 reserve W for WA-Lattice;
 reserve a,b,c for Element of W;
 reserve W for pcs-Compatible pcs-tol-reflexive pcs-tol-symmetric WAP-Lattice;
 reserve a,b for Element of W;
 reserve L for WA_Lattice;

theorem SingleCycle:
  for L being WA-Lattice
  for a being Element of L holds
    {a} is_cycle_of L
  proof
    let L be WA-Lattice;
    let a be Element of L;
    set A = {a};
    for x,y being Element of L st
    x <> y & x in A & y in A holds
      A = Segment (x,y)
    proof
      let x,y be Element of L;
      assume A1: x <> y & x in A & y in A; then
      x = a & y = a by TARSKI:def 1;
      hence thesis by A1;
    end;
    hence thesis;
  end;
