reserve k, l, m, n, i, j for Nat,
  K, N for non empty Subset of NAT,
  Ke, Ne, Me for Subset of NAT,
  X,Y for set;

theorem Th1:
  min N = min* N
proof
A1: for n being ExtReal st n in N holds min* N <= n by NAT_1:def 1;
  min* N in N by NAT_1:def 1;
  hence thesis by A1,XXREAL_2:def 7;
end;
