let p be Prime; :: thesis: ( not p < 13 or p = 2 or p = 3 or p = 5 or p = 7 or p = 11 )
assume p < 13 ; :: thesis: ( p = 2 or p = 3 or p = 5 or p = 7 or p = 11 )
then ( 1 + 1 < p + 1 & p < 12 + 1 ) by XREAL_1:6, INT_2:def 4;

per cases then ( ( 2 <= p & p < 11 ) or ( 11 <= p & p <= 11 + 1 ) ) by NAT_1:13;

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

hence ( p = 2 or p = 3 or p = 5 or p = 7 or p = 11 ) by Ttool11a; :: thesis: verum

end;

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

hence ( p = 2 or p = 3 or p = 5 or p = 7 or p = 11 ) by XPRIMES0:12, NAT_1:9; :: thesis: verum

end;

end;