
theorem Th3:
  for V being RealLinearSpace, x being set holds (x is Element of
  OASpace(V) iff x is VECTOR of V)
proof
  let V be RealLinearSpace, x be set;
  (OASpace(V)) = AffinStruct (#the carrier of V, DirPar(V)#) by ANALOAF:def 4;
  hence thesis;
end;
