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

theorem Th23:
  b <> 0 & b < a & a <> 1 implies a |-count b = 0
proof
  assume that
A1: b <> 0 and
A2: b < a and
A3: a <> 1;
  a |^ 0 = 1 by NEWTON:4;
  then
A4: a |^ 0 divides b by NAT_D:6;
  not a |^ (0+1) divides b by A1,A2,NAT_D:7;
  hence thesis by A1,A3,A4,Def7;
end;
