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

theorem Th1:
  0.G is_a_unity_wrt the addF of G
proof
  now
    let x be Element of G;
    thus (the addF of G).(0.G,x)=0.G + x .= x by RLVECT_1:4;
    thus (the addF of G).(x,0.G)= x + 0.G .= x by RLVECT_1:4;
  end;
  hence thesis by BINOP_1:3;
end;
