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 Th11:
  x<>0.SF & y<>0.SF implies x"*y"=(y*x)"
proof
  assume
A1: x<>0.SF;
  assume
A2: y<>0.SF;
  x"*y"*(y*x) =x"*(y"*(y*x)) by GROUP_1:def 3
    .=x"*(y"*y*x) by GROUP_1:def 3
    .=x"*(1_SF*x) by A2,Th9
    .=x"*x
    .=1_SF by A1,Th9;
  hence thesis by Th10;
end;
