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 Th21:
  p < 37 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
  proof
    assume p < 37;
    then 1+1 < p+1 & p < 36+1 by XREAL_1:6,INT_2:def 4;
    then per cases by NAT_1:13;
    suppose 2 <= p & p < 31;
      hence thesis by Th19;
    end;
    suppose 31 <= p & p <= 31+1;
      hence thesis by XPRIMES0:32,NAT_1:9;
    end;
    suppose 32 <= p & p <= 32+1;
      hence thesis by XPRIMES0:32,33,NAT_1:9;
    end;
    suppose 33 <= p & p <= 33+1;
      hence thesis by XPRIMES0:33,34,NAT_1:9;
    end;
    suppose 34 <= p & p <= 34+1;
      hence thesis by XPRIMES0:34,35,NAT_1:9;
    end;
    suppose 35 <= p & p <= 35+1;
      hence thesis by XPRIMES0:35,36,NAT_1:9;
    end;
  end;
