Expression of type Lambda

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, 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 = 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(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..

stored_expr.style_options()

no style options

# display the expression information
stored_expr.expr_info()

	core type	sub-expressions	expression
0	Lambda	parameters: 34 body: 1
1	Conditional	value: 2 condition: 3
2	Operation	operator: 4 operands: 5
3	Operation	operator: 6 operands: 7
4	Literal
5	ExprTuple	8, 9
6	Literal
7	ExprTuple	10, 11
8	Operation	operator: 13 operand: 17
9	Operation	operator: 13 operand: 18
10	Operation	operator: 29 operands: 15
11	Operation	operator: 29 operands: 16
12	ExprTuple	17
13	Literal
14	ExprTuple	18
15	ExprTuple	45, 19
16	ExprTuple	44, 19
17	Lambda	parameter: 38 body: 20
18	Lambda	parameter: 38 body: 21
19	Literal
20	Conditional	value: 22 condition: 23
21	Conditional	value: 24 condition: 25
22	Operation	operator: 27 operand: 38
23	Operation	operator: 29 operands: 26
24	Operation	operator: 27 operand: 32
25	Operation	operator: 29 operands: 30
26	ExprTuple	38, 31
27	Variable
28	ExprTuple	32
29	Literal
30	ExprTuple	38, 33
31	Operation	operator: 36 operands: 34
32	Operation	operator: 42 operand: 38
33	Operation	operator: 36 operands: 37
34	ExprTuple	45, 44
35	ExprTuple	38
36	Literal
37	ExprTuple	39, 40
38	Variable
39	Operation	operator: 42 operand: 44
40	Operation	operator: 42 operand: 45
41	ExprTuple	44
42	Literal
43	ExprTuple	45
44	Variable
45	Variable