
theorem Th58:
  for G1 being loopless _Graph, G2 being _Graph
  holds G1 == G2 iff G2 is removeLoops of G1
proof
  let G1 be loopless _Graph, G2 be _Graph;
  hereby
    assume A1: G1 == G2;
    G1 is inducedSubgraph of G1, the_Vertices_of G1 by GLIB_000:100;
    then G1 is inducedSubgraph of G1, the_Vertices_of G1, the_Edges_of G1
      by GLIB_000:34;
    hence G2 is removeLoops of G1 by A1, GLIB_000:101;
  end;
  assume G2 is removeLoops of G1;
  then G2 is inducedSubgraph of G1, the_Vertices_of G1 by GLIB_000:34;
  hence G1 == G2 by GLIB_000:94;
end;
