
theorem
for L being right_unital non empty multLoopStr,
    S,T being Subset of L
st 1.L in T holds S c= S * T
proof
let L be right_unital non empty multLoopStr, S,T be Subset of L;
assume A: 1.L in T;
now let x be object;
  assume B: x in S;
  then reconsider a = x as Element of L;
  a * 1.L in
    {s1 * s2 where s1,s2 is Element of L : s1 in S & s2 in T} by A,B;
  hence x in S * T;
  end;
hence thesis;
end;
