proposition: Lemma le5 : forall P : nat -> Prop, P 0 -> P one -> P two -> P three -> P four -> (forall n : nat, four < n -> P n) -> forall n : nat, P n.
proof: Proof. simple induction n; [ auto 2 with arith | simple induction n0; [ auto 2 with arith | simple induction n1; [ auto 2 with arith | simple induction n2; [ auto 2 with arith | simple induction n3; [ auto 2 with arith | intros; apply H4; unfold four in |- *; repeat apply lt_n_S; auto with arith ] ] ] ] ]. Qed.
imports: Arith Constants