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 Th14:
  x<>0.SF implies x""=x
proof
  assume
A1: x<>0.SF;
  then
A2: x"<>0.SF by Th13;
  x""=x""*1_SF
    .=x"" * (x" * x) by A1,Th9
    .=x""*x"*x by GROUP_1:def 3;
  then x""=1_SF*x by A2,Th9;
  hence thesis;
end;
