let p be Prime; :: thesis: ( not p < 157 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 or p = 47 or p = 53 or p = 59 or p = 61 or p = 67 or p = 71 or p = 73 or p = 79 or p = 83 or p = 89 or p = 97 or p = 101 or p = 103 or p = 107 or p = 109 or p = 113 or p = 127 or p = 131 or p = 137 or p = 139 or p = 149 or p = 151 )
assume p < 157 ; :: 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 or p = 47 or p = 53 or p = 59 or p = 61 or p = 67 or p = 71 or p = 73 or p = 79 or p = 83 or p = 89 or p = 97 or p = 101 or p = 103 or p = 107 or p = 109 or p = 113 or p = 127 or p = 131 or p = 137 or p = 139 or p = 149 or p = 151 )
then ( 1 + 1 < p + 1 & p < 156 + 1 ) by XREAL_1:6, INT_2:def 4;

per cases then ( ( 2 <= p & p < 151 ) or ( 151 <= p & p <= 151 + 1 ) or ( 152 <= p & p <= 152 + 1 ) or ( 153 <= p & p <= 153 + 1 ) or ( 154 <= p & p <= 154 + 1 ) or ( 155 <= p & p <= 155 + 1 ) ) by NAT_1:13;

suppose ( 2 <= p & p < 151 ) ; :: 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 or p = 47 or p = 53 or p = 59 or p = 61 or p = 67 or p = 71 or p = 73 or p = 79 or p = 83 or p = 89 or p = 97 or p = 101 or p = 103 or p = 107 or p = 109 or p = 113 or p = 127 or p = 131 or p = 137 or p = 139 or p = 149 or p = 151 )

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 or p = 47 or p = 53 or p = 59 or p = 61 or p = 67 or p = 71 or p = 73 or p = 79 or p = 83 or p = 89 or p = 97 or p = 101 or p = 103 or p = 107 or p = 109 or p = 113 or p = 127 or p = 131 or p = 137 or p = 139 or p = 149 or p = 151 ) by Ttool151a; :: thesis: verum

end;

suppose ( ( 151 <= p & p <= 151 + 1 ) or ( 152 <= p & p <= 152 + 1 ) or ( 153 <= p & p <= 153 + 1 ) or ( 154 <= p & p <= 154 + 1 ) or ( 155 <= p & p <= 155 + 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 or p = 47 or p = 53 or p = 59 or p = 61 or p = 67 or p = 71 or p = 73 or p = 79 or p = 83 or p = 89 or p = 97 or p = 101 or p = 103 or p = 107 or p = 109 or p = 113 or p = 127 or p = 131 or p = 137 or p = 139 or p = 149 or p = 151 )

then p = 151 by XPRIMES0:152, XPRIMES0:153, XPRIMES0:154, XPRIMES0:155, XPRIMES0:156, 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 or p = 47 or p = 53 or p = 59 or p = 61 or p = 67 or p = 71 or p = 73 or p = 79 or p = 83 or p = 89 or p = 97 or p = 101 or p = 103 or p = 107 or p = 109 or p = 113 or p = 127 or p = 131 or p = 137 or p = 139 or p = 149 or p = 151 ) ; :: thesis: verum

end;

end;