Simple proofs are given for two theorems of Duffus and Rival: If a finite poset is dismantled by irreducibles as much as possible, the subposet one finally obtains is unique up to isomorphism. If one dismantles by doubly irreducibles, the subposet is unique.
Mathematics Subject Classifications (1991) Primary 06A06 - secondary 06C10
Key words (Partially) ordered set - dismantlable - irreducible - semimodular
Communicated by I. Rival