
theorem
  for V being RealLinearSpace, M,N being circled Subset of V holds M \/
  N is circled
proof
  let V be RealLinearSpace, M,N be circled Subset of V, x be VECTOR of V, r be
  Real;
  assume that
A1: |.r.| <= 1 and
A2: x in M \/ N;
  x in M or x in N by A2,XBOOLE_0:def 3;
  then r * x in M or r * x in N by A1,Def1;
  hence thesis by XBOOLE_0:def 3;
end;
