
theorem Th100:
  for F being non empty Graph-yielding Function, z being Element of dom F
  holds (the_Edges_of canGFDistinction(F,z)).z = (the_Edges_of F).z
proof
  let F be non empty Graph-yielding Function, z be Element of dom F;
  A1: F.z == F.z | _GraphSelectors by GLIB_000:128;
  reconsider z9 = z as Element of dom canGFDistinction(F,z) by Th94;
  thus (the_Edges_of canGFDistinction(F,z)).z
     = the_Edges_of (canGFDistinction(F,z).z9) by Def9
    .= the_Edges_of (F.z | _GraphSelectors) by Th96
    .= the_Edges_of (F.z) by A1, GLIB_000:def 34
    .= (the_Edges_of F).z by Def9;
end;
