Expression of type Lambda

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, 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 = 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(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..

stored_expr.style_options()

no style options

# display the expression information
stored_expr.expr_info()

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