Arguments ZornsLemma {T}.
Section ZL_preorder.
Variable T:Type.
Variable R:relation T.
Hypothesis Rpreord: preorder R.
Hypothesis ub_of_chain: forall S:Ensemble T, chain R S ->
exists x:T, forall y:T, In S y -> R y x.
Definition premaximal (x:T) : Prop :=
forall y:T, R x y -> R y x.

Lemma ZornsLemmaForPreorders: exists x:T, premaximal x.
End ZL_preorder.