theorem Th31:
  [p,q] in LattRel L iff p [= q
proof
  thus [p,q] in LattRel L implies p [= q
  proof
    assume [p,q] in LattRel L;
    then consider r,s such that
A1: [p,q] = [r,s] and
A2: r [= s;
    thus thesis by A1,A2,XTUPLE_0:1;
  end;
  thus thesis;
end;
