reserve T for TopStruct;
reserve GX for TopSpace;
reserve T for TopStruct,
  x,y for Point of T;

theorem
  for X being Subset of T, Y being Subset of the TopStruct of T st X = Y
  holds the TopStruct of T|X = (the TopStruct of T)|Y
proof
  let X be Subset of T, Y be Subset of the TopStruct of T;
  assume X = Y;
  then
A1: [#](the TopStruct of T|X) = Y by Def5;
  the TopStruct of T|X is strict SubSpace of the TopStruct of T by Th35;
  hence the TopStruct of T|X = (the TopStruct of T)|Y by A1,Def5;
end;
