theorem Th45: :: LEXBFS:45

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