
theorem P0:
for L being right_zeroed non empty addLoopStr,
    S,T being Subset of L
st 0.L in T holds S c= S + T
proof
let L be right_zeroed non empty addLoopStr, S,T be Subset of L;
assume A: 0.L in T;
let x be object;
  assume B: x in S;
  then reconsider a = x as Element of L;
  a + 0.L in {c+b where c,b is Element of L : c in S & b in T} by A,B;
  hence x in S + T by RLVECT_1:def 4;
end;
