let p be Prime; :: thesis:
assume p < 907 ; :: thesis:
then ( 1 + 1 < p + 1 & p < 906 + 1 ) by XREAL_1:6, INT_2:def 4;

suppose ( 2 <= p & p < 887 ) ; :: thesis:

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 or p = 157 or p = 163 or p = 167 or p = 173 or p = 179 or p = 181 or p = 191 or p = 193 or p = 197 or p = 199 or p = 211 or p = 223 or p = 227 or p = 229 or p = 233 or p = 239 or p = 241 or p = 251 or p = 257 or p = 263 or p = 269 or p = 271 or p = 277 or p = 281 or p = 283 or p = 293 or p = 307 or p = 311 or p = 313 or p = 317 or p = 331 or p = 337 or p = 347 or p = 349 or p = 353 or p = 359 or p = 367 or p = 373 or p = 379 or p = 383 or p = 389 or p = 397 or p = 401 or p = 409 or p = 419 or p = 421 or p = 431 or p = 433 or p = 439 or p = 443 or p = 449 or p = 457 or p = 461 or p = 463 or p = 467 or p = 479 or p = 487 or p = 491 or p = 499 or p = 503 or p = 509 or p = 521 or p = 523 or p = 541 or p = 547 or p = 557 or p = 563 or p = 569 or p = 571 or p = 577 or p = 587 or p = 593 or p = 599 or p = 601 or p = 607 or p = 613 or p = 617 or p = 619 or p = 631 or p = 641 or p = 643 or p = 647 or p = 653 or p = 659 or p = 661 or p = 673 or p = 677 or p = 683 or p = 691 or p = 701 or p = 709 or p = 719 or p = 727 or p = 733 or p = 739 or p = 743 or p = 751 or p = 757 or p = 761 or p = 769 or p = 773 or p = 787 or p = 797 or p = 809 or p = 811 or p = 821 or p = 823 or p = 827 or p = 829 or p = 839 or p = 853 or p = 857 or p = 859 or p = 863 or p = 877 or p = 881 or p = 883 or p = 887 ) by Ttool887a; :: thesis:

end;

suppose ( 887 <= p & p <= 896 + 1 ) ; :: thesis:

then ( ( 887 <= p & p <= 887 + 1 ) or ( 888 <= p & p <= 888 + 1 ) or ( 889 <= p & p <= 889 + 1 ) or ( 890 <= p & p <= 890 + 1 ) or ( 891 <= p & p <= 891 + 1 ) or ( 892 <= p & p <= 892 + 1 ) or ( 893 <= p & p <= 893 + 1 ) or ( 894 <= p & p <= 894 + 1 ) or ( 895 <= p & p <= 895 + 1 ) or ( 896 <= p & p <= 896 + 1 ) ) ;
then p = 887 by XPRIMES0:888, XPRIMES0:889, XPRIMES0:890, XPRIMES0:891, XPRIMES0:892, XPRIMES0:893, XPRIMES0:894, XPRIMES0:895, XPRIMES0:896, XPRIMES0:897, 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 or p = 157 or p = 163 or p = 167 or p = 173 or p = 179 or p = 181 or p = 191 or p = 193 or p = 197 or p = 199 or p = 211 or p = 223 or p = 227 or p = 229 or p = 233 or p = 239 or p = 241 or p = 251 or p = 257 or p = 263 or p = 269 or p = 271 or p = 277 or p = 281 or p = 283 or p = 293 or p = 307 or p = 311 or p = 313 or p = 317 or p = 331 or p = 337 or p = 347 or p = 349 or p = 353 or p = 359 or p = 367 or p = 373 or p = 379 or p = 383 or p = 389 or p = 397 or p = 401 or p = 409 or p = 419 or p = 421 or p = 431 or p = 433 or p = 439 or p = 443 or p = 449 or p = 457 or p = 461 or p = 463 or p = 467 or p = 479 or p = 487 or p = 491 or p = 499 or p = 503 or p = 509 or p = 521 or p = 523 or p = 541 or p = 547 or p = 557 or p = 563 or p = 569 or p = 571 or p = 577 or p = 587 or p = 593 or p = 599 or p = 601 or p = 607 or p = 613 or p = 617 or p = 619 or p = 631 or p = 641 or p = 643 or p = 647 or p = 653 or p = 659 or p = 661 or p = 673 or p = 677 or p = 683 or p = 691 or p = 701 or p = 709 or p = 719 or p = 727 or p = 733 or p = 739 or p = 743 or p = 751 or p = 757 or p = 761 or p = 769 or p = 773 or p = 787 or p = 797 or p = 809 or p = 811 or p = 821 or p = 823 or p = 827 or p = 829 or p = 839 or p = 853 or p = 857 or p = 859 or p = 863 or p = 877 or p = 881 or p = 883 or p = 887 ) ; :: thesis:

end;

suppose ( ( 897 <= p & p <= 897 + 1 ) or ( 898 <= p & p <= 898 + 1 ) or ( 899 <= p & p <= 899 + 1 ) or ( 900 <= p & p <= 900 + 1 ) or ( 901 <= p & p <= 901 + 1 ) or ( 902 <= p & p <= 902 + 1 ) or ( 903 <= p & p <= 903 + 1 ) or ( 904 <= p & p <= 904 + 1 ) or ( 905 <= p & p <= 905 + 1 ) ) ; :: thesis:

then contradiction by XPRIMES0:897, XPRIMES0:898, XPRIMES0:899, XPRIMES0:900, XPRIMES0:901, XPRIMES0:902, XPRIMES0:903, XPRIMES0:904, XPRIMES0:905, XPRIMES0:906, 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 or p = 157 or p = 163 or p = 167 or p = 173 or p = 179 or p = 181 or p = 191 or p = 193 or p = 197 or p = 199 or p = 211 or p = 223 or p = 227 or p = 229 or p = 233 or p = 239 or p = 241 or p = 251 or p = 257 or p = 263 or p = 269 or p = 271 or p = 277 or p = 281 or p = 283 or p = 293 or p = 307 or p = 311 or p = 313 or p = 317 or p = 331 or p = 337 or p = 347 or p = 349 or p = 353 or p = 359 or p = 367 or p = 373 or p = 379 or p = 383 or p = 389 or p = 397 or p = 401 or p = 409 or p = 419 or p = 421 or p = 431 or p = 433 or p = 439 or p = 443 or p = 449 or p = 457 or p = 461 or p = 463 or p = 467 or p = 479 or p = 487 or p = 491 or p = 499 or p = 503 or p = 509 or p = 521 or p = 523 or p = 541 or p = 547 or p = 557 or p = 563 or p = 569 or p = 571 or p = 577 or p = 587 or p = 593 or p = 599 or p = 601 or p = 607 or p = 613 or p = 617 or p = 619 or p = 631 or p = 641 or p = 643 or p = 647 or p = 653 or p = 659 or p = 661 or p = 673 or p = 677 or p = 683 or p = 691 or p = 701 or p = 709 or p = 719 or p = 727 or p = 733 or p = 739 or p = 743 or p = 751 or p = 757 or p = 761 or p = 769 or p = 773 or p = 787 or p = 797 or p = 809 or p = 811 or p = 821 or p = 823 or p = 827 or p = 829 or p = 839 or p = 853 or p = 857 or p = 859 or p = 863 or p = 877 or p = 881 or p = 883 or p = 887 ) ; :: thesis:

end;