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

Lemma continuity_P1 : forall (f:R -> R) (x:R), continuity_pt f x <-> (forall W:R -> Prop, neighbourhood W (f x) -> exists V : R -> Prop, neighbourhood V x /\ (forall y:R, V y -> W (f y))).