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 VecAdd, VecSum
from proveit.logic import Equals
from proveit.numbers import Exp, Interval, 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)), VecAdd(VecSum(index_or_indices = sub_expr1, summand = vk, domain = Interval(zero, subtract(sub_expr2, one))), Function(v, [sub_expr2])))

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(\left(\sum_{k=0}^{2^{t} - 1} v\left(k\right)\right) + v\left(2^{t}\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: 12 operand: 8
4	Operation	operator: 6 operands: 7
5	ExprTuple	8
6	Literal
7	ExprTuple	9, 10
8	Lambda	parameter: 27 body: 11
9	Operation	operator: 12 operand: 16
10	Operation	operator: 23 operand: 35
11	Conditional	value: 20 condition: 15
12	Literal
13	ExprTuple	16
14	ExprTuple	35
15	Operation	operator: 25 operands: 17
16	Lambda	parameter: 27 body: 18
17	ExprTuple	27, 19
18	Conditional	value: 20 condition: 21
19	Operation	operator: 29 operands: 22
20	Operation	operator: 23 operand: 27
21	Operation	operator: 25 operands: 26
22	ExprTuple	31, 35
23	Variable
24	ExprTuple	27
25	Literal
26	ExprTuple	27, 28
27	Variable
28	Operation	operator: 29 operands: 30
29	Literal
30	ExprTuple	31, 32
31	Literal
32	Operation	operator: 33 operands: 34
33	Literal
34	ExprTuple	35, 36
35	Operation	operator: 37 operands: 38
36	Operation	operator: 39 operand: 43
37	Literal
38	ExprTuple	41, 42
39	Literal
40	ExprTuple	43
41	Literal
42	Variable
43	Literal