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 eqT_nzero_eqT_divP : forall (a b c : Term A n) (nZb : ~ zeroP (A:=A) A0 eqA (n:=n) b), eqT c (multTerm (A:=A) multA (n:=n) (divTerm c nZb) b) -> ~ zeroP (A:=A) A0 eqA (n:=n) a -> eqT a c -> divP a b.