
theorem
for n being Nat st n < 10 holds Sierp36 n,n
proof
  let n be Nat;
  assume n < 10;
  then digits(n,10)=<%n%> by Th3;
  hence Sum digits(n,10) = n by AFINSQ_2:53;
  thus n divides n;
  per cases;
  suppose n=0;
    hence thesis;
  end;
  suppose A1: n>0;
    hereby
      let m be Nat;
      assume A2: Sum digits(m,10) = n & n divides m;
      now
        assume m=0;
        then digits(m,10) = <%0%> by Th3;
        hence contradiction by A2,A1,AFINSQ_2:53;
      end;
      hence n <= m by A2,INT_2:27;
    end;
  end;
end;
