndexedVar	variable: 37 index: 39
36	Variable
37	Variable
38	ExprTuple	39
39	Variable