
theorem
  for T1,T2 being TopStruct, T, T9 being Refinement of T1,T2 holds
  the TopStruct of T = the TopStruct of T9
proof
  let T1, T2 be TopStruct, T,T9 be Refinement of T1,T2;
A1: the carrier of T = (the carrier of T1) \/ (the carrier of T2) by Def6;
A2: (the topology of T1) \/ (the topology of T2) is prebasis of T by Def6;
A3: the carrier of T9 = (the carrier of T1) \/ (the carrier of T2) by Def6;
  (the topology of T1) \/ (the topology of T2) is prebasis of T9 by Def6;
  hence thesis by A1,A2,A3,Th26;
end;
