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 Th5:
for n be Element of NAT holds min* {n} = n & min {n} = n
proof
 let n be Element of NAT;
A1: min* {n} in {n} by NAT_1:def 1;
  min*{n}=min {n} by Th1;
  hence thesis by A1,TARSKI:def 1;
end;
