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, 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 = Lambda([a, b], 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(a, b\right) \mapsto \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()

no style options

# display the expression information
stored_expr.expr_info()

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