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))).