
theorem
  for G1,G2 being WGraph, G3 being WSubgraph of G1 st G1 == G2 &
  the_Weight_of G1 = the_Weight_of G2 holds G3 is WSubgraph of G2
proof
  let G1,G2 be WGraph, G3 be WSubgraph of G1;
  assume that
A1: G1 == G2 and
A2: the_Weight_of G1 = the_Weight_of G2;
  reconsider G39=G3 as [Weighted] Subgraph of G2 by A1,GLIB_000:91;
  the_Weight_of G3 = (the_Weight_of G2) | the_Edges_of G3 by A2,Def10;
  then G39 is WSubgraph of G2 by Def10;
  hence thesis;
end;
