intros a b; case a; case b; simpl in |- *; auto.
intros a0 m a1 m0 H nZb; split; auto.
apply divA_is_multA with (1 := cs); auto.
apply ppcm_prop_r.
Qed.

(* Specifications: *)
Theorem ppc_nZ :
forall a b c : Term A n,
~ zeroP (A:=A) A0 eqA (n:=n) a ->
~ zeroP (A:=A) A0 eqA (n:=n) b -> ~ zeroP (A:=A) A0 eqA (n:=n) (ppc a b).