
theorem Th16:
  for L being non empty reflexive RelStr, A, B being Subset of L
  st A c= B holds A is_finer_than B & A is_coarser_than B
proof
  let L be non empty reflexive RelStr, A, B be Subset of L such that
A1: A c= B;
  thus A is_finer_than B
  proof
    let a be Element of L such that
A2: a in A;
    take b = a;
    thus b in B & a <= b by A1,A2;
  end;
  let a be Element of L such that
A3: a in A;
  take b = a;
  thus b in B & b <= a by A1,A3;
end;
