
theorem Th85:
  for F being non empty Graph-yielding Function, x being Element of dom F
  for x9 being Element of dom canGFDistinction F st x = x9
  ex G being PGraphMapping of F.x,(canGFDistinction F).x9
  st G_V = renameElementsDistinctlyFunc(the_Vertices_of F,x) &
    G_E = renameElementsDistinctlyFunc(the_Edges_of F,x) &
    G is Disomorphism
proof
  let F be non empty Graph-yielding Function, x be Element of dom F;
  let x9 be Element of dom canGFDistinction F;
  assume x = x9;
  then (canGFDistinction F).x9
     = replaceVerticesEdges(
        renameElementsDistinctlyFunc(the_Vertices_of F,x),
        renameElementsDistinctlyFunc(the_Edges_of F,x)) by Def25;
  hence thesis by Th16;
end;
