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 Lambda, a, b, c, i, v, vi
from proveit.linear_algebra import VecAdd, VecSum
from proveit.logic import Equals, Forall
from proveit.numbers import Add, Integer, Interval, Less, LessEq, one

# build up the expression from sub-expressions
sub_expr1 = [i]
expr = Lambda(v, Forall(instance_param_or_params = [a, b, c], instance_expr = 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)))), domain = Integer, conditions = [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())

v \mapsto \left[\forall_{a, b, c \in \mathbb{Z}~|~a \leq b, b < c}~\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)\right)\right]

stored_expr.style_options()

no style options

# display the expression information
stored_expr.expr_info()

	core type	sub-expressions	expression
0	Lambda	parameter: 50 body: 2
1	ExprTuple	50
2	Operation	operator: 3 operand: 5
3	Literal
4	ExprTuple	5
5	Lambda	parameters: 6 body: 7
6	ExprTuple	60, 65, 62
7	Conditional	value: 8 condition: 9
8	Operation	operator: 10 operands: 11
9	Operation	operator: 12 operands: 13
10	Literal
11	ExprTuple	14, 15
12	Literal
13	ExprTuple	16, 17, 18, 19, 20
14	Operation	operator: 36 operand: 30
15	Operation	operator: 22 operands: 23
16	Operation	operator: 52 operands: 24
17	Operation	operator: 52 operands: 25
18	Operation	operator: 52 operands: 26
19	Operation	operator: 27 operands: 57
20	Operation	operator: 28 operands: 29
21	ExprTuple	30
22	Literal
23	ExprTuple	31, 32
24	ExprTuple	60, 33
25	ExprTuple	65, 33
26	ExprTuple	62, 33
27	Literal
28	Literal
29	ExprTuple	65, 62
30	Lambda	parameter: 55 body: 34
31	Operation	operator: 36 operand: 39
32	Operation	operator: 36 operand: 40
33	Literal
34	Conditional	value: 46 condition: 38
35	ExprTuple	39
36	Literal
37	ExprTuple	40
38	Operation	operator: 52 operands: 41
39	Lambda	parameter: 55 body: 42
40	Lambda	parameter: 55 body: 43
41	ExprTuple	55, 44
42	Conditional	value: 46 condition: 45
43	Conditional	value: 46 condition: 47
44	Operation	operator: 58 operands: 48
45	Operation	operator: 52 operands: 49
46	Operation	operator: 50 operand: 55
47	Operation	operator: 52 operands: 53
48	ExprTuple	60, 62
49	ExprTuple	55, 54
50	Variable
51	ExprTuple	55
52	Literal
53	ExprTuple	55, 56
54	Operation	operator: 58 operands: 57
55	Variable
56	Operation	operator: 58 operands: 59
57	ExprTuple	60, 65
58	Literal
59	ExprTuple	61, 62
60	Variable
61	Operation	operator: 63 operands: 64
62	Variable
63	Literal
64	ExprTuple	65, 66
65	Variable
66	Literal