Expression of type Conditional

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 Conditional, a, b, i, va, vi
from proveit.linear_algebra import VecAdd, VecSum
from proveit.logic import And, Equals, InSet
from proveit.numbers import Add, Integer, Interval, Less, one

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

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=a}^{b} v\left(i\right)\right) = \left(v\left(a\right) + \left(\sum_{i=a + 1}^{b} v\left(i\right)\right)\right) \textrm{ if } a \in \mathbb{Z} ,  b \in \mathbb{Z} ,  a < b\right..

stored_expr.style_options()

name	description	default	current value	related methods
condition_delimiter	'comma' or 'and'	comma	comma	('with_comma_delimiter', 'with_conjunction_delimiter')

# display the expression information
stored_expr.expr_info()

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