reserve m, n for Nat;

theorem
  for n being non zero Nat, p being Prime holds
  { k where k is Element of NAT : 0 < k & k divides Radical n & p divides k }
   c= Seg n
proof
  let n be non zero Nat;
  let p be Prime;
  let x be object;
  assume x in { k where k is Element of NAT : 0 < k & k divides Radical n & p
  divides k };
  then consider k being Element of NAT such that
A1: x = k and
A2: k > 0 and
A3: k divides Radical n and
  p divides k;
A4: 1 <= k by A2,NAT_1:14;
A5: Radical n <= n by Th55,NAT_D:7;
  k <= Radical n by A3,NAT_D:7;
  then k <= n by A5,XXREAL_0:2;
  hence thesis by A1,A4,FINSEQ_1:1;
end;
