 reserve X,a,b,c,x,y,z,t for set;
 reserve R for Relation;

theorem
  for R being non empty RelStr,
      A, B being Subset of R holds
    (LAp R).(A /\ B) = (LAp R).A /\ (LAp R).B
  proof
    let R be non empty RelStr;
    let X, Y be Subset of R;
    set L = LAp R;
    L.(X /\ Y) = LAp (X /\ Y) by ROUGHS_2:def 10
              .= LAp X /\ LAp Y by ROUGHS_2:12
              .= L.X /\ LAp Y by ROUGHS_2:def 10
              .= L.X /\ L.Y by ROUGHS_2:def 10;
    hence thesis;
  end;
