reserve G for _Graph;
reserve V for non empty set, E for Relation of V;

theorem Th77:
  for X,Y being set
  holds Y|`E|X \/ X|`E|Y = createGraph(V,E).edgesBetween(X,Y)
proof
  let X,Y be set;
  set G = createGraph(V,E);
  thus Y|`E|X \/ X|`E|Y = Y|`E|X \/ G.edgesDBetween(Y,X) by Th76
    .= G.edgesDBetween(X,Y) \/ G.edgesDBetween(Y,X) by Th76
    .= G.edgesBetween(X,Y) by GLIB_000:150;
end;
