(* OUT-OF-SCOPE *)

Inductive next_nat : nat -> nat -> Prop :=
  | nn : forall n:nat, next_nat n (S n).(* OUT-OF-SCOPE *)

Inductive next_nat : nat -> nat -> Prop :=
  | nn : forall n:nat, next_nat n (S n).Inductive next_even : nat -> nat -> Prop :=
  | ne_1 : forall n, ev (S n) -> next_even n (S n)
  | ne_2 : forall n, ev (S (S n)) -> next_even n (S (S n)).Inductive next_even : nat -> nat -> Prop :=
  | ne_1 : forall n, ev (S n) -> next_even n (S n)
  | ne_2 : forall n, ev (S (S n)) -> next_even n (S (S n)).Inductive next_even : nat -> nat -> Prop :=
  | ne_1 : forall n, ev (S n) -> next_even n (S n)
  | ne_2 : forall n, ev (S (S n)) -> next_even n (S (S n)).

Theorem lt_S : forall n m, n < m -> n < S m.