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 Boolean, Forall, InSet, Set
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 = InSet(InSet(x, Set(y_1_to_n)), Boolean)), 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(\left(x \in \left\{y_{1}, y_{2}, \ldots, y_{n}\right\}\right) \in \mathbb{B}\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: 25 body: 3
2	ExprTuple	25
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	25, 10
9	Lambda	parameters: 11 body: 12
10	Literal
11	ExprTuple	18, 22
12	Operation	operator: 16 operands: 13
13	ExprTuple	14, 15
14	Operation	operator: 16 operands: 17
15	Literal
16	Literal
17	ExprTuple	18, 19
18	Variable
19	Operation	operator: 20 operands: 21
20	Literal
21	ExprTuple	22
22	ExprRange	lambda_map: 23 start_index: 24 end_index: 25
23	Lambda	parameter: 29 body: 26
24	Literal
25	Variable
26	IndexedVar	variable: 27 index: 29
27	Variable
28	ExprTuple	29
29	Variable