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 NAT327:
  for a be non zero Integer, b be non trivial Nat holds
  b |-count a = 0 iff not b divides a
  proof
    let a be non zero Integer, b be non trivial Nat;
    reconsider c = |.a.| as non zero Nat;
    b > 1 by Def0; then
    not b divides |.a.| iff b |-count |.a.| = 0 by NAT_3:27;
    hence thesis by INT_2:16;
  end;
