Definition image_rec (f:R -> R) (D:R -> Prop) (x:R) : Prop := D (f x).

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Theorem Rsepare :
forall x y:R,
x <> y ->
exists V : R -> Prop,
(exists W : R -> Prop,
neighbourhood V x /\
neighbourhood W y /\ ~ (exists y : R, intersection_domain V W y)).