theorem Th69:
  for A,B be Subset of RLS st A c= Affin B holds Affin (A\/B) = Affin B
 proof
  let A,B be Subset of RLS such that
   A1: A c=Affin B;
  set AB={C where C is Affine Subset of RLS:A\/B c=C};
  B c=Affin B by Lm7;
  then A\/B c=Affin B by A1,XBOOLE_1:8;
  then Affin B in AB;
  then A2: Affin(A\/B)c=Affin B by SETFAM_1:3;
  Affin B c=Affin(A\/B) by Th52,XBOOLE_1:7;
  hence thesis by A2;
 end;
