
theorem Th35: :: LenSubwalk00
  for G being _Graph, W being Walk of G, S being Subwalk of W st
  len S = len W holds S = W
proof
  let G be _Graph, W be Walk of G, S be Subwalk of W such that
A1: len S = len W;
A2: len S = 2*len S.edgeSeq() +1 by GLIB_001:def 15;
A3: S.first() = W.first() by GLIB_001:161;
A4: len W = 2*len W.edgeSeq() +1 by GLIB_001:def 15;
  ex es being Subset of W.edgeSeq() st S.edgeSeq() = Seq es by GLIB_001:def 32;
  hence thesis by A1,A2,A4,A3,Th18,Th34;
end;
