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, Interval, Sum, one, six, subtract, two

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