
theorem
  for G1 being WGraph, G2 being WSubgraph of G1, G3 being WSubgraph of
  G2 holds G3 is WSubgraph of G1
proof
  let G1 be WGraph, G2 be WSubgraph of G1, G3 be WSubgraph of G2;
  reconsider G39=G3 as [Weighted] Subgraph of G1 by GLIB_000:43;
  the_Weight_of G3=(the_Weight_of G2) | the_Edges_of G3 by Def10
    .=((the_Weight_of G1) | the_Edges_of G2) | the_Edges_of G3 by Def10
    .=(the_Weight_of G1)|the_Edges_of G3 by RELAT_1:74;
  then G39 is weight-inheriting;
  hence thesis;
end;
