How to define set in coq without defining set as a list of elements

Question

I am trying to define (1,2,3) as a set of elements in coq. I can define it using list as (1 :: (2 :: (3 :: nil))). Is there any way to define set in coq without using list.

Answer 1

There are many encodings of sets in Coq (lists, function, trees, ...) which can be finite or not. You should have a look at Coq's standard library. For example the 'simplest' set definition I know is this one