reserve a,b,i,k,m,n for Nat;
reserve s,z for non zero Nat;
reserve r for Real;
reserve c for Complex;
reserve e1,e2,e3,e4,e5 for ExtReal;
reserve p for Prime;

theorem Th11:
  p < 17 implies p = 2 or p = 3 or p = 5 or p = 7 or p = 11 or p = 13
  proof
    assume p < 17;
    then 1+1 < p+1 & p < 16+1 by XREAL_1:6,INT_2:def 4;
    then per cases by NAT_1:13;
    suppose 2 <= p & p < 13;
      hence thesis by Th9;
    end;
    suppose 13 <= p & p <= 13+1;
      hence thesis by XPRIMES0:14,NAT_1:9;
    end;
    suppose 14 <= p & p <= 14+1;
      hence thesis by XPRIMES0:14,15,NAT_1:9;
    end;
    suppose 15 <= p & p <= 15+1;
      hence thesis by XPRIMES0:15,16,NAT_1:9;
    end;
  end;
