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;
reserve f for Function of Segm n,Segm k;

theorem Th16:
  n>0 implies min* f"{m} <= n-1
proof
A1: f"{m} c= n
  proof
    let x be object;
    assume x in f"{m};
    then x in dom f by FUNCT_1:def 7;
    hence thesis;
  end;
  assume n>0;
  hence thesis by A1,Th14;
end;
