theorem Th62: :: GLIBPRE0:56

for G2 being _Graph
for v being object
for V being set
for G1 being addAdjVertexAll of G2,v,V
for v1 being Vertex of G1
for v2 being Vertex of G2 st v1 = v2 & not v2 in V holds
( v1 .edgesIn() = v2 .edgesIn() & v1 .inDegree() = v2 .inDegree() & v1 .edgesOut() = v2 .edgesOut() & v1 .outDegree() = v2 .outDegree() & v1 .edgesInOut() = v2 .edgesInOut() & v1 .degree() = v2 .degree() )