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
  for F being add-associative right_zeroed right_complementable
  distributive non degenerated non empty doubleLoopStr for x, y being Element
  of F holds x*y = 1.F implies x<>0.F & y<>0.F;
