Definition point_adherent (D:R -> Prop) (x:R) : Prop :=
  forall V:R -> Prop,
    neighbourhood V x ->  exists y : R, intersection_domain V D y.Definition adherence (D:R -> Prop) (x:R) : Prop := point_adherent D x.

Lemma complementary_P1 : forall D:R -> Prop, ~ (exists y : R, intersection_domain D (complementary D) y).