reserve FT for non empty RelStr;
reserve A for Subset of FT;

theorem
  for FT being non empty RelStr, A,B being Subset of FT holds A c= B
  implies A^i c= B^i
proof
  let FT be non empty RelStr;
  let A,B be Subset of FT;
  assume
A1: A c= B;
  let x be object;
  assume
A2: x in A^i;
  then reconsider y=x as Element of FT;
A3: U_FT y c= A by A2,FIN_TOPO:7;
  for t being Element of FT st t in U_FT y holds t in B
  by A3,A1;
  then U_FT y c= B;
  hence thesis;
end;
