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
  y<>0.SF implies x/y*y=x
proof
  assume
A1: y<>0.SF;
  thus x/y*y=x*(y"*y) by GROUP_1:def 3
    .=x*1_SF by A1,Th9
    .=x;
end;
