Expression of type Equals

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 b
from proveit.core_expr_types import a_1_to_i, c_1_to_j, d_1_to_k
from proveit.logic import Equals, Set

# build up the expression from sub-expressions
expr = Equals(Set(a_1_to_i, b, c_1_to_j, d_1_to_k), Set(a_1_to_i, c_1_to_j, b, d_1_to_k))

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}, b,c_{1}, c_{2}, \ldots, c_{j},d_{1}, d_{2}, \ldots, d_{k}\right\} = \left\{a_{1}, a_{2}, \ldots, a_{i},c_{1}, c_{2}, \ldots, c_{j}, b,d_{1}, d_{2}, \ldots, d_{k}\right\}

stored_expr.style_options()

name	description	default	current value	related methods
operation	'infix' or 'function' style formatting	infix	infix
wrap_positions	position(s) at which wrapping is to occur; '2 n - 1' is after the nth operand, '2 n' is after the nth operation.	()	()	('with_wrapping_at', 'with_wrap_before_operator', 'with_wrap_after_operator', 'without_wrapping', 'wrap_positions')
justification	if any wrap positions are set, justify to the 'left', 'center', or 'right'	center	center	('with_justification',)
direction	Direction of the relation (normal or reversed)	normal	normal	('with_direction_reversed', 'is_reversed')

# display the expression information
stored_expr.expr_info()

	core type	sub-expressions	expression
0	Operation	operator: 1 operands: 2
1	Literal
2	ExprTuple	3, 4
3	Operation	operator: 6 operands: 5
4	Operation	operator: 6 operands: 7
5	ExprTuple	8, 10, 9, 11
6	Literal
7	ExprTuple	8, 9, 10, 11
8	ExprRange	lambda_map: 12 start_index: 17 end_index: 13
9	ExprRange	lambda_map: 14 start_index: 17 end_index: 15
10	Variable
11	ExprRange	lambda_map: 16 start_index: 17 end_index: 18
12	Lambda	parameter: 26 body: 19
13	Variable
14	Lambda	parameter: 26 body: 20
15	Variable
16	Lambda	parameter: 26 body: 21
17	Literal
18	Variable
19	IndexedVar	variable: 22 index: 26
20	IndexedVar	variable: 23 index: 26
21	IndexedVar	variable: 24 index: 26
22	Variable
23	Variable
24	Variable
25	ExprTuple	26
26	Variable