 reserve f,g for Function;
 reserve R for non empty reflexive RelStr;
 reserve R for non empty RelStr;
 reserve f for Function of the carrier of R, bool the carrier of R;

theorem Propl: :: l)
  for f being Function of the carrier of R, bool the carrier of R
  for x,y being Subset of R holds
    (ff_0 f).(x /\ y) c= (ff_0 f).x /\ (ff_0 f).y
  proof
    let f be Function of the carrier of R, bool the carrier of R;
    let x,y be Subset of R;
AB: (ff_0 f).x =
      { u where u is Element of R : f.u meets x } by Defff;
AC: (ff_0 f).y =
      { u where u is Element of R : f.u meets y } by Defff;
    let t be object;
    assume t in (ff_0 f).(x /\ y); then
    t in { u where u is Element of R : f.u meets (x /\ y) } by Defff; then
    consider u being Element of R such that
A1: t = u & f.u meets (x /\ y);
    f.u meets x & f.u meets y by A1,XBOOLE_1:74; then
    t in (ff_0 f).x & t in (ff_0 f).y by A1,AB,AC;
    hence thesis by XBOOLE_0:def 4;
  end;
