Definition eq_Dom (D1 D2:R -> Prop) : Prop :=
  included D1 D2 /\ included D2 D1.Infix "=_D" := eq_Dom (at level 70, no associativity).

Lemma neighbourhood_P1 : forall (D1 D2:R -> Prop) (x:R), included D1 D2 -> neighbourhood D1 x -> neighbourhood D2 x.