Inductive Or3 (A B C : Prop) : Set :=
  | First : A -> Or3 A B C
  | Second : B -> Or3 A B C
  | Third : C -> Or3 A B C.Inductive Or3 (A B C : Prop) : Set :=
  | First : A -> Or3 A B C
  | Second : B -> Or3 A B C
  | Third : C -> Or3 A B C.Inductive Or3 (A B C : Prop) : Set :=
  | First : A -> Or3 A B C
  | Second : B -> Or3 A B C
  | Third : C -> Or3 A B C.Inductive Or3 (A B C : Prop) : Set :=
  | First : A -> Or3 A B C
  | Second : B -> Or3 A B C
  | Third : C -> Or3 A B C.

Lemma Lt_eq_Gt : forall n m : nat, Or3 (n < m) (n = m) (n > m).