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, one, subtract, three, two

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

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} + a_{n - 1} + a_{n} + b - c\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: 36 operands: 5
4	Operation	operator: 36 operands: 6
5	ExprTuple	7, 8
6	ExprTuple	9, 10, 11, 12, 18, 19
7	Operation	operator: 36 operands: 13
8	Operation	operator: 36 operands: 14
9	IndexedVar	variable: 38 index: 31
10	IndexedVar	variable: 38 index: 45
11	IndexedVar	variable: 38 index: 21
12	IndexedVar	variable: 38 index: 40
13	ExprTuple	17, 18
14	ExprTuple	19, 20
15	ExprTuple	21
16	ExprTuple	40
17	ExprRange	lambda_map: 32 start_index: 31 end_index: 40
18	Variable
19	Operation	operator: 43 operand: 25
20	Operation	operator: 43 operand: 26
21	Operation	operator: 36 operands: 24
22	ExprTuple	25
23	ExprTuple	26
24	ExprTuple	40, 27
25	Variable
26	Operation	operator: 36 operands: 28
27	Operation	operator: 43 operand: 31
28	ExprTuple	30
29	ExprTuple	31
30	ExprRange	lambda_map: 32 start_index: 33 end_index: 34
31	Literal
32	Lambda	parameter: 42 body: 35
33	Literal
34	Operation	operator: 36 operands: 37
35	IndexedVar	variable: 38 index: 42
36	Literal
37	ExprTuple	40, 41
38	Variable
39	ExprTuple	42
40	Variable
41	Operation	operator: 43 operand: 45
42	Variable
43	Literal
44	ExprTuple	45
45	Literal