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, seven, 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, seven)), Sum(index_or_indices = sub_expr1, summand = sub_expr2, domain = Interval(eight, 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}^{7} \left(k - 2\right)\right) + \left(\sum_{k = 8}^{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: 27 operands: 6
5	ExprTuple	7
6	ExprTuple	8, 9
7	Lambda	parameter: 33 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: 29 operands: 17
15	Lambda	parameter: 33 body: 18
16	Lambda	parameter: 33 body: 20
17	ExprTuple	33, 21
18	Conditional	value: 23 condition: 22
19	ExprTuple	33
20	Conditional	value: 23 condition: 24
21	Operation	operator: 38 operands: 25
22	Operation	operator: 29 operands: 26
23	Operation	operator: 27 operands: 28
24	Operation	operator: 29 operands: 30
25	ExprTuple	40, 44
26	ExprTuple	33, 31
27	Literal
28	ExprTuple	33, 32
29	Literal
30	ExprTuple	33, 34
31	Operation	operator: 38 operands: 35
32	Operation	operator: 36 operand: 42
33	Variable
34	Operation	operator: 38 operands: 39
35	ExprTuple	40, 41
36	Literal
37	ExprTuple	42
38	Literal
39	ExprTuple	43, 44
40	Variable
41	Literal
42	Literal
43	Literal
44	Literal