
theorem Th21:
  for P1 being Path-like _Graph, v being Vertex of P1
  for P2 being removeVertex of P1,v
  st v is endvertex or P1 is _trivial holds P2 is Path-like
proof
  let P1 be Path-like _Graph, v be Vertex of P1;
  let P2 be removeVertex of P1,v;
  assume v is endvertex or P1 is _trivial;
  then per cases;
  suppose P1 is non _trivial & v is endvertex;
    then P2 is connected by GLIB_002:4;
    hence thesis;
  end;
  suppose P1 is _trivial;
    hence thesis;
  end;
end;
