Require Import
        HoTT.Classes.interfaces.abstract_algebra
        HoTT.Classes.interfaces.orders
        HoTT.Classes.interfaces.naturals
        HoTT.Classes.implementations.peano_naturals.
[Loading ML file number_string_notation_plugin.cmxs (using legacy method) ... done]

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.