Expression of type Lambda

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, Lambda, 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 = Lambda(x, 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())

x \mapsto \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()

no style options

# display the expression information
stored_expr.expr_info()

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