
theorem
  for G1 being simple _Graph, G2 being GraphComplement of G1
  for v1 being Vertex of G1, v2 being Vertex of G2
  st v1 = v2 & G1.order() = 2 holds
    (v1 is endvertex iff v2 is isolated) &
    (v1 is isolated iff v2 is endvertex)
proof
  let G1 be simple _Graph, G2 be GraphComplement of G1;
  let v1 be Vertex of G1, v2 be Vertex of G2;
  assume A1: v1 = v2 & G1.order() = 2;
  then G1 is GraphComplement of G2 & G2.order() = 2 by Th110, Th111;
  hence thesis by A1, Th115;
end;
