
theorem
  for V being non empty set, E being Relation of V
  holds createGraph(V, E \ id V) is removeLoops of createGraph(V,E)
proof
  let V be non empty set, E be Relation of V;
  set G = createGraph(V,E), H = createGraph(V,E\id V);
  V c= V;
  then A1: H is inducedSubgraph of G,V,E\id V by XBOOLE_1:36, GLUNIR00:85;
  the_Edges_of G \ G.loops() = E \ G.loops()
    .= E \ (E /\ id V) by Th130
    .= E \ id V by XBOOLE_1:47;
  hence thesis by A1;
end;
