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, subtract

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

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(\left(\sum_{k = 1}^{\left(m + 1\right) - 1} k\right) + \left(m + 1\right)\right) = \left(\left(\sum_{k = 1}^{m} k\right) + m + 1\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: 32 operands: 5
4	Operation	operator: 32 operands: 6
5	ExprTuple	7, 30
6	ExprTuple	8, 36, 37
7	Operation	operator: 10 operand: 12
8	Operation	operator: 10 operand: 13
9	ExprTuple	12
10	Literal
11	ExprTuple	13
12	Lambda	parameter: 23 body: 14
13	Lambda	parameter: 23 body: 16
14	Conditional	value: 23 condition: 17
15	ExprTuple	23
16	Conditional	value: 23 condition: 18
17	Operation	operator: 20 operands: 19
18	Operation	operator: 20 operands: 21
19	ExprTuple	23, 22
20	Literal
21	ExprTuple	23, 24
22	Operation	operator: 26 operands: 25
23	Variable
24	Operation	operator: 26 operands: 27
25	ExprTuple	37, 28
26	Literal
27	ExprTuple	37, 36
28	Operation	operator: 32 operands: 29
29	ExprTuple	30, 31
30	Operation	operator: 32 operands: 33
31	Operation	operator: 34 operand: 37
32	Literal
33	ExprTuple	36, 37
34	Literal
35	ExprTuple	37
36	Variable
37	Literal