Expression of type Conditional ¶

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, a, b, c, i, vi
from proveit.linear_algebra import VecAdd, VecSum
from proveit.logic import And, Equals, InSet
from proveit.numbers import Integer, Interval, Less, LessEq, one, subtract

# build up the expression from sub-expressions
sub_expr1 = [i]
expr = 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, subtract(b, one))), VecSum(index_or_indices = sub_expr1, summand = vi, domain = Interval(b, c)))), And(InSet(a, Integer), InSet(b, Integer), InSet(c, Integer), Less(a, b), LessEq(b, c)))

# 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\{\left(\sum_{i=a}^{c} v\left(i\right)\right) = \left(\left(\sum_{i=a}^{b - 1} v\left(i\right)\right) + \left(\sum_{i=b}^{c} v\left(i\right)\right)\right) \textrm{ if } a \in \mathbb{Z} ,  b \in \mathbb{Z} ,  c \in \mathbb{Z} ,  a < b ,  b \leq c\right..

stored_expr.style_options()

# display the expression information
stored_expr.expr_info()

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

Expression of type Conditional¶

from the theory of proveit.linear_algebra.addition¶

Expression of type Conditional ¶

from the theory of proveit.linear_algebra.addition ¶