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 ExprRange, Variable, i, x
from proveit.core_expr_types import Len
from proveit.logic import Equals
from proveit.numbers import Add, Exp, Interval, Sum, frac, one, subtract, two, zero

# build up the expression from sub-expressions
sub_expr1 = Variable("_a", latex_format = r"{_{-}a}")
expr = Equals(Len(operands = [Sum(index_or_indices = [i], summand = Exp(x, i), domain = Interval(zero, zero)), frac(subtract(one, Exp(x, Add(zero, one))), subtract(one, x))]), Len(operands = [ExprRange(sub_expr1, sub_expr1, one, two)]))

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(\sum_{i = 0}^{0} x^{i}, \frac{1 - x^{0 + 1}}{1 - x}\right)| = |\left(1, \ldots, 2\right)|

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