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, m, n
from proveit.core_expr_types import a_1_to_m, b_1_to_n
from proveit.logic import And, Forall, InSet, Set, SubsetEq
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_1_to_n], instance_expr = SubsetEq(Set(a_1_to_m), Set(a_1_to_m, b_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_{1}, b_{2}, \ldots, b_{n}}~\left(\left\{a_{1}, a_{2}, \ldots, a_{m}\right\} \subseteq \left\{a_{1}, a_{2}, \ldots, a_{m},b_{1}, b_{2}, \ldots, b_{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	28, 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	11, 12
10	Lambda	parameters: 24 body: 13
11	Operation	operator: 15 operands: 14
12	Operation	operator: 15 operands: 16
13	Operation	operator: 17 operands: 18
14	ExprTuple	28, 19
15	Literal
16	ExprTuple	31, 19
17	Literal
18	ExprTuple	20, 21
19	Literal
20	Operation	operator: 23 operands: 22
21	Operation	operator: 23 operands: 24
22	ExprTuple	25
23	Literal
24	ExprTuple	25, 26
25	ExprRange	lambda_map: 27 start_index: 30 end_index: 28
26	ExprRange	lambda_map: 29 start_index: 30 end_index: 31
27	Lambda	parameter: 37 body: 32
28	Variable
29	Lambda	parameter: 37 body: 33
30	Literal
31	Variable
32	IndexedVar	variable: 34 index: 37
33	IndexedVar	variable: 35 index: 37
34	Variable
35	Variable
36	ExprTuple	37
37	Variable