Expression of type Equals

from the theory of proveit.numbers.summation

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 Function, a, b, f, fx, x
from proveit.logic import Equals
from proveit.numbers import Interval, Neg, Sum

# build up the expression from sub-expressions
sub_expr1 = [x]
expr = Equals(Sum(index_or_indices = sub_expr1, summand = fx, domain = Interval(a, b)), Sum(index_or_indices = sub_expr1, summand = Function(f, [Neg(x)]), domain = Interval(Neg(b), Neg(a))))

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(\sum_{x = a}^{b} f\left(x\right)\right) = \left(\sum_{x = -b}^{-a} f\left(-x\right)\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 operand: 8
4	Operation	operator: 6 operand: 9
5	ExprTuple	8
6	Literal
7	ExprTuple	9
8	Lambda	parameter: 28 body: 10
9	Lambda	parameter: 28 body: 11
10	Conditional	value: 12 condition: 13
11	Conditional	value: 14 condition: 15
12	Operation	operator: 17 operand: 28
13	Operation	operator: 19 operands: 16
14	Operation	operator: 17 operand: 22
15	Operation	operator: 19 operands: 20
16	ExprTuple	28, 21
17	Variable
18	ExprTuple	22
19	Literal
20	ExprTuple	28, 23
21	Operation	operator: 26 operands: 24
22	Operation	operator: 32 operand: 28
23	Operation	operator: 26 operands: 27
24	ExprTuple	35, 34
25	ExprTuple	28
26	Literal
27	ExprTuple	29, 30
28	Variable
29	Operation	operator: 32 operand: 34
30	Operation	operator: 32 operand: 35
31	ExprTuple	34
32	Literal
33	ExprTuple	35
34	Variable
35	Variable