
theorem Th14:
  for p being Nat holds p is prime iff p > 1 &
  for n being Element of NAT holds 1 < n & n*n <= p & n is prime
   implies not n divides p
proof
  now
    let p be Nat;
    assume
A1: p>1;
    assume for n being Element of NAT holds not (1<n & n*n<=p & n is prime)
    or not n divides p;
    then
    for n being Element of NAT holds not n divides p or not (1<n & n*n<=p
    & n is prime);
    hence p is prime by A1,Lm1;
  end;
  hence thesis by Lm1;
end;
