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, 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
expr = Equals(Equals(Sum(index_or_indices = [i], summand = Exp(x, i), domain = Interval(zero, zero)), frac(subtract(one, Exp(x, Add(zero, one))), subtract(one, x))), Equals(one, one)).with_wrapping_at(2)

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())

\begin{array}{c} \begin{array}{l} \left(\left(\sum_{i = 0}^{0} x^{i}\right) = \frac{1 - x^{0 + 1}}{1 - x}\right) =  \\ \left(1 = 1\right) \end{array} \end{array}

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.	()	(2)	('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: 5 operands: 1
1	ExprTuple	2, 3
2	Operation	operator: 5 operands: 4
3	Operation	operator: 5 operands: 6
4	ExprTuple	7, 8
5	Literal
6	ExprTuple	42, 42
7	Operation	operator: 9 operand: 13
8	Operation	operator: 11 operands: 12
9	Literal
10	ExprTuple	13
11	Literal
12	ExprTuple	14, 15
13	Lambda	parameter: 30 body: 17
14	Operation	operator: 39 operands: 18
15	Operation	operator: 39 operands: 19
16	ExprTuple	30
17	Conditional	value: 20 condition: 21
18	ExprTuple	42, 22
19	ExprTuple	42, 23
20	Operation	operator: 35 operands: 24
21	Operation	operator: 25 operands: 26
22	Operation	operator: 28 operand: 32
23	Operation	operator: 28 operand: 37
24	ExprTuple	37, 30
25	Literal
26	ExprTuple	30, 31
27	ExprTuple	32
28	Literal
29	ExprTuple	37
30	Variable
31	Operation	operator: 33 operands: 34
32	Operation	operator: 35 operands: 36
33	Literal
34	ExprTuple	41, 41
35	Literal
36	ExprTuple	37, 38
37	Variable
38	Operation	operator: 39 operands: 40
39	Literal
40	ExprTuple	41, 42
41	Literal
42	Literal