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 Th13:
  x<>0.SF implies x"<>0.SF
proof
  assume
A1: x<>0.SF;
  assume x"=0.SF;
  then x*x"=0.SF;
  then 1.SF=0.SF by A1,Th9;
  hence contradiction;
end;
