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, LessEq, Sum, one

# 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, b)), Sum(index_or_indices = sub_expr1, summand = fx, domain = Interval(Add(b, one), c)))), And(InSet(a, Integer), InSet(b, Integer), InSet(c, Integer), And(LessEq(a, b), LessEq(b, c)).with_total_ordering_style()))

# 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} f\left(x\right)\right) + \left(\sum_{x = b + 1}^{c} f\left(x\right)\right)\right) \textrm{ if } a \in \mathbb{Z} ,  b \in \mathbb{Z} ,  c \in \mathbb{Z} ,  a \leq 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: 17 operands: 5
3	Literal
4	ExprTuple	6, 7
5	ExprTuple	8, 9, 10, 11
6	Operation	operator: 27 operand: 19
7	Operation	operator: 56 operands: 13
8	Operation	operator: 45 operands: 14
9	Operation	operator: 45 operands: 15
10	Operation	operator: 45 operands: 16
11	Operation	operator: 17 operands: 18
12	ExprTuple	19
13	ExprTuple	20, 21
14	ExprTuple	53, 22
15	ExprTuple	58, 22
16	ExprTuple	55, 22
17	Literal
18	ExprTuple	23, 24
19	Lambda	parameter: 48 body: 25
20	Operation	operator: 27 operand: 32
21	Operation	operator: 27 operand: 33
22	Literal
23	Operation	operator: 29 operands: 50
24	Operation	operator: 29 operands: 30
25	Conditional	value: 39 condition: 31
26	ExprTuple	32
27	Literal
28	ExprTuple	33
29	Literal
30	ExprTuple	58, 55
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, 58
51	Literal
52	ExprTuple	54, 55
53	Variable
54	Operation	operator: 56 operands: 57
55	Variable
56	Literal
57	ExprTuple	58, 59
58	Variable
59	Literal

Expression of type Conditional¶

from the theory of proveit.numbers.summation¶

Expression of type Conditional ¶

from the theory of proveit.numbers.summation ¶