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

theorem LApId: :: Theorem 4.1 b)
  LAp R cc= id bool the carrier of R
  proof
    set f = LAp R;
    set g = id bool the carrier of R;
A1: dom f c= dom g;
    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;
      f.ii = LAp ii by ROUGHS_2:def 10;
      hence thesis by ROUGHS_2:35;
    end;
    hence thesis by A1,ALTCAT_2:def 1;
  end;
