
theorem
  for G1,G2 being WGraph, G3 being WGraph st G1 == G2 & the_Weight_of G1
  = the_Weight_of G2 & G1 is WSubgraph of G3 holds G2 is WSubgraph of G3
proof
  let G1,G2 be WGraph, G3 be WGraph;
  assume that
A1: G1 == G2 and
A2: the_Weight_of G1 = the_Weight_of G2 and
A3: G1 is WSubgraph of G3;
  reconsider G29=G2 as [Weighted] Subgraph of G3 by A1,A3,GLIB_000:92;
  the_Edges_of G1 = the_Edges_of G2 by A1;
  then the_Weight_of G2 = (the_Weight_of G3)|the_Edges_of G2 by A2,A3,Def10;
  then G29 is weight-inheriting;
  hence thesis;
end;
