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, c, i, vi
from proveit.linear_algebra import VecAdd, VecSum
from proveit.logic import And, Equals, InSet
from proveit.numbers import Add, Integer, Interval, Less, LessEq, one

# build up the expression from sub-expressions
sub_expr1 = [i]
expr = ExprTuple(Lambda([a, b, c], Conditional(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)))), And(InSet(a, Integer), InSet(b, Integer), InSet(c, Integer), LessEq(a, b), Less(b, 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(\left(a, b, c\right) \mapsto \left\{\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) \textrm{ if } a \in \mathbb{Z} ,  b \in \mathbb{Z} ,  c \in \mathbb{Z} ,  a \leq b ,  b < c\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: 2 body: 3
2	ExprTuple	56, 61, 58
3	Conditional	value: 4 condition: 5
4	Operation	operator: 6 operands: 7
5	Operation	operator: 8 operands: 9
6	Literal
7	ExprTuple	10, 11
8	Literal
9	ExprTuple	12, 13, 14, 15, 16
10	Operation	operator: 32 operand: 26
11	Operation	operator: 18 operands: 19
12	Operation	operator: 48 operands: 20
13	Operation	operator: 48 operands: 21
14	Operation	operator: 48 operands: 22
15	Operation	operator: 23 operands: 53
16	Operation	operator: 24 operands: 25
17	ExprTuple	26
18	Literal
19	ExprTuple	27, 28
20	ExprTuple	56, 29
21	ExprTuple	61, 29
22	ExprTuple	58, 29
23	Literal
24	Literal
25	ExprTuple	61, 58
26	Lambda	parameter: 51 body: 30
27	Operation	operator: 32 operand: 35
28	Operation	operator: 32 operand: 36
29	Literal
30	Conditional	value: 42 condition: 34
31	ExprTuple	35
32	Literal
33	ExprTuple	36
34	Operation	operator: 48 operands: 37
35	Lambda	parameter: 51 body: 38
36	Lambda	parameter: 51 body: 39
37	ExprTuple	51, 40
38	Conditional	value: 42 condition: 41
39	Conditional	value: 42 condition: 43
40	Operation	operator: 54 operands: 44
41	Operation	operator: 48 operands: 45
42	Operation	operator: 46 operand: 51
43	Operation	operator: 48 operands: 49
44	ExprTuple	56, 58
45	ExprTuple	51, 50
46	Variable
47	ExprTuple	51
48	Literal
49	ExprTuple	51, 52
50	Operation	operator: 54 operands: 53
51	Variable
52	Operation	operator: 54 operands: 55
53	ExprTuple	56, 61
54	Literal
55	ExprTuple	57, 58
56	Variable
57	Operation	operator: 59 operands: 60
58	Variable
59	Literal
60	ExprTuple	61, 62
61	Variable
62	Literal