reserve G for _Graph;

theorem
  for v being Vertex of G holds v in Endvertices(G) iff v is endvertex
proof
  let v be Vertex of G;
  hereby
    assume v in Endvertices(G);
    then consider w being Vertex of G such that
      A1: v = w & w is endvertex by Def8;
    thus v is endvertex by A1;
  end;
  thus thesis by Def8;
end;
