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 c, l
from proveit.logic import Equals
from proveit.numbers import Add, Integer, Mult, Sum, one

# build up the expression from sub-expressions
sub_expr1 = [l]
sub_expr2 = Add(l, one)
expr = Equals(Sum(index_or_indices = sub_expr1, summand = Mult(c, sub_expr2), domain = Integer), Sum(index_or_indices = sub_expr1, summand = Mult(sub_expr2, c), domain = Integer))

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_{l \in \mathbb{Z}}~\left(c \cdot \left(l + 1\right)\right)\right] = \left[\sum_{l \in \mathbb{Z}}~\left(\left(l + 1\right) \cdot c\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: 26 body: 10
9	Lambda	parameter: 26 body: 12
10	Conditional	value: 13 condition: 15
11	ExprTuple	26
12	Conditional	value: 14 condition: 15
13	Operation	operator: 17 operands: 16
14	Operation	operator: 17 operands: 18
15	Operation	operator: 19 operands: 20
16	ExprTuple	22, 21
17	Literal
18	ExprTuple	21, 22
19	Literal
20	ExprTuple	26, 23
21	Operation	operator: 24 operands: 25
22	Variable
23	Literal
24	Literal
25	ExprTuple	26, 27
26	Variable
27	Literal