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We reprove and generalize in a combinatorial way the result of A. Bjorner [J.\ Comb.\ Th.\ A {\bf 30}, 1981, pp.~90--100, Theorem 3.3], that order complexes of noncomplemented lattices are contractible, namely by showing that these simplicial complexes are in fact nonevasive, in particular collapsible.

Order complexes of noncomplemented lattices are nonevasive