(** ** Polynomial defined as a sum of a range of variables  - [psum start len] is the polynomial with [start+len] variables and consisting in the sum of the variables [start] to [start+len-1]. *)
Definition psum (start len : nat) : pol :=
pplus (pcst (start+len) 0) (pplusl (map (pproj (start+len)) (seq start len))).

Lemma parity_psum start len :
parity (psum start len) = start + len.