(** Principle of double induction *)

(* Specifications: *)
Theorem nat_double_ind :
forall R:nat -> nat -> Prop,
(forall n:nat, R 0 n) ->
(forall n:nat, R (S n) 0) ->
(forall n m:nat, R n m -> R (S n) (S m)) -> forall n m:nat, R n m.