(* First degre that is used to guess if a vector is homegene *)

(* Specifications: *)
Lemma first_deg0 n : first_deg n 0 = 0%nat.
Lemma first_deg0i n v : first_deg n v = 0%nat -> hom n 0 v.
Lemma hom_first_deg n k x : x <> 0 -> hom n k x -> first_deg n x = k.
Definition lift (n: nat) (v: vect n) : (vect n.+1) :=  ((0: vect n), v).