set G2 = the addEdge of G,v,e,w;

set G3 = the addEdge of G,v,e,w | _GraphSelectors;

take the addEdge of G,v,e,w | _GraphSelectors ; :: thesis: ( the addEdge of G,v,e,w | _GraphSelectors is Supergraph of G & the addEdge of G,v,e,w | _GraphSelectors is addEdge of G,v,e,w & the addEdge of G,v,e,w | _GraphSelectors is plain )

thus ( the addEdge of G,v,e,w | _GraphSelectors is Supergraph of G & the addEdge of G,v,e,w | _GraphSelectors is addEdge of G,v,e,w & the addEdge of G,v,e,w | _GraphSelectors is plain ) by Th9, GLIB_006:101; :: thesis: verum

set G3 = the addEdge of G,v,e,w | _GraphSelectors;

take the addEdge of G,v,e,w | _GraphSelectors ; :: thesis: ( the addEdge of G,v,e,w | _GraphSelectors is Supergraph of G & the addEdge of G,v,e,w | _GraphSelectors is addEdge of G,v,e,w & the addEdge of G,v,e,w | _GraphSelectors is plain )

thus ( the addEdge of G,v,e,w | _GraphSelectors is Supergraph of G & the addEdge of G,v,e,w | _GraphSelectors is addEdge of G,v,e,w & the addEdge of G,v,e,w | _GraphSelectors is plain ) by Th9, GLIB_006:101; :: thesis: verum