fact: Definition lt_cardinal_ens {A B : Type} (U : Ensemble A) (V : Ensemble B) : Prop := le_cardinal_ens U V /\ ~ eq_cardinal_ens V U.
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)