reserve n   for Nat,
        r,s for Real,
        x,y for Element of REAL n,
        p,q for Point of TOP-REAL n,
        e   for Point of Euclid n;
reserve n for non zero Nat;
reserve n for non zero Nat;
reserve n for Nat,
        X for set,
        S for Subset-Family of X;
reserve n for Nat,
        S for Subset-Family of REAL;
reserve n       for Nat,
        a,b,c,d for Element of REAL n;
reserve n for non zero Nat;
reserve n     for non zero Nat,
        x,y,z for Element of REAL n;

theorem Th60:
  (Infty_dist n).(x,y) = (Infty_dist n).(y,x)
  proof
    (Infty_dist n).(x,y) = sup rng abs(x-y) &
    (Infty_dist n).(y,x) = sup rng abs(y-x) by Def7;
    hence (Infty_dist n).(x,y) = (Infty_dist n).(y,x) by Th1;
  end;
