(* 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 posPartAbsMax : forall x : CReal,
CReal_max 0 x == (x + CReal_abs x) * (inject_Q (1#2)).