
theorem Th9:
  for V being RealLinearSpace holds Up((Omega).V) is convex
proof
  let V be RealLinearSpace;
  let u,v be VECTOR of V;
  let r be Real;
  (Omega).V = the RLSStruct of V by RLSUB_1:def 4;
  then r * u + (1-r) * v in the carrier of (Omega).V;
  hence thesis by RUSUB_4:def 5;
end;
