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
for n,k,l be Element of NAT holds min* {n,k,l} = min(n,min(k,l))
proof
let n,k,l be Element of NAT;
A1: min {n,k,l}=min* {n,k,l} by Th1;
  {n,k,l}={n}\/{k,l} by ENUMSET1:2;
  then
A2: min{n,k,l} = min(min {n},min {k,l}) by Th2;
  min {k,l}=min(k,l) by Th6;
  hence thesis by A2,A1,Th5;
end;
