Expression of type ExprTuple

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 ExprTuple, i, m, n, x
from proveit.logic import Equals, InSet, NotEquals
from proveit.numbers import Add, Complex, Exp, Interval, Natural, Sum, frac, one, subtract, zero

# build up the expression from sub-expressions
expr = ExprTuple(InSet(x, Complex), InSet(n, Natural), NotEquals(x, one), InSet(m, Natural), Equals(Sum(index_or_indices = [i], summand = Exp(x, i), domain = Interval(zero, m)), frac(subtract(one, Exp(x, Add(m, one))), subtract(one, x))))

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(x \in \mathbb{C}, n \in \mathbb{N}, x \neq 1, m \in \mathbb{N}, \left(\sum_{i = 0}^{m} x^{i}\right) = \frac{1 - x^{m + 1}}{1 - x}\right)

stored_expr.style_options()

name	description	default	current value	related methods
wrap_positions	position(s) at which wrapping is to occur; 'n' is after the nth comma.	()	()	('with_wrapping_at',)
justification	if any wrap positions are set, justify to the 'left', 'center', or 'right'	left	left	('with_justification',)

# display the expression information
stored_expr.expr_info()

	core type	sub-expressions	expression
0	ExprTuple	1, 2, 3, 4, 5
1	Operation	operator: 34 operands: 6
2	Operation	operator: 34 operands: 7
3	Operation	operator: 8 operands: 9
4	Operation	operator: 34 operands: 10
5	Operation	operator: 11 operands: 12
6	ExprTuple	47, 13
7	ExprTuple	14, 15
8	Literal
9	ExprTuple	47, 52
10	ExprTuple	51, 15
11	Literal
12	ExprTuple	16, 17
13	Literal
14	Variable
15	Literal
16	Operation	operator: 18 operand: 22
17	Operation	operator: 20 operands: 21
18	Literal
19	ExprTuple	22
20	Literal
21	ExprTuple	23, 24
22	Lambda	parameter: 39 body: 26
23	Operation	operator: 49 operands: 27
24	Operation	operator: 49 operands: 28
25	ExprTuple	39
26	Conditional	value: 29 condition: 30
27	ExprTuple	52, 31
28	ExprTuple	52, 32
29	Operation	operator: 44 operands: 33
30	Operation	operator: 34 operands: 35
31	Operation	operator: 37 operand: 41
32	Operation	operator: 37 operand: 47
33	ExprTuple	47, 39
34	Literal
35	ExprTuple	39, 40
36	ExprTuple	41
37	Literal
38	ExprTuple	47
39	Variable
40	Operation	operator: 42 operands: 43
41	Operation	operator: 44 operands: 45
42	Literal
43	ExprTuple	46, 51
44	Literal
45	ExprTuple	47, 48
46	Literal
47	Variable
48	Operation	operator: 49 operands: 50
49	Literal
50	ExprTuple	51, 52
51	Variable
52	Literal