
theorem Th31:
  for L being add-associative right_zeroed right_complementable
  distributive non empty doubleLoopStr, p, q being Polynomial of L st p*'q is
  non-zero holds p is non-zero & q is non-zero
proof
  let L be add-associative right_zeroed right_complementable distributive non
  empty doubleLoopStr, p, q being Polynomial of L;
  assume that
A1: p*'q is non-zero and
A2: p is non non-zero or q is non non-zero;
  len p = 0 or len q = 0 by A2,Th14;
  then len (p*'q) = 0 by Th30;
  hence thesis by A1,Th14;
end;
