theorem
  for L being Lattice, p,q,r being Element of L holds
  p is_less_than {q,r} iff p [= q"/\"r
proof
  let L be Lattice, p,q,r be Element of L;
A1: q in {q,r} by TARSKI:def 2;
A2: r in {q,r} by TARSKI:def 2;
  thus p is_less_than {q,r} implies p [= q"/\"r
  proof
    assume
A3: p is_less_than {q,r};
    then
A4: p [= q by A1;
    p [= r by A2,A3;
    hence thesis by A4,FILTER_0:7;
  end;
  assume
A5: p [= q"/\"r;
  let a be Element of L;
  assume a in {q,r};
  then
A6: a = q or a = r by TARSKI:def 2;
A7: q"/\"r [= q by LATTICES:6;
  r"/\"q [= r by LATTICES:6;
  hence thesis by A5,A6,A7,LATTICES:7;
end;
