proposition: Lemma induced_function_unique: forall fbar:quotient R->B, (forall x:A, fbar (quotient_projection R x) = f x) -> (forall xbar:quotient R, fbar xbar = induced_function xbar).
proof: Proof. intros. destruct (quotient_projection_surjective xbar). rewrite <- H0. rewrite H. rewrite induced_function_correct. reflexivity. Qed.
imports: Ensembles EnsemblesImplicit Image ImageImplicit Relation_Definitions Relation_Definitions_Implicit Description ProofIrrelevance EnsemblesSpec