
theorem Th107:
  for G being _finite _trivial _Graph, v being Vertex of G
  ex S being VertexScheme of G st S = <*v*> & S is perfect
proof
  let G be _finite _trivial _Graph, v being Vertex of G;
  consider v1 being Vertex of G such that
A1: the_Vertices_of G = {v1} by GLIB_000:22;
  set S = <*v*>;
  v1 = v by A1,TARSKI:def 1;
  then
A2: rng S = the_Vertices_of G by A1,FINSEQ_1:39;
  S is one-to-one by FINSEQ_3:93;
  then reconsider S as VertexScheme of G by A2,Def12;
  take S;
  thus S = <*v*>;
  let n be non zero Nat such that
  n <= len S;
  let Gf be inducedSubgraph of G,S.followSet(n);
  thus thesis;
end;
