Inductive ppcm (p q : Term A n) : Term A n -> Prop :=
    ppcm0 :
      forall s : Term A n,
      (forall r : Term A n, divP r p -> divP r q -> divP r s) ->
      divP s p -> divP s q -> ppcm p q s.Inductive ppcm (p q : Term A n) : Term A n -> Prop :=
    ppcm0 :
      forall s : Term A n,
      (forall r : Term A n, divP r p -> divP r q -> divP r s) ->
      divP s p -> divP s q -> ppcm p q s.

Theorem divP_ppcr : forall a b : Term A n, ~ zeroP (A:=A) A0 eqA (n:=n) a -> ~ zeroP (A:=A) A0 eqA (n:=n) b -> divP (ppc a b) b.