proposition: Theorem divTerm_ppcr : forall a b : Term A n, ~ zeroP (A:=A) A0 eqA (n:=n) a -> forall nZb : ~ zeroP (A:=A) A0 eqA (n:=n) b, eqTerm (A:=A) eqA (n:=n) (ppc a b) (multTerm (A:=A) multA (n:=n) (divTerm (ppc a b) nZb) b).
proof: Proof. Proof using plusA minusA invA cs. 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.
imports: Coq(Relation_Definitions List) Buchberger(CoefStructure moreCoefStructure OrderStructure) Buchberger(Monomials Term)