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 Th171:
  for G1 being _Graph, G2 being Subgraph of G1, x,y,e being set
  st e Joins x,y,G2 holds G1.walkOf(x, e, y) = G2.walkOf(x, e, y)
proof
  let G1 be _Graph, G2 be Subgraph of G1, x, y, e be set;
  assume
A1: e Joins x,y,G2;
  then
A2: e Joins x,y,G1 by GLIB_000:72;
  G2.walkOf(x,e,y) = <*x,e,y*> by A1,Def5;
  hence thesis by A2,Def5;
end;
