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 a, k
from proveit.logic import Equals
from proveit.numbers import Add, Interval, Sum, eight, nine, one, subtract, two

# build up the expression from sub-expressions
sub_expr1 = [k]
sub_expr2 = subtract(k, two)
expr = Equals(Sum(index_or_indices = sub_expr1, summand = sub_expr2, domain = Interval(a, nine)), Add(Sum(index_or_indices = sub_expr1, summand = sub_expr2, domain = Interval(a, eight)), Sum(index_or_indices = sub_expr1, summand = sub_expr2, domain = Interval(Add(eight, 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(\sum_{k = a}^{9} \left(k - 2\right)\right) = \left(\left(\sum_{k = a}^{8} \left(k - 2\right)\right) + \left(\sum_{k = 8 + 1}^{9} \left(k - 2\right)\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: 12 operand: 7
4	Operation	operator: 43 operands: 6
5	ExprTuple	7
6	ExprTuple	8, 9
7	Lambda	parameter: 32 body: 10
8	Operation	operator: 12 operand: 15
9	Operation	operator: 12 operand: 16
10	Conditional	value: 23 condition: 14
11	ExprTuple	15
12	Literal
13	ExprTuple	16
14	Operation	operator: 28 operands: 17
15	Lambda	parameter: 32 body: 18
16	Lambda	parameter: 32 body: 20
17	ExprTuple	32, 21
18	Conditional	value: 23 condition: 22
19	ExprTuple	32
20	Conditional	value: 23 condition: 24
21	Operation	operator: 37 operands: 25
22	Operation	operator: 28 operands: 26
23	Operation	operator: 43 operands: 27
24	Operation	operator: 28 operands: 29
25	ExprTuple	39, 42
26	ExprTuple	32, 30
27	ExprTuple	32, 31
28	Literal
29	ExprTuple	32, 33
30	Operation	operator: 37 operands: 34
31	Operation	operator: 35 operand: 40
32	Variable
33	Operation	operator: 37 operands: 38
34	ExprTuple	39, 45
35	Literal
36	ExprTuple	40
37	Literal
38	ExprTuple	41, 42
39	Variable
40	Literal
41	Operation	operator: 43 operands: 44
42	Literal
43	Literal
44	ExprTuple	45, 46
45	Literal
46	Literal