
theorem Th53:
  for G being _Graph, v1, v2 being Vertex of G st v1 is isolated & v1 <> v2
  holds not v2 in G.reachableFrom v1
proof
  let G be _Graph, v1,v2 be Vertex of G;
  assume A1: v1 is isolated & v1 <> v2;
  assume v2 in G.reachableFrom v1;
  then consider W being Walk of G such that
    A2: W is_Walk_from v1,v2 by GLIB_002:def 5;
  A3: W.first() = v1 & W.last() = v2 by A2, GLIB_001:def 23;
  then v1 in W.vertices() by GLIB_001:88;
  hence contradiction by A1, A3, GLIB_001:127, GLIB_001:135;
end;
