Global Instance valid_rnd_N : Valid_rnd Znearest.

Theorem Rcompare_floor_ceil_mid : forall x, Z2R (Zfloor x) <> x -> Rcompare (x - Z2R (Zfloor x)) (/ 2) = Rcompare (x - Z2R (Zfloor x)) (Z2R (Zceil x) - x).