
theorem
  for n being non zero Nat, v being Vertex of canCompleteGraph(n)
  holds v.inDegree() = v & v.outDegree() = n - v - 1
proof
  let n be non zero Nat, v be Vertex of canCompleteGraph(n);
  thus v.inDegree() = card v.inNeighbors() by GLIB_000:109
    .= card v by Th1
    .= v;
  thus v.outDegree() = card v.outNeighbors() by GLIB_000:110
    .= card(n\succ v) by Th1
    .= n - card succ Segm v by ORDINAL1:21, CARD_2:44
    .= n - card Segm(v+1) by NAT_1:38
    .= n - v - 1;
end;
