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 *)

Theorem pred_lt_mono : forall n m, n ~= 0 -> (n < m <-> P n < P m).