proposition: Theorem OlistSupEq : forall (a : A) (L : list A), Olist (a :: L) -> forall b : A, InEq b L -> ltA a b.
proof: Proof. intros a L; elim L; simpl in |- *; auto. intros H' b H'0; inversion H'0. intros a0 l H' H'0 b H'1; inversion_clear H'1. apply ltAeqAComp with (a := a) (b := a0); auto. apply OlistSup with (L := a0 :: l); simpl in |- *; auto. apply H'; auto. apply OlistSkip with (b := a0); auto. Qed.
imports: Coq(Arith) Coq(Lexicographic_Exponentiation)