(* R misc *)

Ltac deep_Rle_trans h :=
  match type of h with
  | ?n <= ?u =>
    match goal with
    | |- (?l <= _)%R =>
      let q := subst_tac n u l
      in apply Rle_trans with q
    | _ => assert (False)
    end
  end.

Lemma Rne_nlt_lt x y: x <> y -> ~ x < y -> y < x.