(* Maximum *)
Definition CRmax {R : ConstructiveReals} (x y : CRcarrier R) : CRcarrier R
:= (x + y + CRabs _ (y - x)) * CR_of_Q _ (1#2).
Add Parametric Morphism {R : ConstructiveReals} : CRmax
with signature (CReq R) ==> (CReq R) ==> (CReq R)
as CRmax_morph.
#[global]
Instance CRmax_morphT
: forall {R : ConstructiveReals},
CMorphisms.Proper
(CMorphisms.respectful (CReq R) (CMorphisms.respectful (CReq R) (CReq R))) (@CRmax R).

Lemma CRmorph_min : forall {R1 R2 : ConstructiveReals}
(f : @ConstructiveRealsMorphism R1 R2)
(a b : CRcarrier R1),
CRmorph f (CRmin a b)
== CRmin (CRmorph f a) (CRmorph f b).