proposition: Lemma Cmult_z_z' : forall (z z' : C) (r a r' a' : R), z <> zeroC -> z' <> zeroC -> z = cons_pol r a -> z' = cons_pol r' a' -> Cmult z z' = cons_pol (r * r') (a + a').
proof: Proof. intros. apply forme_polaire_def; auto with geo. rewrite Cmult_module. rewrite (complexe_pol_module (z:=z) (r:=r) (a:=a)); auto with geo. rewrite (complexe_pol_module (z:=z') (r:=r') (a:=a')); auto with geo. rewrite Cmult_argument; auto with geo. rewrite (complexe_pol_argument (z:=z) (r:=r) (a:=a)); auto with geo. rewrite (complexe_pol_argument (z:=z') (r:=r') (a:=a')); auto with geo. Qed.