let p be Prime; :: thesis: ( not p < 17 or p = 2 or p = 3 or p = 5 or p = 7 or p = 11 or p = 13 )
assume p < 17 ; :: thesis: ( p = 2 or p = 3 or p = 5 or p = 7 or p = 11 or p = 13 )
then ( 1 + 1 < p + 1 & p < 16 + 1 ) by XREAL_1:6, INT_2:def 4;

per cases then ( ( 2 <= p & p < 13 ) or ( 13 <= p & p <= 13 + 1 ) or ( 14 <= p & p <= 14 + 1 ) or ( 15 <= p & p <= 15 + 1 ) ) by NAT_1:13;

suppose ( 2 <= p & p < 13 ) ; :: thesis: ( p = 2 or p = 3 or p = 5 or p = 7 or p = 11 or p = 13 )

hence ( p = 2 or p = 3 or p = 5 or p = 7 or p = 11 or p = 13 ) by Ttool13a; :: thesis: verum

end;

suppose ( ( 13 <= p & p <= 13 + 1 ) or ( 14 <= p & p <= 14 + 1 ) or ( 15 <= p & p <= 15 + 1 ) ) ; :: thesis: ( p = 2 or p = 3 or p = 5 or p = 7 or p = 11 or p = 13 )

then p = 13 by XPRIMES0:14, XPRIMES0:15, XPRIMES0:16, NAT_1:9;
hence ( p = 2 or p = 3 or p = 5 or p = 7 or p = 11 or p = 13 ) ; :: thesis: verum

end;

end;