reserve FS for non empty doubleLoopStr;
reserve F for Field;
reserve R for Abelian add-associative right_zeroed right_complementable non
  empty addLoopStr,
  x, y, z for Scalar of R;
reserve SF for Skew-Field,
  x, y, z for Scalar of SF;

theorem
  x*y = 0.SF implies x = 0.SF or y = 0.SF
proof
  now
    assume that
A1: x*y = 0.SF and
A2: x <> 0.SF;
    x*y = x*(0.SF) by A1;
    hence y = 0.SF by A2,Th8;
  end;
  hence thesis;
end;
