
theorem
  for L being non empty RelStr for T1,T2 being correct TopAugmentation of L
  for T be Refinement of T1, T2
  holds INTERSECTION(the topology of T1, the topology of T2) is Basis of T
proof
  let L be non empty RelStr;
  let T1,T2 be correct TopAugmentation of L;
A1: the RelStr of T1 = the RelStr of L by Def4;
  the RelStr of T2 = the RelStr of L by Def4;
  hence thesis by A1,Th60;
end;
