reserve A for non degenerated comRing;
reserve R for non degenerated domRing;
reserve n for non empty Ordinal;
reserve o,o1,o2 for object;
reserve X,Y for Subset of Funcs(n,[#]R);
reserve S,T for Subset of Polynom-Ring(n,R);
reserve F,G for FinSequence of the carrier of Polynom-Ring(n,R);
reserve x for Function of n,R;

theorem
    for X holds Ideal_X is Ideal of Polynom-Ring(n,R)
    proof
      let X;
A1:   Ideal_X is add-closed by Lm5;
      Ideal_X is right-ideal by Lm7;
      hence thesis by A1;
    end;
