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

# build up the expression from sub-expressions
expr = Equals(Sum(index_or_indices = [i], summand = Exp(x, i), domain = Interval(zero, Add(m, one))), Mult(frac(one, subtract(one, x)), subtract(one, Exp(x, Add(two, m)))))

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_{i = 0}^{m + 1} x^{i}\right) = \left(\frac{1}{1 - x} \cdot \left(1 - x^{2 + m}\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: 5 operand: 9
4	Operation	operator: 7 operands: 8
5	Literal
6	ExprTuple	9
7	Literal
8	ExprTuple	10, 11
9	Lambda	parameter: 26 body: 13
10	Operation	operator: 14 operands: 15
11	Operation	operator: 41 operands: 16
12	ExprTuple	26
13	Conditional	value: 17 condition: 18
14	Literal
15	ExprTuple	43, 19
16	ExprTuple	43, 20
17	Operation	operator: 34 operands: 21
18	Operation	operator: 22 operands: 23
19	Operation	operator: 41 operands: 24
20	Operation	operator: 32 operand: 29
21	ExprTuple	38, 26
22	Literal
23	ExprTuple	26, 27
24	ExprTuple	43, 28
25	ExprTuple	29
26	Variable
27	Operation	operator: 30 operands: 31
28	Operation	operator: 32 operand: 38
29	Operation	operator: 34 operands: 35
30	Literal
31	ExprTuple	36, 37
32	Literal
33	ExprTuple	38
34	Literal
35	ExprTuple	38, 39
36	Literal
37	Operation	operator: 41 operands: 40
38	Variable
39	Operation	operator: 41 operands: 42
40	ExprTuple	45, 43
41	Literal
42	ExprTuple	44, 45
43	Literal
44	Literal
45	Variable