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 V,W be Algebraic_Set of n,R holds V = W iff Ideal_V = Ideal_W
    proof
      let V,W be Algebraic_Set of n,R;
      Ideal_V = Ideal_W implies V = W
      proof
        assume Ideal_V = Ideal_W; then
        V = Zero_(Ideal_W) by Th36 .= W by Th36;
        hence thesis;
      end;
      hence thesis;
    end;
