Definition interc (c : coef) :  K :=
fold_left (fun res v => res + ({m[v]}))%f c 0%f.
Notation "{c[ x ]}" := (interc x).

(* Specifications: *)
Lemma interc_nil : {c[nil]} = 0%f.
Definition c0 : coef := nil.
Lemma c0_c : {c[c0]} = 0%f.
Definition copp (c : coef) : coef := map term_opp c.
Lemma copp_c c : {c[copp c]} = (-{c[c]})%f.
Definition cscale (v : var) (c : coef) : coef :=
map (term_scale v) c.
Lemma cscale_c v c :
{c[cscale v c]} = ({k[v]} * {c[c]})%f.