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

# build up the expression from sub-expressions
sub_expr1 = Add(m, one)
sub_expr2 = subtract(one, x)
expr = Equals(Sum(index_or_indices = [i], summand = Exp(x, i), domain = Interval(zero, sub_expr1)), Add(frac(subtract(one, Exp(x, sub_expr1)), sub_expr2), frac(Variable("_a", latex_format = r"{_{-}a}"), 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(\sum_{i = 0}^{m + 1} x^{i}\right) = \left(\frac{1 - x^{m + 1}}{1 - x} + \frac{{_{-}a}}{1 - x}\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: 8
4	Operation	operator: 41 operands: 7
5	Literal
6	ExprTuple	8
7	ExprTuple	9, 10
8	Lambda	parameter: 26 body: 12
9	Operation	operator: 14 operands: 13
10	Operation	operator: 14 operands: 15
11	ExprTuple	26
12	Conditional	value: 16 condition: 17
13	ExprTuple	18, 20
14	Literal
15	ExprTuple	19, 20
16	Operation	operator: 37 operands: 21
17	Operation	operator: 22 operands: 23
18	Operation	operator: 41 operands: 24
19	Variable
20	Operation	operator: 41 operands: 25
21	ExprTuple	39, 26
22	Literal
23	ExprTuple	26, 27
24	ExprTuple	44, 28
25	ExprTuple	44, 29
26	Variable
27	Operation	operator: 30 operands: 31
28	Operation	operator: 33 operand: 36
29	Operation	operator: 33 operand: 39
30	Literal
31	ExprTuple	35, 40
32	ExprTuple	36
33	Literal
34	ExprTuple	39
35	Literal
36	Operation	operator: 37 operands: 38
37	Literal
38	ExprTuple	39, 40
39	Variable
40	Operation	operator: 41 operands: 42
41	Literal
42	ExprTuple	43, 44
43	Variable
44	Literal