  Let $P$ be a finite poset with an element $s$ such that (1) for all $x\in P$,
either $s\vee x$ or $s\wedge x$ exists; and (2) for all $x,y\in P$ such that
$x<y$, if $s\wedge x$ does not exist but $s\wedge y$ does exist, then $(s\wedge
y)\vee x$ exists. Kozlov, the winner of the 2005 European Prize in
Combinatorics ("for deep combinatorial results obtained by algebraic topology
and particularly for the solution of a conjecture of Lov\'asz"), conjectured in
the 1998 Proceedings of the American Mathematical Society that the order
complex of $P$ is non-evasive. We prove this conjecture.
