
theorem
  for G1 being _Graph, G2 being removeParallelEdges of G1
  holds G1.componentSet() = G2.componentSet()
proof
  let G1 be _Graph, G2 be removeParallelEdges of G1;
  for v1 being Vertex of G1, v2 being Vertex of G2 st v1 = v2
    holds G1.reachableFrom(v1) = G2.reachableFrom(v2) by Th100;
  hence thesis by Th37;
end;
