Expression of type ExprTuple

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, ExprTuple, Lambda, a, b, i, vb, vi
from proveit.linear_algebra import VecAdd, VecSum
from proveit.logic import And, Equals, InSet
from proveit.numbers import Integer, Interval, Less, one, subtract

# build up the expression from sub-expressions
sub_expr1 = [i]
expr = ExprTuple(Lambda([a, b], Conditional(Equals(VecSum(index_or_indices = sub_expr1, summand = vi, domain = Interval(a, b)), VecAdd(VecSum(index_or_indices = sub_expr1, summand = vi, domain = Interval(a, subtract(b, one))), vb)), 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(a, b\right) \mapsto \left\{\left(\sum_{i=a}^{b} v\left(i\right)\right) = \left(\left(\sum_{i=a}^{b - 1} v\left(i\right)\right) + v\left(b\right)\right) \textrm{ if } a \in \mathbb{Z} ,  b \in \mathbb{Z} ,  a < b\right..\right)

stored_expr.style_options()

no style options

# display the expression information
stored_expr.expr_info()

	core type	sub-expressions	expression
0	ExprTuple	1
1	Lambda	parameters: 35 body: 2
2	Conditional	value: 3 condition: 4
3	Operation	operator: 5 operands: 6
4	Operation	operator: 7 operands: 8
5	Literal
6	ExprTuple	9, 10
7	Literal
8	ExprTuple	11, 12, 13
9	Operation	operator: 25 operand: 20
10	Operation	operator: 15 operands: 16
11	Operation	operator: 38 operands: 17
12	Operation	operator: 38 operands: 18
13	Operation	operator: 19 operands: 35
14	ExprTuple	20
15	Literal
16	ExprTuple	21, 22
17	ExprTuple	44, 23
18	ExprTuple	48, 23
19	Literal
20	Lambda	parameter: 40 body: 24
21	Operation	operator: 25 operand: 29
22	Operation	operator: 36 operand: 48
23	Literal
24	Conditional	value: 33 condition: 28
25	Literal
26	ExprTuple	29
27	ExprTuple	48
28	Operation	operator: 38 operands: 30
29	Lambda	parameter: 40 body: 31
30	ExprTuple	40, 32
31	Conditional	value: 33 condition: 34
32	Operation	operator: 42 operands: 35
33	Operation	operator: 36 operand: 40
34	Operation	operator: 38 operands: 39
35	ExprTuple	44, 48
36	Variable
37	ExprTuple	40
38	Literal
39	ExprTuple	40, 41
40	Variable
41	Operation	operator: 42 operands: 43
42	Literal
43	ExprTuple	44, 45
44	Variable
45	Operation	operator: 46 operands: 47
46	Literal
47	ExprTuple	48, 49
48	Variable
49	Operation	operator: 50 operand: 52
50	Literal
51	ExprTuple	52
52	Literal