Expression of type Equals

from the theory of proveit.linear_algebra.addition

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 Function, k, t, v, vk
from proveit.linear_algebra import VecSum
from proveit.logic import Equals
from proveit.numbers import Add, Exp, Interval, Neg, one, subtract, two, zero

# build up the expression from sub-expressions
sub_expr1 = [k]
sub_expr2 = Exp(two, t)
expr = Equals(VecSum(index_or_indices = sub_expr1, summand = vk, domain = Interval(zero, sub_expr2)), VecSum(index_or_indices = sub_expr1, summand = Function(v, [Add(k, one)]), domain = Interval(Neg(one), subtract(sub_expr2, 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(\sum_{k=0}^{2^{t}} v\left(k\right)\right) = \left(\sum_{k=-1}^{2^{t} - 1} v\left(k + 1\right)\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 operand: 8
4	Operation	operator: 6 operand: 9
5	ExprTuple	8
6	Literal
7	ExprTuple	9
8	Lambda	parameter: 30 body: 10
9	Lambda	parameter: 30 body: 11
10	Conditional	value: 12 condition: 13
11	Conditional	value: 14 condition: 15
12	Operation	operator: 18 operand: 30
13	Operation	operator: 20 operands: 17
14	Operation	operator: 18 operand: 23
15	Operation	operator: 20 operands: 21
16	ExprTuple	30
17	ExprTuple	30, 22
18	Variable
19	ExprTuple	23
20	Literal
21	ExprTuple	30, 24
22	Operation	operator: 27 operands: 25
23	Operation	operator: 32 operands: 26
24	Operation	operator: 27 operands: 28
25	ExprTuple	29, 34
26	ExprTuple	30, 42
27	Literal
28	ExprTuple	35, 31
29	Literal
30	Variable
31	Operation	operator: 32 operands: 33
32	Literal
33	ExprTuple	34, 35
34	Operation	operator: 36 operands: 37
35	Operation	operator: 38 operand: 42
36	Literal
37	ExprTuple	40, 41
38	Literal
39	ExprTuple	42
40	Literal
41	Variable
42	Literal