theorem Th22:
  inverse_op(G) is_an_inverseOp_wrt the multF of G
proof
  let h be Element of G;
  thus (the multF of G).(h,inverse_op(G).h) = h * h" by Def6
    .= 1_G by Def5
    .= the_unity_wrt the multF of G by Th21;
  thus (the multF of G).(inverse_op(G).h,h) = h" * h by Def6
    .= 1_G by Def5
    .= the_unity_wrt the multF of G by Th21;
end;
