reserve GX for TopSpace;
reserve A, B, C for Subset of GX;
reserve TS for TopStruct;
reserve K, K1, L, L1 for Subset of TS;

theorem Th1:
  K,L are_separated implies K misses L
proof
  assume that
A1: (Cl K) /\ L = {} and
  K /\ Cl L = {};
  K c= Cl K by PRE_TOPC:18;
  hence K /\ L = {} by A1,XBOOLE_1:3,27;
end;
