Inductive Integers : Ensemble nat :=
    Integers_defn : forall x:nat, In nat Integers x.Inductive Integers : Ensemble nat :=
    Integers_defn : forall x:nat, In nat Integers x.

(* Specifications: *)
Lemma le_reflexive : Reflexive nat le.
Lemma le_antisym : Antisymmetric nat le.
Lemma le_trans : Transitive nat le.
Lemma le_Order : Order nat le.
Lemma triv_nat : forall n:nat, In nat Integers n.