for G being _finite _Graph
for i, j being Nat
for v being Vertex of G st j in (((LexBFS:CSeq G) . i) `2) . v holds
ex w being Vertex of G st
( w in dom (((LexBFS:CSeq G) . i) `1) & (((LexBFS:CSeq G) . i) `1) . w = j & v in G .AdjacentSet {w} )