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 m, x
from proveit.logic import Equals
from proveit.numbers import Add, Exp, Mult, frac, one, subtract, two

# build up the expression from sub-expressions
sub_expr1 = Exp(x, Add(m, one))
sub_expr2 = frac(one, subtract(one, x))
sub_expr3 = subtract(one, sub_expr1)
sub_expr4 = subtract(sub_expr1, Exp(x, Add(two, m)))
expr = Equals(Add(Mult(sub_expr2, sub_expr3), Mult(sub_expr2, sub_expr4)), Mult(sub_expr2, Add(sub_expr3, sub_expr4)))

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(\frac{1}{1 - x} \cdot \left(1 - x^{m + 1}\right)\right) + \left(\frac{1}{1 - x} \cdot \left(x^{m + 1} - x^{2 + m}\right)\right)\right) = \left(\frac{1}{1 - x} \cdot \left(\left(1 - x^{m + 1}\right) + \left(x^{m + 1} - x^{2 + m}\right)\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: 39 operands: 5
4	Operation	operator: 11 operands: 6
5	ExprTuple	7, 8
6	ExprTuple	14, 9
7	Operation	operator: 11 operands: 10
8	Operation	operator: 11 operands: 12
9	Operation	operator: 39 operands: 13
10	ExprTuple	14, 15
11	Literal
12	ExprTuple	14, 16
13	ExprTuple	15, 16
14	Operation	operator: 17 operands: 18
15	Operation	operator: 39 operands: 19
16	Operation	operator: 39 operands: 20
17	Literal
18	ExprTuple	41, 21
19	ExprTuple	41, 22
20	ExprTuple	28, 23
21	Operation	operator: 39 operands: 24
22	Operation	operator: 30 operand: 28
23	Operation	operator: 30 operand: 29
24	ExprTuple	41, 27
25	ExprTuple	28
26	ExprTuple	29
27	Operation	operator: 30 operand: 36
28	Operation	operator: 33 operands: 32
29	Operation	operator: 33 operands: 34
30	Literal
31	ExprTuple	36
32	ExprTuple	36, 35
33	Literal
34	ExprTuple	36, 37
35	Operation	operator: 39 operands: 38
36	Variable
37	Operation	operator: 39 operands: 40
38	ExprTuple	43, 41
39	Literal
40	ExprTuple	42, 43
41	Literal
42	Literal
43	Variable