
theorem Th136:
  for G1 being _Graph, G2 being SimpleGraph 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 SimpleGraph of G1, W1 be Walk of G1;
  consider H being removeParallelEdges of G1 such that
    A1: G2 is removeLoops of H by Th119;
  consider W2 being Walk of H such that
    A2: W2 is_Walk_from W1.first(),W1.last() by Lm4;
  consider W3 being Walk of G2 such that
    A3: W3 is_Walk_from W2.first(),W2.last() by A1, Th61;
  take W3;
  W1.first()=W2.first() & W1.last()=W2.last() by A2, GLIB_001:def 23;
  hence thesis by A3;
end;
