fact: Definition inverse_map_ens {A B : Type} (f : A -> B) (g : B -> A) (U : Ensemble A) (V : Ensemble B) : Prop := (forall a : A, In U a -> g (f a) = a) /\ (forall b : B, In V b -> f (g b) = b).
imports: Coq(ClassicalChoice Description Program.Subset) ZornsLemma(DecidableDec EnsemblesImplicit Families FunctionProperties Image InverseImage Powerset_facts Proj1SigInjective) Coq(RelationClasses)