 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;

theorem LemmaRefl:
  for x being Element of W holds
    x (--) x
  proof
    let x be Element of W;
A1: the ToleranceRel of W is_reflexive_in the carrier of W by PCS_0:def 9;
    [x,x] in the ToleranceRel of W by A1,RELAT_2:def 1;
    hence thesis by PCS_0:def 7;
  end;
