theorem Th69: :: GLIBPRE0:63

for G1 being _Graph
for G2 being removeLoops of G1
for v1 being Vertex of G1
for v2 being Vertex of G2 st v1 = v2 holds
( v2 .inNeighbors() = (v1 .inNeighbors()) \ {v1} & v2 .outNeighbors() = (v1 .outNeighbors()) \ {v1} & v2 .allNeighbors() = (v1 .allNeighbors()) \ {v1} )