Expression of type Conditional

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 Conditional, m, x
from proveit.logic import And, Equals, InSet
from proveit.numbers import Abs, Complex, Exp, Interval, Less, Sum, frac, infinity, one, subtract, zero

# build up the expression from sub-expressions
expr = Conditional(Equals(Sum(index_or_indices = [m], summand = Exp(x, m), domain = Interval(zero, infinity)), frac(one, subtract(one, x))), And(InSet(x, Complex), Less(Abs(x), one)))

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(\sum_{m = 0}^{\infty} x^{m}\right) = \frac{1}{1 - x} \textrm{ if } x \in \mathbb{C} ,  \left|x\right| < 1\right..

stored_expr.style_options()

name	description	default	current value	related methods
condition_delimiter	'comma' or 'and'	comma	comma	('with_comma_delimiter', 'with_conjunction_delimiter')

# display the expression information
stored_expr.expr_info()

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