theorem PP:
  for a,b be Integer, m,n be Nat holds
  a|^n divides b & not a|^m divides b implies m > n
  proof
    let a,b be Integer, m,n be Nat;
    assume a|^n divides b & not a|^m divides b; then
    not a|^m divides a|^n by INT_2:9;
    hence thesis by NEWTON89;
  end;
