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

# build up the expression from sub-expressions
sub_expr1 = [i]
expr = ExprTuple(Lambda(v, Forall(instance_param_or_params = [a, b], instance_expr = 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)), domain = Integer, condition = 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(v \mapsto \left[\forall_{a, b \in \mathbb{Z}~|~a < b}~\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)\right)\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	parameter: 41 body: 3
2	ExprTuple	41
3	Operation	operator: 4 operand: 6
4	Literal
5	ExprTuple	6
6	Lambda	parameters: 40 body: 7
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
14	Operation	operator: 30 operand: 25
15	Operation	operator: 20 operands: 21
16	Operation	operator: 43 operands: 22
17	Operation	operator: 43 operands: 23
18	Operation	operator: 24 operands: 40
19	ExprTuple	25
20	Literal
21	ExprTuple	26, 27
22	ExprTuple	49, 28
23	ExprTuple	53, 28
24	Literal
25	Lambda	parameter: 45 body: 29
26	Operation	operator: 30 operand: 34
27	Operation	operator: 41 operand: 53
28	Literal
29	Conditional	value: 38 condition: 33
30	Literal
31	ExprTuple	34
32	ExprTuple	53
33	Operation	operator: 43 operands: 35
34	Lambda	parameter: 45 body: 36
35	ExprTuple	45, 37
36	Conditional	value: 38 condition: 39
37	Operation	operator: 47 operands: 40
38	Operation	operator: 41 operand: 45
39	Operation	operator: 43 operands: 44
40	ExprTuple	49, 53
41	Variable
42	ExprTuple	45
43	Literal
44	ExprTuple	45, 46
45	Variable
46	Operation	operator: 47 operands: 48
47	Literal
48	ExprTuple	49, 50
49	Variable
50	Operation	operator: 51 operands: 52
51	Literal
52	ExprTuple	53, 54
53	Variable
54	Operation	operator: 55 operand: 57
55	Literal
56	ExprTuple	57
57	Literal