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 Th89:
 for e,x,y being object holds
  e Joins x,y,G implies G.walkOf(x,e,y).vertices() = {x,y}
proof let e,x,y be object;
  set W = G.walkOf(x,e,y);
  assume e Joins x, y, G;
  then W.vertexSeq() = <*x,y*> by Th68;
  hence thesis by FINSEQ_2:127;
end;
