reserve m, n for Nat;

theorem Th24:
  n is square-free implies for p being Prime holds p |-count n <= 1
proof
  assume
A1: n is square-free;
  given p being Prime such that
A2: p |-count n > 1;
  p |-count n >= 1+1 by A2,NAT_1:13;
  then p |^ 2 divides n by A1,Th9,Th21;
  hence thesis by A1;
end;
