proposition: Lemma finite_eq_dec: forall X:Type, FiniteT X -> forall x y:X, {x=y} + {x<>y}.
proof: Proof. intros. apply decidable_dec. induction H. destruct x. decide equality. destruct H0. case (IHFiniteT (g x) (g y)). left. rewrite <- H1. rewrite <- H1 with x. rewrite H2. reflexivity. right. contradict H2. rewrite H2. reflexivity. Qed.
imports: Ensembles EnsemblesImplicit Image ImageImplicit Finite_sets FunctionProperties DecidableDec ProofIrrelevance Description