theorem
  for S,A be Subset of RLS st A c= conv S holds conv S = conv(S\/A)
  proof
    let S,A be Subset of RLS such that
    A1: A c=conv S;
    thus conv S c=conv(S\/A) by Th3,XBOOLE_1:7;
    S c=conv S by Lm1;
    then S\/A c=conv S by A1,XBOOLE_1:8;
    hence thesis by CONVEX1:30;
  end;
