proposition: Lemma le_cardinal_ens_Proper_l {X Y Z : Type} (U : Ensemble X) (V : Ensemble Y) (W : Ensemble Z) : eq_cardinal_ens U V -> le_cardinal_ens U W -> le_cardinal_ens V W.
proof: Proof. intros H0 H1. apply eq_cardinal_ens_sym in H0. apply eq_cardinal_ens_le in H0. eapply le_cardinal_ens_transitive; eauto. Qed.
imports: Coq(ClassicalChoice Description Lia PeanoNat Program.Subset) ZornsLemma(Cardinals CountableTypes CSB DecidableDec Families Finite_sets FiniteTypes FunctionProperties FunctionPropertiesEns InverseImage Powerset_facts Proj1SigInjective ReverseMath.AddSubtract) Coq(RelationClasses)