Section RelElim.
Variable R : relation N.t.
Hypothesis R_wd : Proper (N.eq==>N.eq==>iff) R.
End RelElim.
(** Predecessor and order *)
(* Converse is false for n == m == 0 *)
(* Converse is false for n == m == 0 *)
(* Converse is false for n == 1, m == 0 *)
(* Converse is false for n == m == 0 *)

Theorem lt_pred_lt_succ : forall n m, P n < m -> n < S m.