proposition: Lemma le_cardinal_preorder: preorder le_cardinal.
proof: Proof. constructor. red; intro. apply eq_cardinal_impl_le_cardinal. apply (equiv_refl eq_cardinal_equiv). red; intros. destruct H. inversion H0. exists (fun x:X => f0 (f x)). red; intros. apply H. apply H2. assumption. Qed.
imports: FunctionProperties Relation_Definitions Relation_Definitions_Implicit CSB EnsemblesSpec