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 a, b, c, i, vi
from proveit.linear_algebra import VecAdd, VecSum
from proveit.logic import Equals
from proveit.numbers import Add, Interval, one

# build up the expression from sub-expressions
sub_expr1 = [i]
expr = Equals(VecSum(index_or_indices = sub_expr1, summand = vi, domain = Interval(a, c)), VecAdd(VecSum(index_or_indices = sub_expr1, summand = vi, domain = Interval(a, b)), VecSum(index_or_indices = sub_expr1, summand = vi, domain = Interval(Add(b, one), c))))

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