(* The linear form is defined by its finger print on the base *)
Notation "#< l , x ># " := (contra _ l x) (format "#< l ,  x >#").

(* Specifications: *)
Lemma contraE n l (M : vect n.+1) :
#<l, M ># =
((- (1))%f.* #< snd l, fst M>#,  (fst l : K) .* fst M + #<snd l, snd M>#).