(** Elimination principlies for < and <= for relations *)
Variable R : relation N.t.
Hypothesis R_wd : Proper (N.eq==>N.eq==>iff) R.

(* Specifications: *)
Theorem le_ind_rel :
(forall m, R 0 m) ->
(forall n m, n <= m -> R n m -> R (S n) (S m)) ->
forall n m, n <= m -> R n m.
Theorem lt_ind_rel :
(forall m, R 0 (S m)) ->
(forall n m, n < m -> R n m -> R (S n) (S m)) ->
forall n m, n < m -> R n m.