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 Th159:
  W1 is Subwalk of W2 implies W1.first() = W2.first() & W1.last() = W2.last()
proof
  assume W1 is Subwalk of W2;
  then W1 is_Walk_from W2.first(), W2.last() by Def32;
  hence thesis;
end;
