How do I prove that -LSB- math -RSB- P -LRB- A -RRB- \ cup P -LRB- B -RRB- \ subset P -LRB- A \ cup B -RRB- -LSB- / math -RSB- ?
How do I prove that if all subsets of a poset P have least upper bounds , then all subsets of P have greater lower bounds ?