Section Combinatorial.
Variables (iR : ringType) (f : aR -> rR).
Local Notation "p ^f" := (map_poly f p) : ring_scope.
Hypotheses (inj_f : injective f) (f_0 : f 0 = 0).

Lemma lead_coef_map_inj p : lead_coef p^f = f (lead_coef p).