reserve a, b, n for Nat,
  r for Real,
  f for FinSequence of REAL;
reserve p for Prime;

theorem
  a <> 1 & a <> p implies a |-count p = 0
proof
  assume that
A1: a <> 1 and
A2: a <> p;
  a |^ 0 = 1 by NEWTON:4;
  then
A3: a |^ 0 divides p by NAT_D:6;
  not a |^ (0+1) divides p by A1,A2,INT_2:def 4;
  hence thesis by A1,A3,Def7;
end;
