let p be Prime; :: thesis: ( not p < 47 or p = 2 or p = 3 or p = 5 or p = 7 or p = 11 or p = 13 or p = 17 or p = 19 or p = 23 or p = 29 or p = 31 or p = 37 or p = 41 or p = 43 )
assume p < 47 ; :: thesis: ( p = 2 or p = 3 or p = 5 or p = 7 or p = 11 or p = 13 or p = 17 or p = 19 or p = 23 or p = 29 or p = 31 or p = 37 or p = 41 or p = 43 )
then ( 1 + 1 < p + 1 & p < 46 + 1 ) by XREAL_1:6, INT_2:def 4;

per cases then ( ( 2 <= p & p < 43 ) or ( 43 <= p & p <= 43 + 1 ) or ( 44 <= p & p <= 44 + 1 ) or ( 45 <= p & p <= 45 + 1 ) ) by NAT_1:13;

suppose ( 2 <= p & p < 43 ) ; :: thesis: ( p = 2 or p = 3 or p = 5 or p = 7 or p = 11 or p = 13 or p = 17 or p = 19 or p = 23 or p = 29 or p = 31 or p = 37 or p = 41 or p = 43 )

hence ( p = 2 or p = 3 or p = 5 or p = 7 or p = 11 or p = 13 or p = 17 or p = 19 or p = 23 or p = 29 or p = 31 or p = 37 or p = 41 or p = 43 ) by Ttool43a; :: thesis: verum

end;

suppose ( ( 43 <= p & p <= 43 + 1 ) or ( 44 <= p & p <= 44 + 1 ) or ( 45 <= p & p <= 45 + 1 ) ) ; :: thesis: ( p = 2 or p = 3 or p = 5 or p = 7 or p = 11 or p = 13 or p = 17 or p = 19 or p = 23 or p = 29 or p = 31 or p = 37 or p = 41 or p = 43 )

then p = 43 by XPRIMES0:44, XPRIMES0:45, XPRIMES0:46, NAT_1:9;
hence ( p = 2 or p = 3 or p = 5 or p = 7 or p = 11 or p = 13 or p = 17 or p = 19 or p = 23 or p = 29 or p = 31 or p = 37 or p = 41 or p = 43 ) ; :: thesis: verum

end;

end;