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.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 = IndexedVar(a, sub_expr1)
sub_expr3 = Neg(c)
expr = Equals(Add(Add(ExprRange(sub_expr1, sub_expr2, three, n), b), subtract(sub_expr3, Add(ExprRange(sub_expr1, sub_expr2, one, subtract(n, two))))), Add(IndexedVar(a, subtract(n, one)), IndexedVar(a, n), b, sub_expr3, Neg(IndexedVar(a, one)), Neg(IndexedVar(a, two))))

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_{3} +  a_{4} +  \ldots +  a_{n} + b\right) + \left(-c - \left(a_{1} +  a_{2} +  \ldots +  a_{n - 2}\right)\right)\right) = \left(a_{n - 1} + a_{n} + b - c - a_{1} - a_{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: 40 operands: 5
4	Operation	operator: 40 operands: 6
5	ExprTuple	7, 8
6	ExprTuple	9, 10, 20, 21, 11, 12
7	Operation	operator: 40 operands: 13
8	Operation	operator: 40 operands: 14
9	IndexedVar	variable: 42 index: 23
10	IndexedVar	variable: 42 index: 44
11	Operation	operator: 47 operand: 24
12	Operation	operator: 47 operand: 25
13	ExprTuple	19, 20
14	ExprTuple	21, 22
15	ExprTuple	23
16	ExprTuple	44
17	ExprTuple	24
18	ExprTuple	25
19	ExprRange	lambda_map: 36 start_index: 26 end_index: 44
20	Variable
21	Operation	operator: 47 operand: 30
22	Operation	operator: 47 operand: 31
23	Operation	operator: 40 operands: 29
24	IndexedVar	variable: 42 index: 37
25	IndexedVar	variable: 42 index: 49
26	Literal
27	ExprTuple	30
28	ExprTuple	31
29	ExprTuple	44, 32
30	Variable
31	Operation	operator: 40 operands: 33
32	Operation	operator: 47 operand: 37
33	ExprTuple	35
34	ExprTuple	37
35	ExprRange	lambda_map: 36 start_index: 37 end_index: 38
36	Lambda	parameter: 46 body: 39
37	Literal
38	Operation	operator: 40 operands: 41
39	IndexedVar	variable: 42 index: 46
40	Literal
41	ExprTuple	44, 45
42	Variable
43	ExprTuple	46
44	Variable
45	Operation	operator: 47 operand: 49
46	Variable
47	Literal
48	ExprTuple	49
49	Literal