Local Notation " ' x " := (Zpos x) (at level 20, no associativity) : Z_scope.

(* Specifications: *)
Lemma rational_interpolation: forall (x y:R) (n:positive), x<y -> IZR (' n) > 1/(y-x) -> exists m:Z, x < Q2R (m # n) < y.
Lemma rationals_dense_in_reals: forall x y:R, x<y -> exists q:Q, x < Q2R q < y.