proposition: Theorem InEqNList : forall (a : A) (L : list A), InEq a L -> ~ Olist (a :: L).
proof: Proof. intros a L; elim L; auto. intros H'; inversion H'; auto. intros a0 l H' H'0; inversion H'0; auto. red in |- *; intros H'1; inversion H'1; auto. absurd (eqA a a0); auto. red in |- *; intros H'1; case H'; auto. apply OlistSkip with (b := a0); auto. Qed.
imports: Coq(Arith) Coq(Lexicographic_Exponentiation)