Definition CRmorph_compose {R1 R2 R3 : ConstructiveReals}
(f : @ConstructiveRealsMorphism R1 R2)
(g : @ConstructiveRealsMorphism R2 R3)
: @ConstructiveRealsMorphism R1 R3.

Lemma CRmorph_mult_pos_pos : forall {R1 R2 : ConstructiveReals}
(f : @ConstructiveRealsMorphism R1 R2)
(x y : CRcarrier R1),
CRlt R1 0 y
-> CRmorph f (CRmult R1 x y)
== CRmult R2 (CRmorph f x) (CRmorph f y).