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

theorem Th80:
  for X being set holds E|X \/ X|`E = createGraph(V,E).edgesInOut(X)
proof
  let X be set;
  thus E|X \/ X|`E = createGraph(V,E).edgesOutOf(X) \/ X|`E by Th74
    .= createGraph(V,E).edgesOutOf(X) \/ createGraph(V,E).edgesInto(X) by Th75
    .= createGraph(V,E).edgesInOut(X) by GLIB_000:def 28;
end;
