
theorem
  for G1 being WGraph, G2 be WSubgraph of G1 holds for x being set st x
  in the_Edges_of G2 holds (the_Weight_of G2).x = (the_Weight_of G1).x
proof
  let G1 be WGraph, G2 be WSubgraph of G1;
  let x be set;
  assume x in the_Edges_of G2;
  then
A1: x in dom the_Weight_of G2 by PARTFUN1:def 2;
  the_Weight_of G2 = (the_Weight_of G1) | the_Edges_of G2 by Def10;
  hence thesis by A1,FUNCT_1:47;
end;
