Ordered instances on submodules #
instance
Submodule.toIsOrderedAddMonoid
{R : Type u_1}
{M : Type u_2}
[Semiring R]
[AddCommMonoid M]
[PartialOrder M]
[IsOrderedAddMonoid M]
[Module R M]
(S : Submodule R M)
:
A submodule of an ordered additive monoid is an ordered additive monoid.
instance
Submodule.toIsOrderedCancelAddMonoid
{R : Type u_1}
{M : Type u_2}
[Semiring R]
[AddCommMonoid M]
[PartialOrder M]
[IsOrderedCancelAddMonoid M]
[Module R M]
(S : Submodule R M)
:
A submodule of an ordered cancellative additive monoid is an ordered cancellative additive monoid.