(* 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_plus : forall (x y z : CReal), x + CReal_max y z == CReal_max (x + y) (x + z).