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 Th14:
    Zero_(1_(n,R)) = {}Funcs(n,[#]R)
    proof
      assume Zero_(1_(n,R)) <> {}Funcs(n,[#]R); then
      consider o such that
A2:   o in Zero_(1_(n,R)) by XBOOLE_0:def 1;
      consider x be Function of n,R such that
A3:   o=x & eval(1_(n,R),x) = 0.R by A2;
      thus contradiction by A3,POLYNOM2:21;
    end;
