let p be Prime; :: thesis: ( not p < 97 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 )
assume p < 97 ; :: 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 )
then ( 1 + 1 < p + 1 & p < 96 + 1 ) by XREAL_1:6, INT_2:def 4;

per cases then ( ( 2 <= p & p < 89 ) or ( 89 <= p & p <= 89 + 1 ) or ( 90 <= p & p <= 90 + 1 ) or ( 91 <= p & p <= 91 + 1 ) or ( 92 <= p & p <= 92 + 1 ) or ( 93 <= p & p <= 93 + 1 ) or ( 94 <= p & p <= 94 + 1 ) or ( 95 <= p & p <= 95 + 1 ) ) by NAT_1:13;

suppose ( 2 <= p & p < 89 ) ; :: 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 )

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 ) by Ttool89a; :: thesis: verum

end;

suppose ( ( 89 <= p & p <= 89 + 1 ) or ( 90 <= p & p <= 90 + 1 ) or ( 91 <= p & p <= 91 + 1 ) or ( 92 <= p & p <= 92 + 1 ) or ( 93 <= p & p <= 93 + 1 ) or ( 94 <= p & p <= 94 + 1 ) or ( 95 <= p & p <= 95 + 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 )

then p = 89 by XPRIMES0:90, XPRIMES0:91, XPRIMES0:92, XPRIMES0:93, XPRIMES0:94, XPRIMES0:95, XPRIMES0:96, 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 ) ; :: thesis: verum

end;

end;