let K, M be Subset of POS; ( K _|_ M implies M _|_ K )
assume
K _|_ M
; M _|_ K
then consider a, b, c, d being Element of POS such that
A4:
( a <> b & c <> d & K = Line a,b & M = Line c,d )
and
A5:
a,b _|_ c,d
by Th63;
c,d _|_ a,b
by A5, Def9;
hence
M _|_ K
by A4, Th63; verum