Require Export Reals Qreals.
Open Scope R_scope.
Local Lemma archimed_1
: forall r : R, r < IZR (up r).
Local Notation " ' x " := (Zpos x) (at level 20, no associativity) : Z_scope.

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