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 = Sum(index_or_indices = [k], summand = k, domain = Interval(one, m))
expr = Equals(Add(sub_expr1, m, one), Add(sub_expr1, Add(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}^{m} k\right) + m + 1\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: 11 operands: 5
4	Operation	operator: 11 operands: 6
5	ExprTuple	7, 24, 23
6	ExprTuple	7, 8
7	Operation	operator: 9 operand: 13
8	Operation	operator: 11 operands: 12
9	Literal
10	ExprTuple	13
11	Literal
12	ExprTuple	24, 23
13	Lambda	parameter: 19 body: 15
14	ExprTuple	19
15	Conditional	value: 19 condition: 16
16	Operation	operator: 17 operands: 18
17	Literal
18	ExprTuple	19, 20
19	Variable
20	Operation	operator: 21 operands: 22
21	Literal
22	ExprTuple	23, 24
23	Literal
24	Variable