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 Lambda, x
from proveit.core_expr_types import a_1_to_i, b_1_to_j, c_1_to_k
from proveit.logic import Equals, Set

# build up the expression from sub-expressions
expr = Lambda([a_1_to_i, x, b_1_to_j, c_1_to_k], Equals(Set(a_1_to_i, x, b_1_to_j, x, c_1_to_k), Set(a_1_to_i, x, b_1_to_j, c_1_to_k)).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(a_{1}, a_{2}, \ldots, a_{i}, x, b_{1}, b_{2}, \ldots, b_{j}, c_{1}, c_{2}, \ldots, c_{k}\right) \mapsto \left(\begin{array}{c} \begin{array}{l} \left\{a_{1}, a_{2}, \ldots, a_{i}, x,b_{1}, b_{2}, \ldots, b_{j}, x,c_{1}, c_{2}, \ldots, c_{k}\right\} =  \\ \left\{a_{1}, a_{2}, \ldots, a_{i}, x,b_{1}, b_{2}, \ldots, b_{j},c_{1}, c_{2}, \ldots, c_{k}\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: 8 body: 1
1	Operation	operator: 2 operands: 3
2	Literal
3	ExprTuple	4, 5
4	Operation	operator: 7 operands: 6
5	Operation	operator: 7 operands: 8
6	ExprTuple	9, 10, 11, 10, 12
7	Literal
8	ExprTuple	9, 10, 11, 12
9	ExprRange	lambda_map: 13 start_index: 18 end_index: 14
10	Variable
11	ExprRange	lambda_map: 15 start_index: 18 end_index: 16
12	ExprRange	lambda_map: 17 start_index: 18 end_index: 19
13	Lambda	parameter: 27 body: 20
14	Variable
15	Lambda	parameter: 27 body: 21
16	Variable
17	Lambda	parameter: 27 body: 22
18	Literal
19	Variable
20	IndexedVar	variable: 23 index: 27
21	IndexedVar	variable: 24 index: 27
22	IndexedVar	variable: 25 index: 27
23	Variable
24	Variable
25	Variable
26	ExprTuple	27
27	Variable