reserve G,G1,G2 for _Graph;
reserve W,W1,W2 for Walk of G;
reserve e,x,y,z for set;
reserve v for Vertex of G;
reserve n,m for Element of NAT;

theorem
  for n being Element of NAT st n in dom W.edgeSeq() holds W.edgeSeq().n
  in the_Edges_of G
proof
  let n be Element of NAT;
  assume n in dom W.edgeSeq();
  then W.edgeSeq().n in rng W.edgeSeq() by FUNCT_1:def 3;
  hence thesis;
end;
