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 a, b, 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(a, b, sub_expr2), domain = Integer), Mult(Sum(index_or_indices = sub_expr1, summand = sub_expr2, domain = Integer), a, b))

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(a \cdot b \cdot \left(l + 1\right)\right)\right] = \left(\left[\sum_{l \in \mathbb{Z}}~\left(l + 1\right)\right] \cdot a \cdot b\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: 10 operand: 7
4	Operation	operator: 14 operands: 6
5	ExprTuple	7
6	ExprTuple	8, 18, 19
7	Lambda	parameter: 27 body: 9
8	Operation	operator: 10 operand: 13
9	Conditional	value: 12 condition: 21
10	Literal
11	ExprTuple	13
12	Operation	operator: 14 operands: 15
13	Lambda	parameter: 27 body: 17
14	Literal
15	ExprTuple	18, 19, 20
16	ExprTuple	27
17	Conditional	value: 20 condition: 21
18	Variable
19	Variable
20	Operation	operator: 22 operands: 23
21	Operation	operator: 24 operands: 25
22	Literal
23	ExprTuple	27, 26
24	Literal
25	ExprTuple	27, 28
26	Literal
27	Variable
28	Literal