theorem Th48: :: LEXBFS:48

for G being _finite _Graph
for m, n being Nat
for x being Vertex of G st n in (((LexBFS:CSeq G) . m) `2) . x holds
ex y being Vertex of G st
( LexBFS:PickUnnumbered ((LexBFS:CSeq G) . ((G .order()) -' n)) = y & not y in dom (((LexBFS:CSeq G) . ((G .order()) -' n)) `1) & x in G .AdjacentSet {y} )