theorem :: GLIBPRE0:46

for G2 being _Graph
for v, w, e being object
for G1 being addEdge of G2,v,e,w
for v1 being Vertex of G1
for v2 being Vertex of G2 st v1 = v2 & v2 <> v & v2 <> w 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() )