theorem Th6:
  x,y // x,z iff x,y // y,z or x,z // z,y
proof
  now
    assume x,y // y,z or x,z // z,y;
    then x,y // x,z or x,z // x,y by ANALOAF:def 5;
    hence x,y // x,z by Th2;
  end;
  hence thesis by ANALOAF:def 5;
end;
