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 i
from proveit.logic import Equals
from proveit.numbers import Add, Exp, Interval, Sum, five, nine, one, two

# build up the expression from sub-expressions
sub_expr1 = [i]
sub_expr2 = Exp(i, two)
expr = Equals(Add(Sum(index_or_indices = sub_expr1, summand = sub_expr2, domain = Interval(one, five)), Sum(index_or_indices = sub_expr1, summand = sub_expr2, domain = Interval(Add(five, one), nine))), Sum(index_or_indices = sub_expr1, summand = sub_expr2, domain = Interval(one, nine)))

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_{i = 1}^{5} i^{2}\right) + \left(\sum_{i = 5 + 1}^{9} i^{2}\right)\right) = \left(\sum_{i = 1}^{9} i^{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: 40 operands: 5
4	Operation	operator: 11 operand: 9
5	ExprTuple	7, 8
6	ExprTuple	9
7	Operation	operator: 11 operand: 14
8	Operation	operator: 11 operand: 15
9	Lambda	parameter: 33 body: 13
10	ExprTuple	14
11	Literal
12	ExprTuple	15
13	Conditional	value: 22 condition: 16
14	Lambda	parameter: 33 body: 17
15	Lambda	parameter: 33 body: 19
16	Operation	operator: 28 operands: 20
17	Conditional	value: 22 condition: 21
18	ExprTuple	33
19	Conditional	value: 22 condition: 23
20	ExprTuple	33, 24
21	Operation	operator: 28 operands: 25
22	Operation	operator: 26 operands: 27
23	Operation	operator: 28 operands: 29
24	Operation	operator: 36 operands: 30
25	ExprTuple	33, 31
26	Literal
27	ExprTuple	33, 32
28	Literal
29	ExprTuple	33, 34
30	ExprTuple	43, 39
31	Operation	operator: 36 operands: 35
32	Literal
33	Variable
34	Operation	operator: 36 operands: 37
35	ExprTuple	43, 42
36	Literal
37	ExprTuple	38, 39
38	Operation	operator: 40 operands: 41
39	Literal
40	Literal
41	ExprTuple	42, 43
42	Literal
43	Literal