reserve c,c1,c2 for Cardinal, G,G1,G2 for _Graph, v for Vertex of G;

theorem Th59:
  for G being _Graph holds card G.degreeMap() = G.order() &
    card G.inDegreeMap() = G.order() & card G.outDegreeMap() = G.order()
proof
  let G be _Graph;
  dom G.degreeMap() = the_Vertices_of G &
    dom G.inDegreeMap() = the_Vertices_of G &
    dom G.outDegreeMap() = the_Vertices_of G by PARTFUN1:def 2;
  hence thesis by CARD_1:62;
end;
