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, TRUE
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))), TRUE)

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_{i = 0}^{0} x^{i}\right) = \frac{1 - x^{0 + 1}}{1 - x}\right) = \top

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