(* 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 Rdiv_le_1 a b: 0 < a -> a <= b -> 1 <= b / a.