 reserve f,g for Function;
 reserve R for non empty reflexive RelStr;

theorem :: 4.1 b)
  id bool the carrier of R cc= UAp R
  proof
    set f = id bool the carrier of R;
    set g = UAp R;
A1: dom f c= dom g by FUNCT_2:def 1;
    for i being set st i in dom f holds f.i c= g.i
    proof
      let i be set;
      assume i in dom f; then
      reconsider ii = i as Subset of R;
      g.ii = UAp ii by ROUGHS_2:def 11;
      hence f.i c= g.i by ROUGHS_2:36;
    end;
    hence thesis by A1,ALTCAT_2:def 1;
  end;
