Expression of type Lambda

from the theory of proveit.logic.sets.cartesian_products

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 Lambda, x
from proveit.core_expr_types import A_1_to_m, a_1_to_m
from proveit.logic import And, CartProd, Equals, InSet
from proveit.logic.sets.cartesian_products import a_in_A__1_to_m

# build up the expression from sub-expressions
expr = Lambda([x, A_1_to_m, a_1_to_m], Equals(InSet(x, CartProd(A_1_to_m)), And(Equals(x, [a_1_to_m]), a_in_A__1_to_m)).with_wrapping_at(2))

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(x, A_{1}, A_{2}, \ldots, A_{m}, a_{1}, a_{2}, \ldots, a_{m}\right) \mapsto \left(\begin{array}{c} \begin{array}{l} \left(x \in \left(A_{1} \times  A_{2} \times  \ldots \times  A_{m}\right)\right) =  \\ \left(\left(x = \left(a_{1}, a_{2}, \ldots, a_{m}\right)\right)\land \left(a_{1} \in A_{1}\right) \land  \left(a_{2} \in A_{2}\right) \land  \ldots \land  \left(a_{m} \in A_{m}\right)\right) \end{array} \end{array}\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	18, 17, 22
2	Operation	operator: 14 operands: 3
3	ExprTuple	4, 5
4	Operation	operator: 23 operands: 6
5	Operation	operator: 7 operands: 8
6	ExprTuple	18, 9
7	Literal
8	ExprTuple	10, 11
9	Operation	operator: 12 operands: 13
10	Operation	operator: 14 operands: 15
11	ExprRange	lambda_map: 16 start_index: 26 end_index: 27
12	Literal
13	ExprTuple	17
14	Literal
15	ExprTuple	18, 19
16	Lambda	parameter: 33 body: 20
17	ExprRange	lambda_map: 21 start_index: 26 end_index: 27
18	Variable
19	ExprTuple	22
20	Operation	operator: 23 operands: 24
21	Lambda	parameter: 33 body: 28
22	ExprRange	lambda_map: 25 start_index: 26 end_index: 27
23	Literal
24	ExprTuple	29, 28
25	Lambda	parameter: 33 body: 29
26	Literal
27	Variable
28	IndexedVar	variable: 30 index: 33
29	IndexedVar	variable: 31 index: 33
30	Variable
31	Variable
32	ExprTuple	33
33	Variable