theorem :: GLIB_000:167

for G1 being non _trivial _Graph
for v being Vertex of G1
for G2 being removeVertex of G1,v
for v1 being Vertex of G1
for v2 being Vertex of G2 st v1 = v2 holds
( v2 .edgesIn() = (v1 .edgesIn()) \ (v .edgesOut()) & v2 .edgesOut() = (v1 .edgesOut()) \ (v .edgesIn()) & v2 .edgesInOut() = (v1 .edgesInOut()) \ (v .edgesInOut()) )