reserve a,b,c,h for Integer;
reserve k,m,n for Nat;
reserve i,j,z for Integer;
reserve p for Prime;

theorem Th49:
  for n being non zero Nat st PrimeDivisors(n) is empty holds n = 1
  proof
    let n be non zero Nat;
    set X = PrimeDivisors(n);
    assume
A1: X is empty;
    assume n <> 1;
    then consider p being Prime such that
A2: p divides n by MOEBIUS1:5;
    p in X by A2;
    hence thesis by A1;
  end;
