
theorem
  for V being RealLinearSpace, M being Subset of V holds M c= conv(M)
proof
  let V be RealLinearSpace;
  let M be Subset of V;
  let v be object;
  assume
A1: v in M;
  for Y being set holds Y in Convex-Family M implies v in Y
  proof
    let Y be set;
    assume
A2: Y in Convex-Family M;
    then reconsider Y as Subset of V;
    M c= Y by A2,Def4;
    hence thesis by A1;
  end;
  hence thesis by SETFAM_1:def 1;
end;
