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 k, m
from proveit.logic import Equals
from proveit.numbers import Add, Interval, Sum, one

# build up the expression from sub-expressions
sub_expr1 = [k]
sub_expr2 = Add(m, one)
expr = Equals(Sum(index_or_indices = sub_expr1, summand = k, domain = Interval(one, sub_expr2)), Add(Sum(index_or_indices = sub_expr1, summand = k, domain = Interval(one, m)), sub_expr2))

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_{k = 1}^{m + 1} k\right) = \left(\left(\sum_{k = 1}^{m} k\right) + \left(m + 1\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: 10 operand: 7
4	Operation	operator: 25 operands: 6
5	ExprTuple	7
6	ExprTuple	8, 22
7	Lambda	parameter: 23 body: 9
8	Operation	operator: 10 operand: 13
9	Conditional	value: 23 condition: 12
10	Literal
11	ExprTuple	13
12	Operation	operator: 20 operands: 14
13	Lambda	parameter: 23 body: 16
14	ExprTuple	23, 17
15	ExprTuple	23
16	Conditional	value: 23 condition: 18
17	Operation	operator: 27 operands: 19
18	Operation	operator: 20 operands: 21
19	ExprTuple	29, 22
20	Literal
21	ExprTuple	23, 24
22	Operation	operator: 25 operands: 26
23	Variable
24	Operation	operator: 27 operands: 28
25	Literal
26	ExprTuple	30, 29
27	Literal
28	ExprTuple	29, 30
29	Literal
30	Variable