set G2 = the removeVertices of G,V;

set G3 = the removeVertices of G,V | _GraphSelectors;

take the removeVertices of G,V | _GraphSelectors ; :: thesis: ( the removeVertices of G,V | _GraphSelectors is Subgraph of G & the removeVertices of G,V | _GraphSelectors is removeVertices of G,V & the removeVertices of G,V | _GraphSelectors is plain )

thus ( the removeVertices of G,V | _GraphSelectors is Subgraph of G & the removeVertices of G,V | _GraphSelectors is removeVertices of G,V & the removeVertices of G,V | _GraphSelectors is plain ) by Th9, GLIB_006:16; :: thesis: verum

set G3 = the removeVertices of G,V | _GraphSelectors;

take the removeVertices of G,V | _GraphSelectors ; :: thesis: ( the removeVertices of G,V | _GraphSelectors is Subgraph of G & the removeVertices of G,V | _GraphSelectors is removeVertices of G,V & the removeVertices of G,V | _GraphSelectors is plain )

thus ( the removeVertices of G,V | _GraphSelectors is Subgraph of G & the removeVertices of G,V | _GraphSelectors is removeVertices of G,V & the removeVertices of G,V | _GraphSelectors is plain ) by Th9, GLIB_006:16; :: thesis: verum