Definition CompOpp (r:comparison) :=
  match r with
    | Eq => Eq
    | Lt => Gt
    | Gt => Lt
  end.

(* Specifications: *)
Lemma CompOpp_involutive c : CompOpp (CompOpp c) = c.
Lemma CompOpp_inj c c' : CompOpp c = CompOpp c' -> c = c'.
Lemma CompOpp_iff : forall c c', CompOpp c = c' <-> c = CompOpp c'.