let p be Prime; :: thesis: ( not p < 79 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 )
assume p < 79 ; :: 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 )
then ( 1 + 1 < p + 1 & p < 78 + 1 ) by XREAL_1:6, INT_2:def 4;

per cases then ( ( 2 <= p & p < 73 ) or ( 73 <= p & p <= 73 + 1 ) or ( 74 <= p & p <= 74 + 1 ) or ( 75 <= p & p <= 75 + 1 ) or ( 76 <= p & p <= 76 + 1 ) or ( 77 <= p & p <= 77 + 1 ) ) by NAT_1:13;

suppose ( 2 <= p & p < 73 ) ; :: 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 )

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 ) by Ttool73a; :: thesis: verum

end;

suppose ( ( 73 <= p & p <= 73 + 1 ) or ( 74 <= p & p <= 74 + 1 ) or ( 75 <= p & p <= 75 + 1 ) or ( 76 <= p & p <= 76 + 1 ) or ( 77 <= p & p <= 77 + 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 )

then p = 73 by XPRIMES0:74, XPRIMES0:75, XPRIMES0:76, XPRIMES0:77, XPRIMES0:78, 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 ) ; :: thesis: verum

end;

end;