Theorem inf_geom_sum of type Forall

from the theory of proveit.numbers.summation

see dependencies

import proveit
# Automation is not needed when only building an expression:
proveit.defaults.automation = False # This will speed things up.
proveit.defaults.inline_pngs = False # Makes files smaller.
%load_theorem_expr # Load the stored theorem expression as 'stored_expr'
# import the special expression
from proveit.numbers.summation import inf_geom_sum

# check that the built expression is the same as the stored expression
assert inf_geom_sum.expr == stored_expr
assert inf_geom_sum.expr._style_id == stored_expr._style_id
print("Passed sanity check: inf_geom_sum matches stored_expr")

Passed sanity check: inf_geom_sum matches stored_expr

# Show the LaTeX representation of the expression for convenience if you need it.
print(stored_expr.latex())

\forall_{x \in \mathbb{C}~|~\left|x\right| < 1}~\left(\left(\sum_{m = 0}^{\infty} x^{m}\right) = \frac{1}{1 - x}\right)

stored_expr.style_options()

name	description	default	current value	related methods
with_wrapping	If 'True', wrap the Expression after the parameters	None	None/False	('with_wrapping',)
condition_wrapping	Wrap 'before' or 'after' the condition (or None).	None	None/False	('with_wrap_after_condition', 'with_wrap_before_condition')
wrap_params	If 'True', wraps every two parameters AND wraps the Expression after the parameters	None	None/False	('with_params',)
justification	justify to the 'left', 'center', or 'right' in the array cells	center	center	('with_justification',)

# display the expression information
stored_expr.expr_info()

	core type	sub-expressions	expression
0	Operation	operator: 1 operand: 3
1	Literal
2	ExprTuple	3
3	Lambda	parameter: 43 body: 4
4	Conditional	value: 5 condition: 6
5	Operation	operator: 7 operands: 8
6	Operation	operator: 9 operands: 10
7	Literal
8	ExprTuple	11, 12
9	Literal
10	ExprTuple	13, 14
11	Operation	operator: 15 operand: 22
12	Operation	operator: 17 operands: 18
13	Operation	operator: 37 operands: 19
14	Operation	operator: 20 operands: 21
15	Literal
16	ExprTuple	22
17	Literal
18	ExprTuple	33, 23
19	ExprTuple	43, 24
20	Literal
21	ExprTuple	25, 33
22	Lambda	parameter: 41 body: 27
23	Operation	operator: 28 operands: 29
24	Literal
25	Operation	operator: 30 operand: 43
26	ExprTuple	41
27	Conditional	value: 31 condition: 32
28	Literal
29	ExprTuple	33, 34
30	Literal
31	Operation	operator: 35 operands: 36
32	Operation	operator: 37 operands: 38
33	Literal
34	Operation	operator: 39 operand: 43
35	Literal
36	ExprTuple	43, 41
37	Literal
38	ExprTuple	41, 42
39	Literal
40	ExprTuple	43
41	Variable
42	Operation	operator: 44 operands: 45
43	Variable
44	Literal
45	ExprTuple	46, 47
46	Literal
47	Literal