reserve x, y for set,
  T for TopStruct,
  GX for TopSpace,
  P, Q, M, N for Subset of T,
  F, G for Subset-Family of T,
  W, Z for Subset-Family of GX,
  A for SubSpace of T;

theorem
  M c= union (F|M) implies M c= union F
proof
  assume
A1: M c= union(F|M);
  union(F|M) c= union F by Th34;
  hence thesis by A1;
end;
