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 Th15:
  p < 23 implies
  p = 2 or p = 3 or p = 5 or p = 7 or p = 11 or p = 13 or p = 17 or p = 19
  proof
    assume p < 23;
    then 1+1 < p+1 & p < 22+1 by XREAL_1:6,INT_2:def 4;
    then per cases by NAT_1:13;
    suppose 2 <= p & p < 19;
      hence thesis by Th13;
    end;
    suppose 19 <= p & p <= 19+1;
      hence thesis by XPRIMES0:20,NAT_1:9;
    end;
    suppose 20 <= p & p <= 20+1;
      hence thesis by XPRIMES0:20,21,NAT_1:9;
    end;
    suppose 21 <= p & p <= 21+1;
      hence thesis by XPRIMES0:21,22,NAT_1:9;
    end;
  end;
