reserve x, y, z, v for set,
  n, m, k for Nat;
reserve G, G1, G2, G3 for Graph;
reserve x, y for Element of (the carrier of G);

theorem
  for v being set holds v in the carrier' of G implies
  (the Source of G).v in the carrier of G &
  (the Target of G).v in the carrier of G by FUNCT_2:5;
