theorem
  A,A9 Is p implies ex E being Subset of S st E is_plane & A c= E &
  A9 c= E & Plane(A,A9) = E
  proof
    assume
A1: A,A9 Is p;
    then p in A /\ A9 by XBOOLE_0:def 4;
    then consider r be POINT of S such that
A2: not r in A and r in A9 and
A3: Plane(A,A9) = Plane(A,r) by A1,Def13;
    consider E be Subset of S such that
A4: E is_plane and A c= E and r in E and
A5: Plane(A,r) = E by A1,A2,Th50;
    take E;
    thus thesis by A1,A3,A4,A5,Th43;
  end;
