Definition czerop (c : coef) :=
match c with nil => true | _ => false end.

(* Specifications: *)
Lemma czerop_c c : if czerop c then {c[c]} = 0%f else True.
Lemma natc_id n : natc n n = Eq.
Lemma cadd_opp a: cadd a (copp a) = nil.
Lemma czerop_opp a : czerop (cadd a (copp a)) = true.