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, V, i, j, k, v
from proveit.linear_algebra import ScalarMult, VecSum
from proveit.logic import Equals, InSet
from proveit.numbers import Add, Interval, one, subtract

# build up the expression from sub-expressions
expr = Conditional(Equals(VecSum(index_or_indices = [i], summand = v, domain = Interval(j, k)), ScalarMult(Add(subtract(k, j), one), v)), InSet(v, V))

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=j}^{k} v\right) = \left(\left(\left(k - j\right) + 1\right) \cdot v\right) \textrm{ if } v \in V\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: 22 operands: 5
3	Literal
4	ExprTuple	6, 7
5	ExprTuple	18, 8
6	Operation	operator: 9 operand: 13
7	Operation	operator: 11 operands: 12
8	Variable
9	Literal
10	ExprTuple	13
11	Literal
12	ExprTuple	14, 18
13	Lambda	parameter: 26 body: 16
14	Operation	operator: 24 operands: 17
15	ExprTuple	26
16	Conditional	value: 18 condition: 19
17	ExprTuple	20, 21
18	Variable
19	Operation	operator: 22 operands: 23
20	Operation	operator: 24 operands: 25
21	Literal
22	Literal
23	ExprTuple	26, 27
24	Literal
25	ExprTuple	33, 28
26	Variable
27	Operation	operator: 29 operands: 30
28	Operation	operator: 31 operand: 34
29	Literal
30	ExprTuple	34, 33
31	Literal
32	ExprTuple	34
33	Variable
34	Variable