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, Function, a, b, f, fx, x
from proveit.logic import And, Equals, InSet
from proveit.numbers import Integer, Interval, Neg, Sum

# build up the expression from sub-expressions
sub_expr1 = [x]
expr = Conditional(Equals(Sum(index_or_indices = sub_expr1, summand = fx, domain = Interval(a, b)), Sum(index_or_indices = sub_expr1, summand = Function(f, [Neg(x)]), domain = Interval(Neg(b), Neg(a)))), And(InSet(a, Integer), InSet(b, Integer)))

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\{\left(\sum_{x = a}^{b} f\left(x\right)\right) = \left(\sum_{x = -b}^{-a} f\left(-x\right)\right) \textrm{ if } a \in \mathbb{Z} ,  b \in \mathbb{Z}\right..

stored_expr.style_options()

name	description	default	current value	related methods
condition_delimiter	'comma' or 'and'	comma	comma	('with_comma_delimiter', 'with_conjunction_delimiter')

# display the expression information
stored_expr.expr_info()

	core type	sub-expressions	expression
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
7	Operation	operator: 12 operand: 16
8	Operation	operator: 12 operand: 17
9	Operation	operator: 28 operands: 14
10	Operation	operator: 28 operands: 15
11	ExprTuple	16
12	Literal
13	ExprTuple	17
14	ExprTuple	44, 18
15	ExprTuple	43, 18
16	Lambda	parameter: 37 body: 19
17	Lambda	parameter: 37 body: 20
18	Literal
19	Conditional	value: 21 condition: 22
20	Conditional	value: 23 condition: 24
21	Operation	operator: 26 operand: 37
22	Operation	operator: 28 operands: 25
23	Operation	operator: 26 operand: 31
24	Operation	operator: 28 operands: 29
25	ExprTuple	37, 30
26	Variable
27	ExprTuple	31
28	Literal
29	ExprTuple	37, 32
30	Operation	operator: 35 operands: 33
31	Operation	operator: 41 operand: 37
32	Operation	operator: 35 operands: 36
33	ExprTuple	44, 43
34	ExprTuple	37
35	Literal
36	ExprTuple	38, 39
37	Variable
38	Operation	operator: 41 operand: 43
39	Operation	operator: 41 operand: 44
40	ExprTuple	43
41	Literal
42	ExprTuple	44
43	Variable
44	Variable