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 Th1:
    for L being right_zeroed add-associative right_complementable
    well-unital distributive non trivial doubleLoopStr, n being Ordinal holds
    Support 0_(n,L) = {}
    proof
      let L be right_zeroed add-associative right_complementable
      well-unital distributive non trivial doubleLoopStr, n be Ordinal;
      assume Support 0_(n,L) <> {}; then
      consider o such that
A2:   o in Support 0_(n,L) by XBOOLE_0:def 1;
      reconsider b = o as bag of n by A2;
      b in dom 0_(n,L) & (0_(n,L)).b <> 0.L by A2,POLYNOM1:def 3;
      hence contradiction by POLYNOM1:22;
    end;
