reserve G for Graph,
  v, v1, v2 for Vertex of G,
  c for Chain of G,
  p, p1, p2 for Path of G,
  vs, vs1, vs2 for FinSequence of the carrier of G,
  e, X for set,
  n, m for Nat;
reserve G for finite Graph,
  v for Vertex of G,
  c for Chain of G,
  vs for FinSequence of the carrier of G,
  X1, X2 for set;

theorem Th24:
  Degree v = Degree(v, the carrier' of G)
proof
  thus Degree v = card Edges_In v + EdgesOut v by Th22
    .= card Edges_In(v, the carrier' of G) + card Edges_Out v by Th23
    .= Degree(v, the carrier' of G);
end;
