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 CountD:
  for b be non zero Integer, a be Integer st |.a.| <> 1 holds
  a|^(|.a.| |-count |.b.|) divides b &
    not a|^((|.a.||-count |.b.|)+1) divides b
proof
  let b be non zero Integer, a be Integer such that
  A0: |.a.| <> 1;
  reconsider k = |.a.|, l = |.b.| as Nat;
  A1: |.a.||^(k |-count l) = |. a|^(k |-count l).| &
  |.a.||^((k |-count l) +1) = |.a|^((k |-count l) +1).| by TAYLOR_2:1;
  k|^(k |-count l) divides l & not k|^((k |-count l)+1) divides l
    by A0,NAT_3:def 7;
  hence thesis by A1,INT_2:16;
end;
