set G2 = the addAdjVertex of G,v,e,w;
set G3 = the addAdjVertex of G,v,e,w | _GraphSelectors;
take the addAdjVertex of G,v,e,w | _GraphSelectors ; :: thesis: ( the addAdjVertex of G,v,e,w | _GraphSelectors is Supergraph of G & the addAdjVertex of G,v,e,w | _GraphSelectors is addAdjVertex of G,v,e,w & the addAdjVertex of G,v,e,w | _GraphSelectors is plain )
thus ( the addAdjVertex of G,v,e,w | _GraphSelectors is Supergraph of G & the addAdjVertex of G,v,e,w | _GraphSelectors is addAdjVertex of G,v,e,w & the addAdjVertex of G,v,e,w | _GraphSelectors is plain ) by Th9, GLIB_006:124; :: thesis: verum