
theorem Th137:
  for G1 being _Graph, G2 being DSimpleGraph of G1, W1 being Walk of G1
  ex W2 being Walk of G2 st W2 is_Walk_from W1.first(),W1.last()
proof
  let G1 be _Graph, G2 be DSimpleGraph of G1, W1 be Walk of G1;
  set G3 = the SimpleGraph of G2;
  G3 is SimpleGraph of G1 by Th133;
  then consider W3 being Walk of G3 such that
    A1: W3 is_Walk_from W1.first(),W1.last() by Th136;
  reconsider W2 = W3 as Walk of G2 by GLIB_001:167;
  take W2;
  thus thesis by A1, GLIB_001:19;
end;
