Expression of type Equals

from the theory of proveit.numbers.addition

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 ExprRange, IndexedVar, Variable, a, b, c, n
from proveit.core_expr_types import a_1_to_n
from proveit.logic import Equals
from proveit.numbers import Add, Neg, subtract, three, two

# build up the expression from sub-expressions
sub_expr1 = Variable("_a", latex_format = r"{_{-}a}")
sub_expr2 = Neg(c)
sub_expr3 = ExprRange(sub_expr1, IndexedVar(a, sub_expr1), three, subtract(n, two))
expr = Equals(Add(Add(a_1_to_n, b), Add(sub_expr2, Add(sub_expr3))), Add(a_1_to_n, b, sub_expr2, sub_expr3))

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(a_{1} +  a_{2} +  \ldots +  a_{n} + b\right) + \left(-c + \left(a_{3} +  a_{4} +  \ldots +  a_{n - 2}\right)\right)\right) = \left(a_{1} +  a_{2} +  \ldots +  a_{n} + b - c+ a_{3} +  a_{4} +  \ldots +  a_{n - 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: 24 operands: 5
4	Operation	operator: 24 operands: 6
5	ExprTuple	7, 8
6	ExprTuple	11, 12, 13, 19
7	Operation	operator: 24 operands: 9
8	Operation	operator: 24 operands: 10
9	ExprTuple	11, 12
10	ExprTuple	13, 14
11	ExprRange	lambda_map: 20 start_index: 15 end_index: 28
12	Variable
13	Operation	operator: 31 operand: 18
14	Operation	operator: 24 operands: 17
15	Literal
16	ExprTuple	18
17	ExprTuple	19
18	Variable
19	ExprRange	lambda_map: 20 start_index: 21 end_index: 22
20	Lambda	parameter: 30 body: 23
21	Literal
22	Operation	operator: 24 operands: 25
23	IndexedVar	variable: 26 index: 30
24	Literal
25	ExprTuple	28, 29
26	Variable
27	ExprTuple	30
28	Variable
29	Operation	operator: 31 operand: 33
30	Variable
31	Literal
32	ExprTuple	33
33	Literal