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 Th10:
  y*x = 1_SF implies x = y" & y = x"
proof
A1: y*x = 1_SF implies y = x"
  proof
    assume
A2: y*x = 1_SF;
    then x<>0.SF;
    hence thesis by A2,Def2;
  end;
  y*x = 1_SF implies x = y"
  proof
    assume y*x = 1_SF;
    then y<>0.SF & x*y = 1_SF by Th7;
    hence thesis by Def2;
  end;
  hence thesis by A1;
end;
