reserve X for set;
reserve a,b,c,k,m,n for Nat;
reserve i for Integer;
reserve r for Real;
reserve p for Prime;

theorem
  {n where n is Nat: n divides 2|^n+2} is infinite
  proof
    set S = {n where n is Nat: n divides 2|^n+2};
    set X =
    {n where n is non zero even Nat: n divides 2|^n+2 & n-1 divides 2|^n+1};
    X c= S
    proof
      let x be object;
      assume x in X;
      then ex n being non zero even Nat st x = n &
      n divides 2|^n+2 & n-1 divides 2|^n+1;
      hence thesis;
    end;
    hence thesis by Th16;
  end;
