let p be Prime; :: thesis: ( not p < 101 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 )
assume p < 101 ; :: 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 )
then ( 1 + 1 < p + 1 & p < 100 + 1 ) by XREAL_1:6, INT_2:def 4;

per cases then ( ( 2 <= p & p < 97 ) or ( 97 <= p & p <= 97 + 1 ) or ( 98 <= p & p <= 98 + 1 ) or ( 99 <= p & p <= 99 + 1 ) ) by NAT_1:13;

suppose ( 2 <= p & 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 or p = 97 )

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 ) by Th47; :: thesis: verum

end;

suppose ( 97 <= p & p <= 97 + 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 )

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 ) by XPRIMES0:98, NAT_1:9; :: thesis: verum

end;

suppose ( 98 <= p & p <= 98 + 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 )

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 ) by XPRIMES0:98, XPRIMES0:99, NAT_1:9; :: thesis: verum

end;

suppose ( 99 <= p & p <= 99 + 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 )

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 ) by XPRIMES0:99, XPRIMES0:100, NAT_1:9; :: thesis: verum

end;

end;