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 Forall, InSet, NotInSet, Set
from proveit.logic.sets import x_notequals_all_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 = x_notequals_all_y, condition = NotInSet(x, Set(y_1_to_n))), 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}~|~x \notin \left\{y_{1}, y_{2}, \ldots, y_{n}\right\}}~\left(\left(x \neq y_{1}\right) \land  \left(x \neq y_{2}\right) \land  \ldots \land  \left(x \neq y_{n}\right)\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: 31 body: 3
2	ExprTuple	31
3	Conditional	value: 4 condition: 5
4	Operation	operator: 6 operand: 10
5	Operation	operator: 8 operands: 9
6	Literal
7	ExprTuple	10
8	Literal
9	ExprTuple	31, 11
10	Lambda	parameters: 12 body: 13
11	Literal
12	ExprTuple	32, 26
13	Conditional	value: 14 condition: 15
14	Operation	operator: 16 operands: 17
15	Operation	operator: 18 operands: 19
16	Literal
17	ExprTuple	20
18	Literal
19	ExprTuple	32, 21
20	ExprRange	lambda_map: 22 start_index: 30 end_index: 31
21	Operation	operator: 23 operands: 24
22	Lambda	parameter: 36 body: 25
23	Literal
24	ExprTuple	26
25	Operation	operator: 27 operands: 28
26	ExprRange	lambda_map: 29 start_index: 30 end_index: 31
27	Literal
28	ExprTuple	32, 33
29	Lambda	parameter: 36 body: 33
30	Literal
31	Variable
32	Variable
33	IndexedVar	variable: 34 index: 36
34	Variable
35	ExprTuple	36
36	Variable