
theorem FOT1:
  for n being non zero Nat holds
    n - (n div 2) * 2 <= 1
  proof
    let n be non zero Nat;
A2: n = 2 * (n div 2) + (n mod 2) by NAT_D:2;
    per cases by NAT_1:23,NAT_D:1;
    suppose n mod 2 = 0;
      hence thesis by A2;
    end;
    suppose n mod 2 = 1;
      hence thesis by A2;
    end;
  end;
