reserve a,b,c,d,x,j,k,l,m,n,o,xi,xj for Nat,
  p,q,t,z,u,v for Integer,
  a1,b1,c1,d1 for Complex;

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;
