Require Import HoTT.Classes.interfaces.abstract_algebra HoTT.Classes.interfaces.orders HoTT.Classes.interfaces.naturals HoTT.Classes.implementations.peano_naturals.
Section round_up.
Class RoundUpStrict A `{IsSemiCRing A} `{StrictSemiRingOrder A} := round_up_strict : forall a : A, {n : nat & a < naturals_to_semiring nat A n}.
Global Arguments round_up_strict A {_ _ _ _ _ _ _ _ _ _ _ _} _.
End round_up.