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

theorem Th76:
  for X,Y being set holds Y|`E|X = createGraph(V,E).edgesDBetween(X,Y)
proof
  let X,Y be set;
  thus Y|`E|X = Y|`E /\ E|X by GLIBPRE0:9
    .= createGraph(V,E).edgesInto(Y) /\ E|X by Th75
    .= createGraph(V,E).edgesInto(Y) /\ createGraph(V,E).edgesOutOf(X) by Th74
    .= createGraph(V,E).edgesDBetween(X,Y) by GLIB_000:152;
end;
