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<>0.SF implies x*((1_SF)/x)=1_SF & ((1_SF)/x)*x=1_SF by Th9;
