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, b, m, n
from proveit.core_expr_types import a_1_to_m, c_1_to_n
from proveit.logic import And, Forall, InSet, Set
from proveit.numbers import Natural

# build up the expression from sub-expressions
expr = ExprTuple(Lambda([m, n], Conditional(Forall(instance_param_or_params = [a_1_to_m, b, c_1_to_n], instance_expr = InSet(b, Set(a_1_to_m, b, c_1_to_n))), And(InSet(m, Natural), 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(\left(m, n\right) \mapsto \left\{\forall_{a_{1}, a_{2}, \ldots, a_{m}, b, c_{1}, c_{2}, \ldots, c_{n}}~\left(b \in \left\{a_{1}, a_{2}, \ldots, a_{m}, b,c_{1}, c_{2}, \ldots, c_{n}\right\}\right) \textrm{ if } m \in \mathbb{N} ,  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	parameters: 2 body: 3
2	ExprTuple	26, 29
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	11, 12
10	Lambda	parameters: 21 body: 13
11	Operation	operator: 16 operands: 14
12	Operation	operator: 16 operands: 15
13	Operation	operator: 16 operands: 17
14	ExprTuple	26, 18
15	ExprTuple	29, 18
16	Literal
17	ExprTuple	23, 19
18	Literal
19	Operation	operator: 20 operands: 21
20	Literal
21	ExprTuple	22, 23, 24
22	ExprRange	lambda_map: 25 start_index: 28 end_index: 26
23	Variable
24	ExprRange	lambda_map: 27 start_index: 28 end_index: 29
25	Lambda	parameter: 35 body: 30
26	Variable
27	Lambda	parameter: 35 body: 31
28	Literal
29	Variable
30	IndexedVar	variable: 32 index: 35
31	IndexedVar	variable: 33 index: 35
32	Variable
33	Variable
34	ExprTuple	35
35	Variable