Section HornerMorph.
Variable u : rR.
Hypothesis cfu : commr_rmorph f u.
Canonical horner_additive := Additive horner_is_lrmorphism.
Canonical horner_rmorphism := RMorphism horner_is_lrmorphism.
Canonical horner_linear := AddLinear horner_is_lrmorphism.
Canonical horner_lrmorphism := [lrmorphism of horner_morph cfu].
End HornerMorph.

Lemma deriv_map p : p^f^`() = (p^`())^f.