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, 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 = ExprTuple(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())

\left(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]\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: 51 body: 3
2	ExprTuple	51
3	Operation	operator: 4 operand: 6
4	Literal
5	ExprTuple	6
6	Lambda	parameters: 7 body: 8
7	ExprTuple	61, 66, 63
8	Conditional	value: 9 condition: 10
9	Operation	operator: 11 operands: 12
10	Operation	operator: 13 operands: 14
11	Literal
12	ExprTuple	15, 16
13	Literal
14	ExprTuple	17, 18, 19, 20, 21
15	Operation	operator: 37 operand: 31
16	Operation	operator: 23 operands: 24
17	Operation	operator: 53 operands: 25
18	Operation	operator: 53 operands: 26
19	Operation	operator: 53 operands: 27
20	Operation	operator: 28 operands: 58
21	Operation	operator: 29 operands: 30
22	ExprTuple	31
23	Literal
24	ExprTuple	32, 33
25	ExprTuple	61, 34
26	ExprTuple	66, 34
27	ExprTuple	63, 34
28	Literal
29	Literal
30	ExprTuple	66, 63
31	Lambda	parameter: 56 body: 35
32	Operation	operator: 37 operand: 40
33	Operation	operator: 37 operand: 41
34	Literal
35	Conditional	value: 47 condition: 39
36	ExprTuple	40
37	Literal
38	ExprTuple	41
39	Operation	operator: 53 operands: 42
40	Lambda	parameter: 56 body: 43
41	Lambda	parameter: 56 body: 44
42	ExprTuple	56, 45
43	Conditional	value: 47 condition: 46
44	Conditional	value: 47 condition: 48
45	Operation	operator: 59 operands: 49
46	Operation	operator: 53 operands: 50
47	Operation	operator: 51 operand: 56
48	Operation	operator: 53 operands: 54
49	ExprTuple	61, 63
50	ExprTuple	56, 55
51	Variable
52	ExprTuple	56
53	Literal
54	ExprTuple	56, 57
55	Operation	operator: 59 operands: 58
56	Variable
57	Operation	operator: 59 operands: 60
58	ExprTuple	61, 66
59	Literal
60	ExprTuple	62, 63
61	Variable
62	Operation	operator: 64 operands: 65
63	Variable
64	Literal
65	ExprTuple	66, 67
66	Variable
67	Literal