End TwoDimensionalInduction.
Section DoubleInduction.
Variable R : N.t -> N.t -> Prop.
Hypothesis R_wd : Proper (N.eq==>N.eq==>iff) R.

Theorem double_induction :
(forall m, R 0 m) ->
(forall n, R (S n) 0) ->
(forall n m, R n m -> R (S n) (S m)) -> forall n m, R n m.