
theorem Th6:
  for G being _Graph, E being one-to-one ManySortedSet of the_Edges_of G
  for e,v,w being object st e DJoins v,w,G
  holds E.e DJoins v,w,replaceEdges(E)
proof
  let G be _Graph;
  let E be one-to-one ManySortedSet of the_Edges_of G;
  let e,v,w be object;
  assume A1: e DJoins v,w,G;
  then e Joins v,w,G by GLIB_000:16;
  then A2: v in the_Vertices_of G & w in the_Vertices_of G by GLIB_000:13;
  E.e DJoins (id the_Vertices_of G).v,(id the_Vertices_of G).w,
    replaceEdges(E) by A1, Th4;
  then E.e DJoins v,(id the_Vertices_of G).w,replaceEdges(E) by A2, FUNCT_1:18;
  hence thesis by A2, FUNCT_1:18;
end;
