theorem
  2 * h = 0_G iff -h = h
proof
  thus 2 * h = 0_G implies h = -h
  proof
    assume 2 * h = 0_G;
    then h + h = 0_G by Th26;
    hence thesis by Th11;
  end;
  assume h = -h;
  hence 2 * h = h + -h by Th26
    .= 0_G by Def5;
end;
