reconsider GG = G as [Weighted] [ELabeled] Subgraph of G by GLIB_000:40;
take GG ; :: thesis: ( GG is weight-inheriting & GG is elabel-inheriting )
thus GG is weight-inheriting ; :: thesis: GG is elabel-inheriting
dom (the_ELabel_of G) c= the_Edges_of G by Lm1;
then the_ELabel_of GG = (the_ELabel_of G) | (the_Edges_of G) by RELAT_1:68;
hence GG is elabel-inheriting ; :: thesis: verum