proposition: Theorem divTerm_on_plusM_minusM : forall a b : Term A n, ~ zeroP (A:=A) A0 eqA (n:=n) a -> forall nZb : ~ zeroP (A:=A) A0 eqA (n:=n) b, T2M a = mult_mon n (div_mon n (T2M a) (T2M b)) (T2M b) -> eqTerm (A:=A) eqA (n:=n) a (multTerm (A:=A) multA (n:=n) (divTerm a nZb) b).
proof: Proof. Proof using plusA minusA invA cs A1. intros a b; case a; case b; simpl in |- *; auto. split; auto. apply divA_is_multA with (1 := cs); auto. Qed.
imports: Coq(Relation_Definitions List) Buchberger(CoefStructure moreCoefStructure OrderStructure) Buchberger(Monomials Term)