theorem ::  General Topology Th 4.1.10
  for B be Subset of T,F be Subset of T|A st F = B holds T|A|F = T|B
proof
  let B be Subset of T,F be Subset of T|A such that
A1: F = B;
  (T|A|F) is SubSpace of T & [#](T|A|F)=F by PRE_TOPC:def 5,TSEP_1:7;
  hence thesis by A1,PRE_TOPC:def 5;
end;
