Expression of type Lambda

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, 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 = 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(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..

stored_expr.style_options()

no style options

# display the expression information
stored_expr.expr_info()

	core type	sub-expressions	expression
0	Lambda	parameters: 1 body: 2
1	ExprTuple	55, 60, 57
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, 14, 15
9	Operation	operator: 31 operand: 25
10	Operation	operator: 17 operands: 18
11	Operation	operator: 47 operands: 19
12	Operation	operator: 47 operands: 20
13	Operation	operator: 47 operands: 21
14	Operation	operator: 22 operands: 52
15	Operation	operator: 23 operands: 24
16	ExprTuple	25
17	Literal
18	ExprTuple	26, 27
19	ExprTuple	55, 28
20	ExprTuple	60, 28
21	ExprTuple	57, 28
22	Literal
23	Literal
24	ExprTuple	60, 57
25	Lambda	parameter: 50 body: 29
26	Operation	operator: 31 operand: 34
27	Operation	operator: 31 operand: 35
28	Literal
29	Conditional	value: 41 condition: 33
30	ExprTuple	34
31	Literal
32	ExprTuple	35
33	Operation	operator: 47 operands: 36
34	Lambda	parameter: 50 body: 37
35	Lambda	parameter: 50 body: 38
36	ExprTuple	50, 39
37	Conditional	value: 41 condition: 40
38	Conditional	value: 41 condition: 42
39	Operation	operator: 53 operands: 43
40	Operation	operator: 47 operands: 44
41	Operation	operator: 45 operand: 50
42	Operation	operator: 47 operands: 48
43	ExprTuple	55, 57
44	ExprTuple	50, 49
45	Variable
46	ExprTuple	50
47	Literal
48	ExprTuple	50, 51
49	Operation	operator: 53 operands: 52
50	Variable
51	Operation	operator: 53 operands: 54
52	ExprTuple	55, 60
53	Literal
54	ExprTuple	56, 57
55	Variable
56	Operation	operator: 58 operands: 59
57	Variable
58	Literal
59	ExprTuple	60, 61
60	Variable
61	Literal