
theorem
  for L being Lattice,
      a,b being Element of L holds
    b in PseudoCocomplements a iff b "\/" a = Top L
  proof
    let L be Lattice,
        a,b be Element of L;
    hereby assume
      b in PseudoCocomplements a; then
      consider x being Element of L such that
A1:   b = x & a "\/" x = Top L;
      thus b "\/" a = Top L by A1;
    end;
    assume b "\/" a = Top L;
    hence thesis;
  end;
