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 Th25:
  p < 43 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
  proof
    assume p < 43;
    then 1+1 < p+1 & p < 42+1 by XREAL_1:6,INT_2:def 4;
    then per cases by NAT_1:13;
    suppose 2 <= p & p < 41;
      hence thesis by Th23;
    end;
    suppose 41 <= p & p <= 41+1;
      hence thesis by XPRIMES0:42,NAT_1:9;
    end;
  end;
