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, 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 = 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(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..

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	25, 28
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: 20 body: 12
10	Operation	operator: 15 operands: 13
11	Operation	operator: 15 operands: 14
12	Operation	operator: 15 operands: 16
13	ExprTuple	25, 17
14	ExprTuple	28, 17
15	Literal
16	ExprTuple	22, 18
17	Literal
18	Operation	operator: 19 operands: 20
19	Literal
20	ExprTuple	21, 22, 23
21	ExprRange	lambda_map: 24 start_index: 27 end_index: 25
22	Variable
23	ExprRange	lambda_map: 26 start_index: 27 end_index: 28
24	Lambda	parameter: 34 body: 29
25	Variable
26	Lambda	parameter: 34 body: 30
27	Literal
28	Variable
29	IndexedVar	variable: 31 index: 34
30	IndexedVar	variable: 32 index: 34
31	Variable
32	Variable
33	ExprTuple	34
34	Variable