 reserve R for finite Approximation_Space;
 reserve X,Y,Z for Subset of R;
 reserve kap for RIF of R;

theorem ME7: ::: Discerning
  for X being non empty set
  for f being nonnegative-yielding discerning triangle Reflexive
          Function of [:X,X:], REAL,
      x,y being Element of X st x <> y holds
    f.(x,y) > 0
  proof
    let X be non empty set;
    let f be nonnegative-yielding discerning triangle Reflexive
            Function of [:X,X:], REAL,
        x,y be Element of X;
    assume x <> y; then
    f.(x,y) <> 0 by METRIC_1:def 3;
    hence thesis by Non;
  end;
