
theorem Th13:
  for n,k being Nat st n divides k & 1 < n
  ex p being Element of NAT st p divides k & p <= n & p is prime
proof
  let n,k be Nat;
  assume
A1: n divides k;
  assume
A2: 1<n;
  then 1+1<n+1 by XREAL_1:6;
  then 2<=n by NAT_1:13;
  then consider p be Element of NAT such that
A3: p is prime and
A4: p divides n by INT_2:31;
  take p;
  thus p divides k by A1,A4,NAT_D:4;
  thus p<=n by A2,A4,NAT_D:7;
  thus thesis by A3;
end;
