theorem Th22:
  add_inverse(G) is_an_inverseOp_wrt the addF of G
proof
  let h be Element of G;
  thus (the addF of G).(h,add_inverse(G).h) = h + -h by Def6
    .= 0_G by Def5
    .= the_unity_wrt the addF of G by Th21;
  thus (the addF of G).(add_inverse(G).h,h) = -h + h by Def6
    .= 0_G by Def5
    .= the_unity_wrt the addF of G by Th21;
end;
