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, Mult, Sum, frac, one, two

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

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(\frac{m \cdot \left(m + 1\right)}{2} + \frac{2 \cdot \left(m + 1\right)}{2}\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: 5 operand: 8
4	Operation	operator: 30 operands: 7
5	Literal
6	ExprTuple	8
7	ExprTuple	9, 10
8	Lambda	parameter: 24 body: 12
9	Operation	operator: 14 operands: 13
10	Operation	operator: 14 operands: 15
11	ExprTuple	24
12	Conditional	value: 24 condition: 16
13	ExprTuple	17, 26
14	Literal
15	ExprTuple	18, 26
16	Operation	operator: 19 operands: 20
17	Operation	operator: 22 operands: 21
18	Operation	operator: 22 operands: 23
19	Literal
20	ExprTuple	24, 25
21	ExprTuple	32, 29
22	Literal
23	ExprTuple	26, 29
24	Variable
25	Operation	operator: 27 operands: 28
26	Literal
27	Literal
28	ExprTuple	33, 29
29	Operation	operator: 30 operands: 31
30	Literal
31	ExprTuple	32, 33
32	Variable
33	Literal