Global Instance valid_rnd_N : Valid_rnd Znearest.

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