(* Min and max *)

Definition CReal_min (x y : CReal) : CReal
  := (x + y - CReal_abs (y - x)) * inject_Q (1#2).Definition CReal_max (x y : CReal) : CReal
  := (x + y + CReal_abs (y - x)) * inject_Q (1#2).Add Parametric Morphism : CReal_min
    with signature CRealEq ==> CRealEq ==> CRealEq
      as CReal_min_morph.Add Parametric Morphism : CReal_max
    with signature CRealEq ==> CRealEq ==> CRealEq
      as CReal_max_morph.

Lemma CReal_max_contract : forall x y a : CReal, CReal_abs (CReal_max x a - CReal_max y a) <= CReal_abs (x - y).