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 H1, H2 being strict Subgraph of G st
  the carrier of H1 = the carrier of H2 &
  the carrier' of H1 = the carrier' of H2
  holds H1 = H2 by Lm3;
