reserve a,b,c for set;

theorem Th4:
  for T being non empty TopStruct holds Chi(T) = union the set of all Chi(x,T)
  where x is Point of T
proof
  let T be non empty TopStruct;
  set X = the set of all Chi(x,T) where x is Point of T;
  reconsider m = union X as cardinal number by Lm1;
A1: for M being cardinal number st for x being Point of T holds Chi(x,T) c=
  M holds m c= M by Lm1;
  for x being Point of T holds Chi(x,T) c= m by Lm1;
  hence thesis by A1,Def2;
end;
