
theorem Th105:
  for G, H being _finite _Graph, g being VertexScheme of G st G ==
  H holds g is VertexScheme of H
proof
  let G,H be _finite _Graph, g be VertexScheme of G such that
A1: G == H;
  rng g = the_Vertices_of G by Def12;
  then
A2: rng g = the_Vertices_of H by A1;
A3: g is one-to-one by Def12;
  g is FinSequence of the_Vertices_of H by A1;
  hence thesis by A3,A2,Def12;
end;
