Expression of type ExprTuple

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, ExprTuple, Function, Lambda, 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 = ExprTuple(Lambda([a, b], 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(a, b\right) \mapsto \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..\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	parameters: 35 body: 2
2	Conditional	value: 3 condition: 4
3	Operation	operator: 5 operands: 6
4	Operation	operator: 7 operands: 8
5	Literal
6	ExprTuple	9, 10
7	Literal
8	ExprTuple	11, 12
9	Operation	operator: 14 operand: 18
10	Operation	operator: 14 operand: 19
11	Operation	operator: 30 operands: 16
12	Operation	operator: 30 operands: 17
13	ExprTuple	18
14	Literal
15	ExprTuple	19
16	ExprTuple	46, 20
17	ExprTuple	45, 20
18	Lambda	parameter: 39 body: 21
19	Lambda	parameter: 39 body: 22
20	Literal
21	Conditional	value: 23 condition: 24
22	Conditional	value: 25 condition: 26
23	Operation	operator: 28 operand: 39
24	Operation	operator: 30 operands: 27
25	Operation	operator: 28 operand: 33
26	Operation	operator: 30 operands: 31
27	ExprTuple	39, 32
28	Variable
29	ExprTuple	33
30	Literal
31	ExprTuple	39, 34
32	Operation	operator: 37 operands: 35
33	Operation	operator: 43 operand: 39
34	Operation	operator: 37 operands: 38
35	ExprTuple	46, 45
36	ExprTuple	39
37	Literal
38	ExprTuple	40, 41
39	Variable
40	Operation	operator: 43 operand: 45
41	Operation	operator: 43 operand: 46
42	ExprTuple	45
43	Literal
44	ExprTuple	46
45	Variable
46	Variable