reserve L for non empty doubleLoopStr;
reserve a,b,c,x,y,z for Element of L;

theorem Th3:
  for G being Abelian left_add-cancelable add-right-invertible
  non empty addLoopStr, a being Element of G holds -(-a) = a
proof
  let G be Abelian left_add-cancelable add-right-invertible non empty
  addLoopStr, a be Element of G;
  -a+a = 0.G by Def1;
  hence thesis by Def1;
end;
