
theorem Th99:
  for G1 being _Graph, G2 being removeDParallelEdges of G1, W1 being Walk of G1
  ex W2 being Walk of G2 st W1.vertexSeq() = W2.vertexSeq()
proof
  let G1 be _Graph, G2 be removeDParallelEdges of G1;
  let W1 be Walk of G1;
  set G3 = the removeParallelEdges of G2;
  G3 is removeParallelEdges of G1 by Th95;
  then consider W3 being Walk of G3 such that
    A1: W1.vertexSeq() = W3.vertexSeq() by Th98;
  reconsider W2 = W3 as Walk of G2 by GLIB_001:167;
  take W2;
  thus thesis by A1, GLIB_001:76;
end;
