
theorem
  for G1 being non locally-finite _Graph, v being Vertex of G1
  for G2 being removeVertex of G1, v st v.edgesInOut() is finite
  holds G2 is non locally-finite
proof
  let G1 be non locally-finite _Graph, v be Vertex of G1;
  let G2 be removeVertex of G1, v;
  assume A1: v.edgesInOut() is finite;
  for w being Vertex of G1 st w in {v} holds w.edgesInOut() is finite
    by A1, TARSKI:def 1;
  hence thesis by Th30;
end;
