(** Such inequality statements are frequent enough to warrant a special notation, [x <> y]: *)
Check (0 <> 1).
(* ===> Prop *)

(* Specifications: *)
Theorem zero_not_one' : 0 <> 1.
(** It takes a little practice to get used to working with negation in Coq.  Even though you can see perfectly well why a statement involving negation is true, it can be a little tricky at first to get things into the right configuration so that Coq can understand it!  Here are proofs of a few familiar facts to get you warmed up. *)
Theorem not_False :
~ False.