
theorem Th4:
  for n,b being Nat st b > 1 holds len digits(n,b) >= 1
proof
  let n,b be Nat;
  assume
A1: b > 1;
  per cases;
  suppose
    n=0;
    then digits(n,b)=<%0%> by A1,Def2;
    hence thesis by AFINSQ_1:33;
  end;
  suppose
    n<>0;
    then digits(n,b).(len digits(n,b) -1) <> 0 by A1,Def2;
    then len digits(n,b) -1 in dom digits(n,b) by FUNCT_1:def 2;
    hence thesis by NAT_1:14;
  end;
end;
