Expression of type ExprTuple

from the theory of proveit.logic.sets.enumeration

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, ExprTuple, Lambda, n, x
from proveit.core_expr_types import y_1_to_n
from proveit.logic import Equals, Forall, InSet, Set
from proveit.logic.sets import x_equals_any_y
from proveit.numbers import Natural

# build up the expression from sub-expressions
expr = ExprTuple(Lambda(n, Conditional(Forall(instance_param_or_params = [x, y_1_to_n], instance_expr = Equals(InSet(x, Set(y_1_to_n)), x_equals_any_y).with_wrapping_at(2)), InSet(n, Natural))))

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(n \mapsto \left\{\forall_{x, y_{1}, y_{2}, \ldots, y_{n}}~\left(\begin{array}{c} \begin{array}{l} \left(x \in \left\{y_{1}, y_{2}, \ldots, y_{n}\right\}\right) =  \\ \left(\left(x = y_{1}\right) \lor  \left(x = y_{2}\right) \lor  \ldots \lor  \left(x = y_{n}\right)\right) \end{array} \end{array}\right) \textrm{ if } n \in \mathbb{N}\right..\right)

stored_expr.style_options()

no style options

# display the expression information
stored_expr.expr_info()

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