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 DX:
  for a be non zero Integer, b be non trivial Nat, c be Integer holds
  a = b|^(b |-count a)*c implies not b divides c
  proof
    let a be non zero Integer, b be non trivial Nat, c be Integer;
A0: b > 1 by Def0;
    assume
A1: a = b|^(b |-count a)*c;
    assume not thesis; then
    consider d be Integer such that
A2: c = b*d;
    a = b|^(b|-count a)*b*d by A1,A2; then
    b*b|^(b |-count a) divides a; then
    b|^((b |-count a)+1) divides a by NEWTON:6;
    hence contradiction by Def6,A0;
  end;
