reserve G for Abelian add-associative right_complementable right_zeroed
  non empty addLoopStr;

theorem Th2:
  for G being AbGroup holds comp G is_an_inverseOp_wrt the addF of G
proof
  let G be AbGroup;
A1: 0.G is_a_unity_wrt the addF of G by Th1;
  now
    let x be Element of G;
    thus (the addF of G).(x,(comp G).x)= x+(-x) by VECTSP_1:def 13
      .= 0.G by RLVECT_1:5
      .= the_unity_wrt the addF of G by A1,BINOP_1:def 8;
    thus (the addF of G).((comp G).x,x)=((comp G).x)+x
      .= x+(-x) by VECTSP_1:def 13
      .= 0.G by RLVECT_1:5
      .= the_unity_wrt the addF of G by A1,BINOP_1:def 8;
  end;
  hence thesis;
end;
