reserve a,b,i,k,m,n for Nat;
reserve s,z for non zero Nat;
reserve r for Real;
reserve c for Complex;
reserve e1,e2,e3,e4,e5 for ExtReal;
reserve p for Prime;

theorem Th47:
  p < 97 implies
  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
  proof
    assume p < 97;
    then 1+1 < p+1 & p < 96+1 by XREAL_1:6,INT_2:def 4;
    then per cases by NAT_1:13;
    suppose 2 <= p & p < 89;
      hence thesis by Th45;
    end;
    suppose 89 <= p & p <= 89+1;
      hence thesis by XPRIMES0:90,NAT_1:9;
    end;
    suppose 90 <= p & p <= 90+1;
      hence thesis by XPRIMES0:90,91,NAT_1:9;
    end;
    suppose 91 <= p & p <= 91+1;
      hence thesis by XPRIMES0:91,92,NAT_1:9;
    end;
    suppose 92 <= p & p <= 92+1;
      hence thesis by XPRIMES0:92,93,NAT_1:9;
    end;
    suppose 93 <= p & p <= 93+1;
      hence thesis by XPRIMES0:93,94,NAT_1:9;
    end;
    suppose 94 <= p & p <= 94+1;
      hence thesis by XPRIMES0:94,95,NAT_1:9;
    end;
    suppose 95 <= p & p <= 95+1;
      hence thesis by XPRIMES0:95,96,NAT_1:9;
    end;
  end;
