let G1 be _Graph; :: thesis: for G2 being Subgraph of G1
for v1 being Vertex of G1
for v2 being Vertex of G2 st v1 = v2 holds
( v2 .inDegree() c= v1 .inDegree() & v2 .outDegree() c= v1 .outDegree() & v2 .degree() c= v1 .degree() )
let G2 be Subgraph of G1; :: thesis: for v1 being Vertex of G1
for v2 being Vertex of G2 st v1 = v2 holds
( v2 .inDegree() c= v1 .inDegree() & v2 .outDegree() c= v1 .outDegree() & v2 .degree() c= v1 .degree() )
let v1 be Vertex of G1; :: thesis: for v2 being Vertex of G2 st v1 = v2 holds
( v2 .inDegree() c= v1 .inDegree() & v2 .outDegree() c= v1 .outDegree() & v2 .degree() c= v1 .degree() )
let v2 be Vertex of G2; :: thesis: ( v1 = v2 implies ( v2 .inDegree() c= v1 .inDegree() & v2 .outDegree() c= v1 .outDegree() & v2 .degree() c= v1 .degree() ) )
assume A1: v1 = v2 ; :: thesis: ( v2 .inDegree() c= v1 .inDegree() & v2 .outDegree() c= v1 .outDegree() & v2 .degree() c= v1 .degree() )
then v2 .edgesIn() c= v1 .edgesIn() by GLIB_000:78;
hence A2: v2 .inDegree() c= v1 .inDegree() by CARD_1:11; :: thesis: ( v2 .outDegree() c= v1 .outDegree() & v2 .degree() c= v1 .degree() )
thus v2 .outDegree() c= v1 .outDegree() by A1, GLIB_000:78, CARD_1:11; :: thesis: v2 .degree() c= v1 .degree()
hence v2 .degree() c= v1 .degree() by A2, CARD_2:83; :: thesis: verum