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

theorem
  for T being TopStruct, S being SubSpace of the TopStruct of T holds S
  is SubSpace of T
proof
  let T be TopStruct, S be SubSpace of the TopStruct of T;
  [#]S c= [#]the TopStruct of T by Def4;
  hence
  [#]S c= [#]T & for P being Subset of S holds P in the topology of S iff
  ex Q being Subset of T st Q in the topology of T & P = Q /\ [#]S by Def4;
end;
