
theorem
  for G being _Graph
  for V being non empty one-to-one ManySortedSet of the_Vertices_of G
  for W2 being Walk of replaceVertices(V) ex W1 being Walk of G
  st V*(W1.vertexSeq()) = W2.vertexSeq() & W1.edgeSeq() = W2.edgeSeq()
proof
  let G be _Graph;
  let V be non empty one-to-one ManySortedSet of the_Vertices_of G;
  let W2 be Walk of replaceVertices(V);
  consider W1 being Walk of G such that
    A1: V*(W1.vertexSeq()) = W2.vertexSeq() and
    A2: (id the_Edges_of G)*(W1.edgeSeq()) = W2.edgeSeq() by Th21;
  take W1;
  rng(W1.edgeSeq()) c= the_Edges_of G;
  hence thesis by A1, A2, RELAT_1:53;
end;
