Definition Pcond_simpl_gen :=
fcons_ok _ PFcons00_fcons_inv.
(* Specific case when the equality test of coefs is complete w.r.t. the field equality: non-zero coefs can be eliminated, and opposite can be simplified (if -1 <> 0) *)
Hypothesis ceqb_complete : forall c1 c2, [c1] == [c2] -> ceqb c1 c2 = true.

Theorem PFcons1_fcons_inv:
forall l a l1, PCond l (Fcons1 a l1) -> ~ a @ l == 0 /\ PCond l l1.