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, b, j
from proveit.logic import Equals
from proveit.numbers import Add, Interval, Sum, subtract, three

# build up the expression from sub-expressions
sub_expr1 = [j]
expr = Equals(Sum(index_or_indices = sub_expr1, summand = j, domain = Interval(a, b)), Sum(index_or_indices = sub_expr1, summand = subtract(j, three), domain = Interval(Add(a, three), Add(b, three))))

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_{j = a}^{b} j\right) = \left(\sum_{j = a + 3}^{b + 3} \left(j - 3\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: 22 body: 10
9	Lambda	parameter: 22 body: 12
10	Conditional	value: 22 condition: 13
11	ExprTuple	22
12	Conditional	value: 14 condition: 15
13	Operation	operator: 18 operands: 16
14	Operation	operator: 32 operands: 17
15	Operation	operator: 18 operands: 19
16	ExprTuple	22, 20
17	ExprTuple	22, 21
18	Literal
19	ExprTuple	22, 23
20	Operation	operator: 27 operands: 24
21	Operation	operator: 25 operand: 36
22	Variable
23	Operation	operator: 27 operands: 28
24	ExprTuple	34, 35
25	Literal
26	ExprTuple	36
27	Literal
28	ExprTuple	29, 30
29	Operation	operator: 32 operands: 31
30	Operation	operator: 32 operands: 33
31	ExprTuple	34, 36
32	Literal
33	ExprTuple	35, 36
34	Variable
35	Variable
36	Literal