reserve X for set;

theorem
  for g being SimpleGraph of X, v,e being set st e in the SEdges of g &
  degree (g,v)=0 holds not v in e
proof
  let g be SimpleGraph of X, v,e be set;
  assume that
A1: e in the SEdges of g and
A2: degree(g,v)=0;
  consider Y be finite set such that
A3: for z being set holds (z in Y iff z in the SEdges of g & v in z) and
A4: degree(g,v)=card(Y) by Def8;
  assume v in e;
  then Y is non empty by A1,A3;
  hence contradiction by A2,A4;
end;
