Expression of type Conditional ¶

from the theory of proveit.numbers.summation ¶

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, fx, x
from proveit.logic import And, Equals, InSet
from proveit.numbers import Add, Integer, Interval, Less, LessEq, Sum, one, subtract

# build up the expression from sub-expressions
sub_expr1 = [x]
expr = Conditional(Equals(Sum(index_or_indices = sub_expr1, summand = fx, domain = Interval(a, c)), Add(Sum(index_or_indices = sub_expr1, summand = fx, domain = Interval(a, subtract(b, one))), Sum(index_or_indices = sub_expr1, summand = fx, 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_{x = a}^{c} f\left(x\right)\right) = \left(\left(\sum_{x = a}^{b - 1} f\left(x\right)\right) + \left(\sum_{x = b}^{c} f\left(x\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: 28 operand: 22
8	Operation	operator: 55 operands: 15
9	Operation	operator: 44 operands: 16
10	Operation	operator: 44 operands: 17
11	Operation	operator: 44 operands: 18
12	Operation	operator: 19 operands: 20
13	Operation	operator: 21 operands: 51
14	ExprTuple	22
15	ExprTuple	23, 24
16	ExprTuple	52, 25
17	ExprTuple	57, 25
18	ExprTuple	54, 25
19	Literal
20	ExprTuple	52, 57
21	Literal
22	Lambda	parameter: 47 body: 26
23	Operation	operator: 28 operand: 31
24	Operation	operator: 28 operand: 32
25	Literal
26	Conditional	value: 38 condition: 30
27	ExprTuple	31
28	Literal
29	ExprTuple	32
30	Operation	operator: 44 operands: 33
31	Lambda	parameter: 47 body: 34
32	Lambda	parameter: 47 body: 35
33	ExprTuple	47, 36
34	Conditional	value: 38 condition: 37
35	Conditional	value: 38 condition: 39
36	Operation	operator: 50 operands: 40
37	Operation	operator: 44 operands: 41
38	Operation	operator: 42 operand: 47
39	Operation	operator: 44 operands: 45
40	ExprTuple	52, 54
41	ExprTuple	47, 46
42	Variable
43	ExprTuple	47
44	Literal
45	ExprTuple	47, 48
46	Operation	operator: 50 operands: 49
47	Variable
48	Operation	operator: 50 operands: 51
49	ExprTuple	52, 53
50	Literal
51	ExprTuple	57, 54
52	Variable
53	Operation	operator: 55 operands: 56
54	Variable
55	Literal
56	ExprTuple	57, 58
57	Variable
58	Operation	operator: 59 operand: 61
59	Literal
60	ExprTuple	61
61	Literal

Expression of type Conditional¶

from the theory of proveit.numbers.summation¶

Expression of type Conditional ¶

from the theory of proveit.numbers.summation ¶