 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
  for L being WA-Lattice,
      a,b,x being Element of L st
    x in Segment (a,b) holds
      a <= x <= b or b <= x <= a
  proof
    let L be WA-Lattice,
        a,b,x be Element of L;
    assume x in Segment (a,b); then
    consider xx being Element of L such that
D1: x = xx & (a <= xx <= b or b <= xx <= a);
    thus thesis by D1;
  end;
