
theorem Th27:
  for G1, G2 being _Graph, F being PGraphMapping of G1, G2
  st F is isomorphism holds (G1 is Path-like iff G2 is Path-like)
proof
  let G1, G2 be _Graph, F be PGraphMapping of G1, G2;
  assume A1: F is isomorphism;
  then reconsider F0 = F as one-to-one PGraphMapping of G1, G2;
  F0" is isomorphism by A1, GLIB_010:75;
  hence G1 is Path-like implies G2 is Path-like by Lm5;
  thus thesis by A1, Lm5;
end;
